Análisis de la varianza (II)

Transcription

1 01:43 Thursday, March 10, AGRO 6005 Análisis de la varianza (II) 1. Evaluación de supuestos. Los siguientes datos son recuentos de un áfido en trigo en 6 semanas diferentes. En cada ocasión se muestrearon cuarenta plantas aleatoriamente escogidas, y se contaron los insectos en cