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<= span style=3D'mso-bookmark:_Toc440896900'>Verificación= de supuestos en las pruebas de comparación de medias. Una revisión.

 

 

Verification of assumptions in the tests of comparison of means. A review.<= /span>

 

 

Pablo Flores. [1]= , Jordi Ocańa.= [2]= & Tania Sánchez[3]

 <= /span>

Recibido: 13-07-2017 / Revisado: 07-09-2018 Aceptado: 05-10-2018/ Publicado: 01-11-2018=

 

Abstract.                                                 =                                                                         

The Student’s t test for the significance of differences between means requires the fulfillment of normality and homoscedasticity assumptions. This paper collects the results of researches showing that when these assumptions are verified by means of other traditio= nal hypothesis tests (e.g., the F or the Levene’s t= est for homoscedasticity; goodness of fit to normality tests… ), there is a high risk of a type I error. In addition, these pretesting procedures present some theoretical difficulties. On the other hand, when t= hese assumptions are verified through an equivalence approach, using an appropri= ate irrelevance interval, these risks are better controlled. As a consequence, = the equivalence approach is recommended, instead of the traditional one, whose = use is not advisable. Advances in this type of studies and suggestions of future research are presented.

Keywords: equivalence, pre-testing, assumptions, Type I Error, Simulation.

 

Resumen.

La validez de la prueba t de Student para determin= ar la existencia de diferencias significativas entre medias está limitada al cumplimiento de los supuestos de normalidad y homocedasticidad. El presente trabajo recopila los resultados de investigaciones que muestran que cuando estos supuestos se verifican mediante otros test de hipótesis tradicionales (por ejemplo, el test F o el test de Levene para la ho= moscedasticidad; tests de bondad de ajuste a una distribución no= rmal…) existe un alto riesgo de cometer un error tipo I, además de la existencia de dificultades teóricas. Por otra parte cuando los supuestos se verifican mediante un enfoque de equivalencia con adecuados intervalos de irrelevanci= a, estos riesgos quedan mejor controlados, por lo que se recomienda el uso de = este enfoque en lugar del tradicional, el cual se desaconseja. Se presentan los avances realizados en este tipo de estudios así como sugerencias de posibles desarrollos futuros en esta línea.

Palabras clave:<= /b> equivalencia, pre-testear, supuestos, Error Tip= o I, Simulación.

 

1.      Introducción.

La prueba t de = Student (Student,= 1908) para probar posibles diferencias significativas entre dos medias poblacionales está sujeta a la verificación= de los supuestos de normalidad y homocedasticidad. No es extrańo encontrar en = la mayoría de libros sobre estadística inferencial (Gutierre= z, 2008; Triola, 2009; Wackerly, Mendenhall, & Scheaffer, 2010; Wallpole &= amp; Myers, 2012) la restricción del uso de esta prueba únicamente para muestras en las que se asume su cumplimiento. Comúnmente, e= stos supuestos son probados previamente a través de otros test estadísticos, a l= os cuales llamaremos pre-test. Cuando en un pre-test de normalidad (Shapiro-Wi= lk, Anderson Darling, Kolmogorov-Smirnov, etc… (Darling = & Anderson, 1954; KOLMOGOROV, 1933; Shapiro & Wilk, 1965; Smirnov, 1948)<= /span>) la hipótesis nula se rechaza, se suele utilizar un test no paramétrico (Wilcoxon, Mann-Whitney,…  (Mann &am= p; Whitney, 1947; Wilcoxon, 1945)) asumiendo implícitamente robustez ante c= asos de no homocedasticidad, lo cual no necesariamente es un hecho que se pueda asegurar en estas pruebas. Por otra parte, cuando la mencionada hipótesis n= ula de perfecta normalidad no se rechaza se suele asumir que existe normalidad = y a continuación se realiza sobre la misma muestra un segundo pre-test (F, Levene, Bartlet (Brown &a= mp; Forsythe, 1974; Snedecor & Cochran, 1989)) para verificar el supuesto de homoscedasticidad.  Cuando en este pre-test  no = existe evidencia para rechazar la hipótesis nula de perfecta igualdad entre varian= zas, la t de Studentsuele ser utilizada, en caso con= trario una modificación de esta prueba para datos heteroscedá= sticos (Test de Welch (Welch, 1= 951)) se puede considerar como la alternativa adecuada.

A pesar de que = el proceso descrito (o alguna variante del mismo) se aplica comúnmente en el ámbito de la estadística inferencial, existen estudios (Albers, = Boon, & Kallenberg, 1998; Hsu, 1938; Overall, John E and Atlas, Robert S and Gibson, 1995; Scheffé, 1970) que muestran que este proceso altera la probabilidad global de cometer un error de Tipo I (TIEP, por sus siglas en inglés), manteniéndola muy alejada  del nivel de significancia planteado para la prueba de comparación de medias, especialmente para casos de muestras pequeńas y desbalanceadas. En ocasione= s, en estos estudios los autores concluyen advirtiendo de los peligros de pre-testear y recomiendan evitar este proceso y substituirlo  por el uso directo del test de Welch (s= in pre-testear), ya que parece ser que esta prueba manti= ene estable la TIEP alrededor del nivel de significancia planteado en la prueba= de comparación de medias.  Al respecto, un estudio= (Moder, R= asch, & Kubinger, 2009; Rasch, Kubinger, & Moder, 2011), que estima la TIEP global cuando ambos supuestos son pre-testeados a través de de Kolmogorov – Smirnov y Le= vene (que es un test que permanece robusto ante desviaciones de la normalidad (Rasch &a= mp; Guiard, 2004)), usando muestras balanceadas, desbalance= adas y con diferentes niveles de no normalidad y heterocedasticidad, muestra que pre-testear conduce a graves riesgos desconocidos en las probabilidades de cometer un error de tipo I y tipo II, por lo que hacerlo no vale la pena. Aplicar directamente el t de Studento la prueba= no paramétrica de Wilcoxon conduce incluso a peores alteraciones de la TIEP, e= n su lugar la aplicación directa del test de Welch parece ser la mejor opción, aunque se observa que esta deja de ser efectiva para muestras pequeńas y co= n un grado severo de no normalidad. Otro estudio (Zimmerma= n, 2004), donde únicamente se pre-testeó el supues= to de homocedasticidad mediante la prueba de Levene tuvo resultados similares, nuevamente el uso directo de Welch resultó ser una alternativa que mantiene controlada la TIEP independientemente del tamańo muestral y el grado de heteroscedasticidad de las muestras. Además se concluyó que, pre-testear, especialmente para muestras pequeńas y desbalanceadas altera significativam= ente la TIEP, aunque esta empieza a decrecer conforme el nivel de significancia = del pre-test es mayor, pero esto a partir del valor poco práctico del nivel de significancia .

Aunque estos estudios preliminares muestran que aplicar directamente (sin pre-testear) el test de Welch es una buena opción y además más simple de implementar y apli= car que el proceso de pre-test (Rasch &a= mp; Schott, 2018), un estudio realizado para comparar más de dos medias (Flores M, 2018) mediante la versión generalizada del test= de Welch como alternativa del ANOVA de un factor para muestras heterocedásticas, revela que cuando se verifica el supuesto de homocedasticidad,  el procedimiento deja de ser efectivo. = Además se confirma que el proceso de pre-testear altera significativamente la TIEP= de manera similar a lo que ocurría en el proceso de comparación de dos medias.=

Parece ser que existe suficiente evidencia para pensar que pre-testear mediante el enfoque tradicional no es un buena idea. En su libro “Testing<= /span> statistical hypotheses of equivalence and noninferiority”, (Wellek, = 2010) plantea la posibilidad de aplicar pruebas= de equivalencia como alternativa a los pre-tests antes citados.= En ellas se contrastaría una hipótesis nula que afirma la existencia de un ele= vado grado de incumplimiento de la condición de validez bajo estudio (por ejempl= o, homoscedasticidad) frente a una alternativa que afirm= a que este grado de incumplimiento, quizás no sea nulo pero es suficientemente pequeńo, irrelevante, como para alterar de forma importante la validez de la prueba t de Student. (La idea de Wellek es de alcance más general, a otras condiciones de validez de técnicas estadísticas, pero aquí nos centramos en el problema de la comparación de medias.)

Parece ser que existe suficiente evidencia para pensar que pre-testear mediante el enfoque tradicional no es un buena idea. El presente artículo de revisión pretende = recopilar los fundamentos teóricos que sustentan la validez de un test tanto tradicio= nal como de equivalencia en el proceso de verificación de supuestos, así como l= os resultados de investigaciones realizadas con el objetivo de determinar la efectividad = de estos enfoques en el proceso de pre-testeo para pruebas de comparación de d= os medias en el sentido de la medición de la probabilidad de cometer errores. = En este sentido, la siguiente sección muestra una argumentación teórica del enfoque tradicional usado para pre-testear los supuestos de normalidad y homocedasticidad. La sección tres muestra un análisis similar pero para el enfoque de equivalencia. La sección cuatro muestra un resumen de los principales resultados de la estimación de la TIEP cuando se pre-testea los supuestos usando ambos enfoques y finalmente la sección cinco muestra algun= as conclusiones generales y discusión sobre posibles investigaciones futuras.<= o:p>

1.      = Verificación de supuest= os mediante el enfoque tradicional.

 

1.1.Respecto al supuesto normalidad

Refiriéndose a la normalidad, (G. E. Box, 1979) mencionó: “en la vida real no existe una distribución perfectamente normal, sin embargo, con modelos, que se sabe que son falsos, a menudo se puede derivar resultados que coinciden, con una aproximación útil a los que se encuentran en el mundo real”. Entonces, = de acuerdo a lo mencionado por Box, es evidente que los test orientados a prob= ar una perfecta normalidad (como lo hacen los pre-test tradicionales) no tienen sentido, a lo mejor tienen algún tipo de utilidad pero no prueban algo real= . En este sentido podríamos mencionar lo que el mismo autor concluyó de forma más general: “Todos los modelos son err= óneos pero algunos son útiles” (G. Box & Drapper, 1987).

Siguiendo el enunciado de (G. E. Box, 1979), podemos deducir que lo importante no es determinar si una muestra proviene = de una perfecta distribución normal –ya sabemos que no. En su lugar lo que verdaderamente importa es saber si la aproximación del modelo para verifica= r el supuesto es lo suficientemente buena como para ser considerada útil.  En este sentido, el criterio de Cochran sugiere que un modelo de prueba de hipótesis puede ser considerado útil o preciso si la TIEP tiene una desviación respecto al nivel de significancia = de máximo del 20% de su valor, esto es la TIEP de la prueba tiene que ubicarse dentro del intervalo [  = (Cochran, 1942). En esencia este mismo criterio es utilizado para definir la robustez de una prueba de hipótesis (Rasch & Guiard, 2004)<= !--[if supportFields]>.

1.2.Respecto al supuesto de homocedasticidad.

En el enfoque tradicional, la hipótesis nula de = una prueba de homocedasticidad establece perfecta igualdad de los parámetros comparados ( ). Trasladando la idea de Box a este pre-test, podríamos también concluir que verificar perfecta igualdad de varianzas car= ece de sentido, ya que en la realidad esto  tampoco existe. Sin embargo establecerem= os un análisis adicional respecto a los test tradicionales para verificar este supuesto.

El hecho es que cuando un investigador está prob= ando homocedasticidad bajo el enfoque tradicional se enfrenta a la dificultad ló= gica de que no rechazar la hipótesis nula de perfecta igualdad de varianzas solo significa ausencia de evidencia para concluir diferencias significativas en= tre los parámetros comparados, lo cual no es necesariamente una prueba de la existencia de homocedasticidad, como en este mismo sentido ADDIN CSL_CITATION { "citationItems" := [ { "id" : "ITEM-1", "itemData" : { "author" : [ { "dropping-particle" : "", "family" : "Altman, Douglas G and Bland", "given&q= uot; : "J Martin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Bmj", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1995" ] ] }, "page" : "485", "title&quo= t; : "Statistics notes: Absence of evidence is not evidence of absence"= ;, "type" : "article-journal", "volume" : "= 311" }, "uris" : [ "http://www.mendeley.com/documents/?uuid=3Dce707bd0-7140-4079-9d33-46c= 57d14238c" ] } ], "mendeley" : { "formattedCitation" : "(Altm= an, Douglas G and Bland, 1995)", "plainTextFormattedCitation" : "(Altman, Douglas G and Bland, 1995)", "previouslyFormattedCitation" : "(Altman, Douglas G and Bland 1995)" }, "properties" : {  }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-cita= tion.json" }(Altman, Douglas G and Bland, 1995) mencionó “Ausencia de evidencia no es evidencia de ausencia” y (Wellek, 2010) también al respecto dijo “Una diferencia no significativa no debe ser confundida con una significativa homogeneidad= ”. La parte izquierda del Figura 1 ayuda a visualizar de mejor manera esta ide= a. Por otra parte, rechazar esta hipótesis nula podría estar sugiriendo tan so= lo una irrelevante o despreciable heterocedasticidad. En ambos casos basándono= s en la decisión de rechazo o no rechazo, existe la duda de saber si las pruebas tradicionales están realmente probando lo que necesitamos saber previo a un test de comparación de medias.

Ya podemos notar con más claridad que además de = los estudios técnicos realizados por simulación, existen argumentos teóricos que muestran las dificultades conceptuales y peligros que tenemos al pre-testear los supuestos de normalidad y homocedasticidad usando el enfoque tradiciona= l. Es interesante a continuación analizar lo que sucede con el enfoque de equivalencia  

2.      = Verificación de supuest= os mediante el enfoque de equivalencia.

(Wellek, 2010) en su libro, usa el término de equivalencia como una forma dilatada de una rel= ación de identidad entre los parámetros analizados y considera que esta dilatació= n en la hipótesis de equivalencia se induce al ańadir en la hipótesis tradicional una zona de irrelevancia alrededor de la correspondiente región o punto en = el espacio paramétrico que denota la igualdad perfecta de varianzas (o el perf= ecto ajuste a la normalidad). Esta zona de irrelevancia está limitada por los llamados límites de equivalencia cuyos valores son constantes positivas que deben ser asignadas a priori y sin mayor conocimiento de la muestra a anali= zar. Inverso al test de hipótesis tradicional donde en la hipótesis nula se especifica la igualdad de los parámetros comparados, este tipo de pruebas se plantean de tal forma que la hipótesis nula establece la no equivalencia, mientras que la alternativa establece la equivalencia. Este cambio de inter= és en la investigación conduce a diseńar un estudio que pretende demostrar ausencia de una diferencia relevante entre los efectos de dos o más tratamientos, es decir equivalencia (Flores, 2017). Además es muy importante notar que las pruebas de equivalencia no buscan pr= obar normalidad u homocedasticidad perfecta, en lugar de esto, la intención es declarar el cumplimiento de los supuestos incluso para desviaciones que pue= den ser consideradas como irrelevantes o despreciables. Parece ser que con estas precisiones, este enfoque supera las dificultades lógicas analizadas en la Sección 2.

Con el fin de ilustrar de forma adecuada el planteamiento de una prueba de irrelevancia, presentamos a continuación  el correspondiente test para determinar= una posible equivalencia entre las varianzas  y   , lo cual se traduciría en homocedasticidad:

Para las hipótesis:

  ŕ No equivalencia (Diferencia relevantes de varianzas)

        =      ŕ Equivalencia (Diferencias irrelevantes de varianzas)

Con límites de irrelevancia . Un test invariante uniformemente más  potente (UMPI), es aquel cuya región crí= tica está dada por:  <= /span>

Donde el estadístico de prueba  viene d= ado por

Y los valores críticos =  están determinados al resolver el sistema de ecuaciones:

Donde  corresponde a la función de distribución acumula= da de una distribución F centrada, con  grados = de libertad en el numerador y  =  grados = de libertad en el denominador.

Notemos que en esta ocasión, cuando se rechaza la hipótesis nula de no equivalencia podemos concluir afirmando la existencia = de evidencia para inferir diferencias irrelevantes entre las varianzas compara= das, lo cual sí se puede considerar como homocedasticidad (desde el punto de vis= ta de la equivalencia). Esto, desde el punto de vista teórico supera las dificultades lógicas tratadas en la Sección 2.2. La Figura 1 muestra claramente estas diferencias entre el enfoque tradicional y de equivalencia cuando se pretende verificar el cumplimiento del supuesto de homocedasticidad. 

Figura 1. Comparación entre el enfoque tradicional y de equivalencia en las pruebas para verificar homocedasticidadNote

2.1.Los límites de equivalencia

Con lo expuesto hasta ahora sobre pruebas de equivalencia para verificar el supuesto de homocedasticidad, estaremos conscientes de que el planteamiento de una adecuada zona de irrelevancia es fundamental para establecer una correcta equivalencia entre los parámetros a compararse. Sin embargo, Wellek no plantea un criterio técnico para determinar los límites de esta zona y en su lugar pro= pone un criterio que nos parece subjetivo basado en la experiencia del investiga= dor o en lo que él denomina como un sentido estadístico común.

(Flores M & Ocana, 2018), plantean un algoritmo computacional para determinar los límites de equivale= ncia en función del tamańo muestral, nivel de significancia y nivel de permisivi= dad, el cual se muestra como un criterio más técnico al momento de establecer una adecuada zona de irrelevancia.  El algoritmo se encuentra implementado en la función “lim= varRatio” creada con el paquete base del software R (Team, 2016).

Para explicar la lógica de esta función es neces= ario definir el llamado nivel de permisividad <= span lang=3DES-EC style=3D'font-size:11.0pt;line-height:107%;font-family:"Calibr= i",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-= 4.0pt; mso-ansi-language:ES-EC;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= >  como la distancia máxima por encima y por debajo del nivel de significancia = <= span lang=3DES-EC style=3D'font-size:11.0pt;line-height:107%;font-family:"Calibr= i",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-= 4.0pt; mso-ansi-language:ES-EC;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= >  que se = puede tolerar en una prueba de hipótesis para considerar que el modelo es lo suficientemente bueno como para ser considerado útil --lógicamente el mejor valor para esta permisividad basado en el criterio de Cochran será <= /span><= span lang=3DES-EC style=3D'font-size:11.0pt;line-height:107%;font-family:"Calibr= i",sans-serif; mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareas= t-theme-font: minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times Ne= w Roman"; mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-= 4.0pt; mso-ansi-language:ES-EC;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'= > . Luego, debemos tener en cuenta que para una pr= ueba t - Student de comparación de medias en muestras donde se garantice el cumplimiento de la normalidad y homocedasticidad, la = TIEP coincide con el nivel de significancia  plantea= do y que cuando empiezan a existir desviaciones de la homocedasticidad, la TIEP = de la prueba puede ser estimada mediante Simulación de Montecarlo como la proporción de rechazos de la hipótesis nula de igualdad de medias cuando es= ta es verdadera.

Con base a estas precisiones, la función “limvarRatios” para determinar una adecuada zona de irrelevancia en las pruebas de equivalencia para verificar homocedasticidad, consiste en un algoritmo que busca de manera iterativa los valores más alej= ados entre  y  que pro= ducen muestras que al ser sometidas mediante un proceso de simulación a una t de = Studentpara comparar medias provocan una estimación (= por intervalos de confianza) de la TIEP que se encuentra dentro del intervalo de permisividad = , pero no solo es necesario que se ubique dentro= de este intervalo, además debe verificarse que se encuentre lo más cerca posib= le a uno de sus límites, esto debido a que para un  fijo (lo mejor siempre será ), a medida que aumenta el tamańo muestral, la z= ona de indiferencia debe ser más amplia, para que de esta forma la hipótesis de equivalencia tenga una región paramétrica lo más ancha posible, lo cual garantiza que la prueba de equivalencia no sea menos potente de lo que podr= ía llegar a ser. Finalmente la razón al cuadrado entre los valores  y  hallados serán considerados los límites del intervalo de irrelevancia = . Ya que para casos balanceados existe una compl= eta simetría entre los límites de equivalencia, es suficiente obtener una sola razón entre estos valores que determine un , esto no se cumple en casos desbalanceados, don= de se debe determinar dos razones  y  por enc= ima y por debajo de la perfecta igualdad entre varianzas, las cuales no necesariamente son simétricas.

Utilizando un nivel de permisividad basado en el criterio de Cochran, la Tabla 1 muestra límites de irrelevancia calculados = con la función “limvarRatios”, a partir de 100000 réplicas de simulación,  usando los niveles de significancia más comunes y para distintos tamańos muestrales ta= nto balanceados como desbalanceados. Los resultados muestran que el área de irrelevancia es más ancha para casos balanceados que para desbalanceados y además que para casos balanceados los tamańos muestrales más grandes corresponden a los intervalos de equivalencia más anchos, algo que no ocurre con los casos desbalanceados donde independientemente del tamańo muestral l= os límites de equivalencia son muy parecidos. Este comportamiento se mantiene = para los distintos niveles de significancia utilizados.=

Tabla 1: Zona de Indiferencia  con

n =3D (5,5)

(0.130 - 7.691)

(0.225 - 4.428)

(0.397 - 2.519)

n =3D (3,7)

(0.709 - 1.412)

(0.779 - 1.289)

(0.819 - 1.163)

n =3D (7,3)

(0.711 - 1.410)

(0.776 - 1.325)

(0.832 - 1.166)

n =3D (10,10)

(0.002 - 501.0)

(0.097 - 10.325)

(0.282 - 3.542)

n =3D (6,14)

(0.727 - 1.408)

(0.783 - 1.292)

(0.846 - 1.157)

n =3D (14,6)

(0.716 - 1.362)

(0.787 - 1.264)

(0.859 - 1.148)

n =3D (5,10)

(0.679 - 1.387)

(0.741 - 1.286)

(0.819 - 1.196)

n =3D (10,5)

(0.716 - 1.452)

(0.786 - 1.331)

(0.862 - 1.256

3.      = Estimación de la tiep en el proceso de pre – testeo.=

 

3.1.Para muestras normales cuando se pre-testea homocedasticidad

Un primer estudio de simulación usando ambos enfoques, cuando se asegura la normalidad y se pre-testea homocedasticidad =  (Flores M & Ocana, 2018) confirma los resultados de las investigaciones preliminares presentados en la introducción, en el sentido de obtener valores muy inflados de la TIEP esti= mada cuando el proceso de pre-testeo se lleva a cabo con el enfoque tradicional, especialmente para muestras pequeńas y desbalanceadas.

Por otro lado, cuando el enfoque de equivalencia= con los adecuados límites de irrelevancia  proporcionados por “limvarRatios” es usa= do para pre-testear homocedasticidad, la TIEP de una prueba de comparación de medias queda controlada en todos los casos alrededor  del nivel de significancia , siempre y cuando se asegure el cumplimiento de= la normalidad e independientemente del nivel de significancia, el tamańo de la muestra y el nivel de heterocedasticidad. Más aún, en todos estos casos la = TIEP estimada siempre se encuentra dentro del intervalo = , establecido por el Criterio de Cochran, lo cual indica que todos estos procedimientos son los suficientemente buenos y segu= ros para ser utilizados.

Esta TIEP estimada siempre presenta valores muy similares (o casi idénticos) a los calculados cuando se usa directamente el test de Welch, esto resulta ser favorable, puesto que lo que está ocurriend= o es que la prueba de homocedasticidad funciona de tal forma que declara heterocedasticidad en todos los casos que debe hacerlo y es por eso que sie= mpre se aplica el test que corresponde para muestras hetero= cedásticas, es decir Welch.

Es importante mencionar que en todos las estimaciones realizadas se utilizó la técnica de reducción de la varianza denominada “Variables de control” (Ocańa & Vegas, 1995; Vegas & Ocana, 200= 0), la cual permitió reducir la variabilidad y tener una mejor precisión de la simulación sin necesidad de incrementar exageradamente las réplicas de simulación que para todos los casos fueron 100000. La variable de control utilizada es el número de rechazos de la hipótesis nula de una prueba t de = Studentpara comparar dos medias cuando se asegura normalidad y homocedasticidad, la cual se encuentra altamente correlacionada con la variable de interés y además se conoce su esperanza matemática ya que coincide con el nivel de significancia . Los resultados de este trabajo se muestran en conjunto con los resultados del siguiente, el cual analiza la estimación de= la TIEP en aquellos casos donde no se puede asegurar el cumplimiento de la normalidad.

Además de este trabajo mencionaremos un estudio = de simulación realizado cuando se utiliza una prueba de equivalencia para demostrar homocedasticidad entre más de dos poblaciones previo a una prueba= de comparación de medias de un factor – ANOVA (Kim & Cribbie, 2017). El estudio utiliza límites de irrelevancia arbitrarios, es decir propuestos= por un simple sentido estadístico común. La conclusión principal de este trabaj= o es que cuando se pre-testea igualdad de varianzas mediante enfoque de irrelevancia, el test ANOVA tiene una TIEP menor a la provocada que cuando = se pre-testea con el enfoque tradicional (Levene), a pesar de que para ciertos niveles de heterocedasticidad y tamańos muestrales la TIEP está muy alejada= del nivel de significancia usado y fuera del intervalo de Cochran, por lo que pensamos que en realidad, esta investigación no brinda una solución a la alteración del error tipo I cuando se pre-testea. =

El uso válido del procedimiento tradicional ANOV= A de muestras independientes requiere que las variaciones de población sean igua= les. Investigaciones anteriores han investigado si las pruebas de homogeneidad d= e la varianza, como la prueba de Levene, son satisfactorias como guardianes para identificar cuándo utilizar o no el procedimiento ANOVA. Esta investigación= se centra en una nueva prueba de homogeneidad de la varianza que incorpora un enfoque de prueba de equivalencia. En lugar de probar la hipótesis nula de = que las varianzas son iguales contra una hipótesis alternativa de que las varia= nzas no son iguales, la prueba basada en equivalencia evalúa la hipótesis nula de que la diferencia en las varianzas queda fuera o en el límite de un interva= lo predeterminado frente a una alternativa hipótesis de que la diferencia en l= as variaciones cae dentro del intervalo predeterminado. Por lo tanto, con el procedimiento basado en equivalencia, la hipótesis alternativa se alinea co= n la hipótesis de investigación (igualdad de varianza). Un estudio de simulación demostró que la prueba de homogeneidad de la varianza poblacional basada en= la equivalencia es un mejor guardián para el ANOVA que la homogeneidad tradici= onal de las pruebas de varianza

3.2.Para separaciones de la normal cuando se pretestea homocedasticidad.

Otro trabajo en el cual se aplicó la misma metodología de simulación que el anterior se realizó (Flores & Ocańa, 2018)<= !--[if supportFields]>, pero ahora se ańade  el estudio de = la estimación de la TIEP para muestras que presentan ciertos alejamientos de la normal. Estos alejamientos fueron obtenidos a partir de los coeficientes de= Fleishman (Fleishman, 1978). El procedimiento de Fleishman para obtener mues= tras no normales, considera que cualquier distribución para la cual los primeros= cuatro momentos existen, se puede obtener a partir de la transformación , donde  es una variable normal estándar y  es una variable con distribución desconocida y parámetros , donde la simetría  y la cu= rtosis  definen= los grados de separación o contaminación de la normal. Finalmente una variable =  tiene distribución desconocida con parámetros .

Se definió diferentes niveles de contaminación d= e la normalidad de acuerdo a distintas combinaciones de la simetría y curtosis estudiadas en investigaciones previas (Bendayan, Arnau, Blanca, & Bono, 2013; Blan= ca, Arnau, López, Bono, & Bendayan, 2013). Los coeficientes de Fleishman para estos nivele= s de no normalidad fueron calculados usando la función “fle= ishman.coef” del paquete “BinNonNor” (Inan & Hakan, 2018) . Todos estos resultados se muestran en la Tabla 2, a partir de los cuales = se pudieron establecer y simular muestras  no normales para realizar el proceso de estimación de la TIEP.<= /o:p>

 

 

 

Tabla 2: Coeficientes de Fleishman, Simetría y Curtosis = para diferentes niveles de contaminación de la normalidad.<= /span>

Nivel de
Contaminación

Simetría

Curtosis

Coeficientes de= Fleishman

(a, b, c, d)

Cont. Cero=

0

0

(0, 1, 0, 0)

Cont. Leve=

0.25

0.7

(-0.037, 0.933, 0.037, 0.021)<= /span>

Cont. Moderada<= o:p>

0.75

1

(-0.119, 0.956, 0.119, 0.0098)=

Cont. Alta=

1.3

2

(-0.249, 0.984, 0.249, -0.016)=

Cont. Severa

2

6

(-0.314, 0.826, 0.314, 0.023)<= /span>

Dado que los resultados del estudio anterior don= de se aseguraba normalidad son parte de los resultados de este nuevo trabajo estamos analizando, se presentan a continuación gráficas condensadas de los resultados para ambas investigaciones, donde las estimaciones correspondien= tes al grado de contaminación cero coinciden exactamente con las obtenidas en el trabajo para muestras normales anterior. Todas las gráficas tienen un área sombreada representando el Criterio de Cochran, el procedimiento que deje su respectiva TIEP dentro del área será considerado como robusto o lo suficientemente bueno para ser utilizado. Como se puede observar, en todos = los casos se realiza la estimación usando 5 procedimientos diferentes, dos de e= stos tienen que ver con el uso directo sin pre-test del t de Studenty el test de Welch, otros dos utilizan los test tradicionales de Levene y F respectivamente para pre-testear el supuesto de homocedasticidad previa la prueba de comparación de medias  y finalmente el último procedimiento tiene que ver con pre-testear el supuest= o a través del enfoque de equivalencia.

Figura 2. Estimación Global de la TIEP cuando se pre-testea igualdad de varianzas para distintos niveles de no normalidad y heterocedasticidad, usando un <= /span>  y

La Figura 2 muestra la estimación de la TIEP par= a un caso balanceado de tamańo 5. Se puede observar que los diferentes procedimientos utilizados muestran un comportamiento similar, en el sentido= que siempre uno es mejor que otro. En ningún caso aplicar directamente el t de = Studento pre-testear bajo= el enfoque tradicional es recomendado puesto que la TIEP de estos procedimient= os se encuentran siempre alterados con mayor intensidad que los demás. La TIEP estimada, independientemente del nivel de heterocedasticidad, se controla bastante bien alrededor del nivel de significancia cuando se utiliza directamente el test de Welch o el pre-test de equivalencia, esto únicamente para niveles de contaminación de la normalidad cero, leve y moderado, donde la TIEP siempre se encuentra dentro del Criter= io de Cochran para cualquier grado de heterocedasticidad. A partir de una contaminación alta de la normalidad parece ser que no podemos asegurar que ninguno de los procedimientos aplicado sea un método seguro a utilizar.

Figura 3. Estimación Global de la TIEP cuando se pre-testea igualdad de varianzas para distintos niveles de no normalidad y heterocedasticidad, usando un <= /span>  y .

La Figura 3 muestra la estimación de la TIEP par= a un caso balanceado de tamańo 10. En general como casi todo lo que pasa en estadística cuando el tamańo muestral aumenta, estos resultados mejoran, si= endo efectivos (desde el punto de vista del Criterio de Cochran) ciertos procedimientos que para muestras más pequeńas no funcionaban del todo bien.= Sin embargo se observa que aunque existen procedimientos que se encuentran dent= ro del área sombreada, siempre el aplicar directamente Welch o pre - testear usando el enfoque de equivalencia mantiene la TIEP más cerca del nivel de s= ignificancia que los otros procedimientos. Nuevamente, esto parece ser adecuado pero solo hasta un nivel moderado de contaminación de la normalidad, luego de lo cual= ya no existe un procedimiento que podamos recomendar.=

Figura 4. Estimación Global de la TIEP cuando se pre-testea igualdad de varianzas para distintos niveles de no normalidad y heterocedasticidad, usando un <= /span>  y .

La Figura 4 y La Figura 5, muestran las estimaciones de la TIEP para muestras desbalanceadas de tamańo (5, 10) y (10, 5) respectivamente. Se observa que cuando a la muestra más pequeńa le corresponde la varianza teórica más gran= de, la estimación de la TIEP se ubica por encima del nivel de significancia, mientras que cuando a la muestra más grande le corresponde la varianza más grande, la estimación de la TIEP se ubica por debajo del nivel de significancia. En estos casos desbalanceados, la alteración de la TIEP es m= ás evidente, de tal forma que únicamente los procedimientos que consisten en u= sar directamente Welch o pre-testear mediante equivalencia mantienen a la TIEP dentro del área sombreada,  todos los demás procedimientos presenta= n para alguna desviación de la normalidad o de la homocedasticidad alguna alteraci= ón de la TEP que se aleja demasiado del nivel de significancia. Pero de igual forma que lo ocurrido en los casos balanceados, el uso directo de Welch y <= span class=3DSpellE>pre-testear usando un test de equivalencia deja de ser efectivo a partir de un nivel alto de no normalidad.

Figura 5. Estimación Global de la TIEP cuando se pre-testea igualdad de varianzas para distintos niveles de no normalidad y heterocedasticidad, usando un <= /span>  y

 

4.      = Conclusiones= .

ˇ&nb= sp;        Está claro que pre-testear los supuestos de normalidad u homocedasticidad usando los enfoques tradicionales no es una b= uena idea,  hacerlo<= /span> aumenta considerablemente la probabilidad de cometer un error tipo I. Al ig= ual que ya lo hacen investigaciones previas, recomendamos dejar de usar estas pruebas como un método de verificación de supuestos y en su lugar   utilizar el enfoque de equivalencia, e= l cual provoca estimaciones aceptables de la TIEP al menos en su versión dedicada a pre-testear el supuesto de homocedasticidad y cuando se puede asegurar normalidad o a lo mucho una desviación moderada de la misma, que es lo que = se ha investigado hasta ahora. Sería interesante en este sentido averiguar qué ocurre con la TIEP cuando la normalidad es pre-testeada ya sea con el enfoq= ue tradicional o de equivalencia.

ˇ&nb= sp;        Enfocándonos en el procedimiento que consi= ste en aplicar el pre – test de equivalencia, el hecho de que exista desviacion= es de la normalidad para las cuales la TIEP empiece a alejarse demasiado del n= ivel de significancia y además saber que estas desviaciones pueden ser controlad= as por los coeficientes de Fleishman, propone investigaciones futuras como el planteamiento de niveles adecuados de irrelevancia para pruebas de equivalencia dedicadas a probar el supuesto de normalidad. El procedimiento podría consistir nuevamente en un algoritmo iterativo que encuentre valores para los coeficientes de Fleishman que hagan que la TIEP estimada se encuentre dentro y lo más cercano posible= a los límites establecidos por el criterio de Cochran.

ˇ         Finalmente, muy poco se ha hecho respecto = al estudio generalizado para más de dos medias, aunque ya se conoce que de man= era similar a lo que sucede en el caso particular de dos poblaciones, el proces= o de pre – testear bajo el enfoque tradicional deja serias alteraciones en la pr= obabilidad de cometer un error de tipo I. En este sentido una investigación análoga a = las presentadas en la presente revisión, dedicada a estudiar el comportamiento = de la TIEP en pruebas de comparación de más de dos medias cuando se pre – test= ea sus supuestos mediante equivalencia sería de gran interés.

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Para citar el artículo indexado.

 

Flores P., Ocańa J., Sánchez T., (2018). Verificación = de Supuestos en las Pruebas de Comparación de medis. Una revisión. Revista electrónica Cienc= ia Digital 2(4.1.), 5-22. Recuperado desde: http://cienciadigital.org/revistacienciadigital2/index.php/CienciaDigital/= article/view/187/165

 

 


 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

 

El articulo queda en propiedad de= la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Ciencia Digital.

 

 

 

 



[1] Escuela Superior Polité= cnica de Chimborazo, Facultad de Ciencias, Grupo de Investigación en Ciencia de D= atos CIDED, Riobamba – Ecuador,  p_flores@espoch.edu.ec

[2] De= partament de Genética, Microbiologia i Estadística, Secció d’ Estadística, Universitat de Barcelona, Facult= at de Biologia,  = Barcelona – Espańa,  jocana@ub.edu=

[3] Escuela Superior Polité= cnica de Chimborazo, Facultad de Ciencias, Grupo de Investigación en Ciencia de D= atos CIDED, Riobamba – Ecuador.  =

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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAAAA////AAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAD///8AAAD///////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////8AAAD///8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////8AAAD///////////////////////////////////// //////////8AAAD///////////////////////////////////////////8AAAAAAAD///////8A AAD///////////////////////////////////////////////////////////////////8AAAD/ //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAAA////AAAA//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////AAAAAAAA////AAAAAAAAAAAA////////AAAA////////AAAAAAAA////AAAAAAAAAAAA AAAAAAAA////////AAAAAAAAAAAA////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAA////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAA////////////AAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA ////////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAA//////////////////////////////////////////////// ////////////////////////////////////////////////////////AAAAAP///wAAAP////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAAAAAAAAAAAAAAAAAAAAP// /////wAAAP///////wAAAAAAAP///wAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAP///wAA AP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAAAAAAAA AAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP// /////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////////// /wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAA AP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAD///8AAAD///////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////8AAAD///////////////////////// //////////////////////8AAAD///////////////////////8AAAD///8AAAAAAAAAAAD///// //////////////////////////8AAAD///////////////////////////////////////////// //////////////////8AAAD///////////////////////////////////////////////////// //////8AAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAD///////////////// //////////////8AAAD///////////8AAAD///////////////////////////////////////// //////////////////////////////////////////////////////////////8AAAAA////AAAA //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////AAAA//// AAAA////////AAAAAAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAA//////////////////////////////////////////////////////// AAAAAAAA//////////////////////////////////////////////////////////////////// ////////AAAAAAAA//////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////AAAAAP///wAAAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////////wAAAP///wAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAP///wAAAAAAAAAAAP///////wAA AAAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////wAA AAAAAAAAAP///wAAAAAAAAAAAP///////wAAAP///wAAAP///////wAAAAAAAAAAAAAAAAAAAP// /wAAAAAAAP///wAAAAAAAP///////wAAAP///wAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAA AAAAAAAAAP///////////wAAAAAAAAAAAP///wAAAP////////////////////////////////// /////////////////////////////////////////////////////////////////////wAAAAD/ //8AAAD///////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAD///////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///// //8AAAAAAAAAAAD///8AAAAAAAAAAAD///////8AAAAAAAD///////8AAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAD///8AAAAAAAD///////////// //////8AAAD///////8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///8AAAAAAAD///////8AAAD/ //8AAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAD///////////8AAAAAAAAAAAD/ //8AAAD///////////////////////////////////////////////////////////////////// //////////////////////////////////8AAAAA////AAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////AAAA//////////////////////////////////////////// ////AAAA////////////////AAAA////AAAA//////////////////////////////////////// ////////////AAAA////////////////////////////////////////AAAA////AAAA//////// ////////////////////////////////////////////////////AAAAAAAA//////////////// ////////////////////////////////////////////////AAAA////////////AAAA//////// ////////////////////AAAA////////////////////AAAA////AAAA////AAAA//////////// ////AAAA////AAAA////////////////////////AAAA//////////////////////////////// //////////////////////////////////////////////////////////////////////////// AAAAAP///wAAAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////wAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAAAAAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAAAAAAD///8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAAAA////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////AAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAA////////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAA////////////////AAAAAAAAAAAAAAAAAAAAAAAA////////////////AAAA AAAAAAAAAAAA////AAAA////////////////AAAAAAAAAAAAAAAA////////////AAAA//////// ////////AAAAAAAAAAAA////////////AAAAAAAAAAAAAAAA////////////AAAAAAAAAAAAAAAA ////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////////AAAAAAAAAAAAAAAAAAAA//////// ////AAAAAAAAAAAAAAAA//////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAAAP///wAAAP////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////wAAAAAAAAAAAAAAAAAAAAAAAAAAAP////// /////wAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////////////// /wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////////wAA AAAAAAAAAAAAAAAAAAAAAP///////////////wAAAAAAAAAAAAAAAAAAAP////////////////// /wAAAAAAAAAAAAAAAP///////////wAAAAAAAP///////////wAAAAAAAAAAAP///////////wAA AAAAAAAAAAAAAP///////////wAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP// /////////////wAAAAAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAAAAAP////////////// //////////////////////////////////////////////////////////////////////////// /////////////wAAAAD///8AAAD///////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////8AAAD///////////////////////////////////////////8AAAAAAAAA AAD///////////////////8AAAD///////////////8AAAD///////////////////////////8A AAD///////////8AAAD///////////////////////////////////////////////////////// //////////////////////////////////////////////8AAAD///////////////////8AAAAA AAD///////////////////////////////////////8AAAD///////////////////8AAAD///// //////////////////////////////8AAAD///////////////////////////////////////// //////////////8AAAD///////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAAA////AAAA//////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////AAAAAP///wAAAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////wAAAP////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAP////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////wAAAAD///8AAAD/ //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAD///////8AAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAD///////8A AAAAAAAAAAD///8AAAD///////////////8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAA AAAAAAAAAAD///8AAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAD///////////8AAAAAAAAAAAAAAAD///////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD/ //////8AAAAAAAAAAAD///////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAD/ //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAAAA////AAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAA//// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAA////AAAA////AAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAA////AAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////AAAAAAAAAAAAAAAA//// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAA////AAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAA//////////////////////////////////// ////////////////////////////////////////////////////////////////////AAAAAP// /wAAAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAP///////////////////////wAAAP////////////////////////////////// /////wAAAP///////////////////////wAAAP///////////////////wAAAP////////////// /////////wAAAP///////////////////////////wAAAP///////////////////////wAAAP// /////////////////////////////////////////////////////////////////wAAAP////// /////////////////////////////////////////////////////////wAAAP///wAAAP////// /wAAAP///////wAAAP////////////////////////////////////////////////////////// /////wAAAP////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAAD///8AAAD///////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAAA////AAAA//////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////AAAA////////////////////////////////////////////AAAA//// ////////////////////////////////////////////////////////////////AAAA//////// ////AAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////AAAAAP///wAAAP////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAP///////wAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAA AAAAAAAAAAAAAP///////wAAAP///wAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAA AP///wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////// /wAAAP///wAAAAAAAAAAAP///////wAAAAAAAAAAAP///wAAAAAAAAAAAAAAAP///wAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAP////////////////// //////////////////////////////////////////////////////////////////////////// /////wAAAAD///8AAAD///////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAD/ //8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAD///8AAAAA AAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8A AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAD///8AAAAAAAD///8AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////////8AAAD///8AAAAAAAAAAAD///////8AAAAA AAAAAAD///8AAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///// //8AAAAAAAAAAAAAAAAAAAD///////////////////////////////////////////////////// //////////////////////////////////////////////8AAAAA////AAAA//////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAA////AAAAAAAA////AAAA//////// ////////////////////////////////////////AAAA//////////////////////////////// ////AAAAAAAA////////////////////////////////AAAA////AAAA//////////////////// ////////////////////////////////AAAA////////////AAAA////////AAAA//////////// ////////////////////////////////////////////////AAAA//////////////////////// ////////AAAAAAAAAAAAAAAA//////////////////////////////////////////////////// ////////////AAAA////////////////////////////////AAAA//////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAAAP///wAAAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAP////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////wAAAAD///8AAAD///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////8AAAD///8AAAAAAAAAAAAAAAD///8A AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAD///////8AAAD///8AAAAAAAAAAAAA AAAAAAD///8AAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAD///8AAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAAA AAD///////8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAAAAAD///8A AAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////8AAAAAAAAAAAAAAAAAAAD///// //////////////////////////////////////////////////////////////////////////// //////////////////8AAAAA////AAAA//////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAA////AAAAAAAAAAAAAAAA////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAA////AAAA////////AAAA////AAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAA////AAAA AAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAA AAAAAAAAAAAA////AAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA//// AAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAA////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAA////////AAAAAAAAAAAAAAAAAAAA//////////////////////////////////////// ////////////////////////////////////////////////////////////AAAAAP///wAAAP// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////wAAAAAAAAAAAP////////// /////wAAAAAAAP///////////wAAAP///////////////wAAAP////////////////////////// /////////////////////wAAAP///////////////wAAAP///////////////////wAAAP////// /////wAAAP///wAAAP///////////////////////////////////////////////////wAAAP// /wAAAAAAAP///wAAAAAAAP///////////////////////////////////////////wAAAP////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAP///////////////////////wAAAP////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAAD///8AAAD///////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////8AAAAA//// AAAA//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////AAAAAP///wAAAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////wAA AAD///8AAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAAAA////AAAA//////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////AAAAAP///wAAAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////wAAAAD///8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////+yegD///////////////////////////////////////// //////////////////////////////////////////////////////////////////////+yegD/ //////////8AAAAA////AAAA//////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////AAAAAAAA////AAAAAAAA////AAAAAAAA////AAAAAAAA////AAAAAAAA//////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAAAA////AAAAAAAAAAAA//////// snoA////snoAsnoAsnoAsnoAsnoA////snoAsnoAsnoAsnoAsnoAsnoA////snoAsnoAsnoAsnoA snoAsnoA////////snoA////snoAsnoAsnoA////snoA////snoA////snoA////snoAsnoA//// snoAsnoA////snoA////snoA////snoAsnoAsnoAsnoA////snoAAAAAAP///wAAAP////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAP///wAAAAAAAP///wAAAAAA AAAAAAAAAAAAAAAAAAAAAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAAAAAP///wAAAAAAAAAAAAAAAP///////////7J6ALJ6AP///////7J6AP////// /////////7J6AP///////7J6AP///////////////7J6AP///7J6AP///7J6AP///////7J6ALJ6 AP///7J6AP///7J6AP///7J6AP///////////7J6AP///////////////7J6AP///////////7J6 AP///7J6ALJ6ALJ6AAAAAAD///8AAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAD///8AAAD///////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAAAA////AAAA//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////AAAAAP///wAAAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAD///8A AAD///////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAAAA////AAAA//////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AP///wAAAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////wAAAAD///8AAAD///////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAAAA////AAAA//////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAP///wAAAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAAD///8AAAD///////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////EckT///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAAAA////AAAA//////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////xHJE////xHJExHJE////xHJE////xHJE////xHJE ////////////xHJExHJE////////xHJExHJE////////xHJExHJE////xHJE////xHJE////xHJE xHJE////xHJExHJE////xHJExHJExHJExHJE////xHJE////////xHJE////xHJE////xHJE//// xHJE////xHJE////xHJExHJE////xHJE////xHJExHJExHJExHJExHJE////xHJExHJExHJE//// xHJE////////xHJE////xHJE////xHJE////xHJE////xHJE////xHJExHJE////xHJE////xHJE xHJE////xHJE////xHJExHJExHJE////xHJExHJE////xHJE////////xHJE////xHJE////xHJE ////xHJE////xHJE////xHJExHJE////xHJE//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAAAP///wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /8RyRMRyRP///////////8RyRP///////////////////////////8RyRMRyRP///8RyRMRyRMRy RP///8RyRMRyRMRyRP///8RyRP///8RyRP///////8RyRMRyRP////////////////////////// /////////////////8RyRP///8RyRMRyRMRyRP///8RyRMRyRMRyRP///8RyRMRyRP///8RyRP// /////////////////////////8RyRP///////////////////////8RyRP///8RyRMRyRMRyRP// /8RyRMRyRMRyRP///8RyRMRyRP///8RyRP///////8RyRP///////////8RyRMRyRP////////// /////////////////////8RyRP///8RyRMRyRMRyRP///8RyRMRyRMRyRP///8RyRMRyRP///8Ry RP////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////wAAAAD///8AAAD///// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAA////AAAA//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////AAAAAP///wAA AP////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////wAAAAD///8AAAD///////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8AAAAA ////AAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////AAAAAP///wAAAP////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /wAAAAD///8AAAD///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAAAA////AAAA//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////AAAAAP///wAAAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAD///8AAAD///////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAAA////AAAA//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////AAAAAP///wAAAP////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAD///8AAAD///////////////////////////////////////// //////////////////////////////////////////////////////////8AAAD///8AAAAAAAAA AAAAAAAAAAAAAAD///8AAAD///8AAAAAAAAAAAAAAAAAAAAAAAAAAAD///////////////////8A AAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///8AAAAAAAD///8AAAAAAAAAAAAAAAD///// //8AAAAAAAAAAAD///8AAAD///8AAAD///8AAAAAAAAAAAD///////8AAAAAAAAAAAD///8AAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAD///////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAAAA////AAAA //////////////////////////////////////////////////////////////////////////// ////////////////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAA////////AAAA////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAA ////AAAAAAAAAAAA////AAAAAAAAAAAA////AAAA////AAAA////AAAA////AAAA////AAAA//// AAAAAAAAAAAA////////AAAA////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////AAAAAP///wAAAP////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAAAAP// /wAAAP///wAAAP///////////wAAAAAAAAAAAP///////////////////////////wAAAP////// /////wAAAP///////////////wAAAAAAAP///wAAAAAAAP///////////////wAAAP////////// /wAAAP///wAAAAAAAP///////wAAAAAAAP///////////wAAAP///////////wAAAAAAAP////// /////////////wAAAP///////////////wAAAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////wAAAAD/ //8AAAD///////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////8AAAAA////AAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// AAAAAP///wAAAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////wAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAAAA////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAAAP///wAAAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////wAAAAD///8AAAD///////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAAA////AAAA//////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////AAAAAP///wAAAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////wAAAAD///8AAAD/ //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAAAA////AAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////ISEh//////////////////////////////////////////////////////// ////ISEh////////////////////////////////////////////////////ISEh//////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////ISEh//////////////////////////////////// ISEh////////////////////////////////////////////////////////ISEh//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////AAAAAP// /wAAAP////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////yEhIf///yEhISEhISEhISEhIf///yEh ISEhISEhIf///yEhISEhISEhISEhISEhISEhIf///yEhISEhISEhIf///////yEhISEhISEhISEh If///yEhISEhISEhISEhIf///yEhISEhIf///yEhISEhISEhISEhISEhISEhISEhIf///yEhIf// /yEhISEhIf///yEhISEhISEhISEhIf///////yEhISEhIf///yEhIf///yEhISEhIf///////yEh ISEhISEhIf///yEhIf///yEhISEhISEhISEhIf///yEhISEhISEhISEhISEhIf///yEhISEhIf// /yEhISEhISEhISEhIf///yEhISEhISEhIf///yEhISEhIf///yEhIf///yEhISEhISEhISEhIf// /yEhISEhIf///yEhISEhIf///////yEhISEhIf///////////yEhISEhIf///////////////yEh If////////////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAAD///8AAAD///////////////////////////// //////////////////////////////////////////////////////////////////////////8h ISEhISH///////8hISEhISEhISEhISEhISH///////8hISEhISH///8hISEhISH///8hISEhISEh ISH///////8hISEhISH///////////8hISEhISEhISH///8hISH///8hISEhISEhISEhISEhISH/ //8hISEhISH///8hISEhISEhISEhISH///8hISH///8hISEhISH///8hISH///8hISH///8hISH/ //8hISH///8hISEhISH///8hISEhISH///////////8hISEhISH///////8hISH///8hISEhISEh ISEhISEhISEhISH///8hISEhISEhISEhISEhISH///////8hISEhISEhISH///////8hISEhISH/ //8hISEhISEhISH///8hISH///8hISEhISEhISH///8hISH///////8hISEhISH///////8hISEh ISEhISEhISEhISEhISH///8hISEhISEhISEhISH///////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAAA////AAAA//////////////////////////////////////////////////////////////// ////////////////////////////////////////ISEhISEhISEh////////////////ISEhISEh ////////////////////////////////////////////////////////ISEhISEh//////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////ISEh//////////////////////////////////////////////// ////////////ISEhISEh//////////////////////////////////////////////////////// ////////////////////////////////////ISEhISEh//////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////AAAAAP///wAAAP////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////wAAAAD///8AAAD///////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////8AAAAA////AAAA//////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAAAP///wAAAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////wAAAAD///8AAAD///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////8AAAAA////AAAA//////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////AAAAAP///wAAAP// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAAD///8AAAD///////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////8AAAAA//// AAAA//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////AAAAAP///wAAAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////wAA AAD///8AAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAAAA////AAAA//////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////AAAAAP///wAAAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////wAAAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////wAAAAD///8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAAAAAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///8AAAD/ //8AAAAAAAD///8AAAAAAAAAAAD///8AAAAAAAD///8AAAAAAAD///////8AAAAAAAD///8AAAAA AAD///////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///8AAAD///8AAAAAAAD///8AAAAAAAAA AAD///////8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///////////8AAAD///8AAAAAAAD///// //8AAAAAAAD///8AAAAAAAAAAAAAAAAAAAD///8AAAAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAAAA////AAAA//////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////AAAAAAAAAAAAAAAA////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAA////AAAAAAAA////AAAAAAAAAAAA////AAAA AAAA////AAAAAAAA////////AAAAAAAA////AAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAA////AAAA////AAAAAAAA////AAAA////////////////AAAA////AAAAAAAAAAAA//// AAAAAAAA////////////AAAA////AAAAAAAA////AAAA////AAAA////AAAA////AAAAAAAAAAAA ////AAAAAAAA//////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////AAAAAP///wAAAP////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////wAAAP// /////////////////////////////////////////////wAAAP////////////////////////// /////////////////wAAAAAAAAAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////wAAAAD///8AAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAAAA////AAAA//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////AAAAAP///wAAAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAD///8A AAD///////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////8AAAD///////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAD///////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAAAA////AAAA//////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAA////////AAAAAAAA////AAAA ////AAAA////AAAAAAAA////AAAAAAAAAAAAAAAA////AAAAAAAA////AAAAAAAAAAAA////AAAA AAAA////////AAAAAAAA////AAAAAAAA////////AAAAAAAAAAAAAAAA////AAAAAAAA////AAAA AAAA////AAAAAAAAAAAAAAAAAAAA////AAAAAAAA////AAAAAAAA////AAAAAAAA////AAAAAAAA ////////AAAA////AAAAAAAAAAAAAAAA////////AAAAAAAA////AAAA////AAAAAAAA////AAAA AAAA////AAAAAAAA////AAAAAAAAAAAAAAAA////////AAAAAAAA////AAAAAAAA//////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AP///wAAAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////wAAAAAAAP///wAAAAAAAP///wAAAP///wAAAP///wAAAAAAAP///wAAAAAAAAAA AAAAAP///wAAAAAAAP///wAAAAAAAAAAAP///wAAAAAAAP///////wAAAAAAAP///wAAAAAAAP// /////wAAAP///wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAP///wAAAP///wAA AAAAAP///wAAAP///////wAAAAAAAP///wAAAAAAAP///////wAAAP///wAAAAAAAAAAAP////// /////wAAAAAAAAAAAAAAAP///wAAAAAAAP///wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAP// /////////wAAAAAAAP///wAAAAAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////wAAAAD///8AAAD///////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAAAAAAAAAAD///////////// //////////////////8AAAD///////////////////////////////////////////////////// //////////////////////8AAAD///////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAD///////////////////////////////////////////////////////// //////////////8AAAD///////////////////////////////////8AAAD///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAAAA////AAAA//////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAP///wAAAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAAD///8AAAD///////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAAAA////AAAA//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAAAP///wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////wAAAAD///8AAAD///// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAA////AAAA//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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                                                 =                                                                 ISSN: 2602-8085<= /span>

      =                           Vol. 2, N°4.1, p. 5-22, octubre - diciembre, 2018

Estadís= tica                                                =                                                       =                                        Página 16 de 17

 

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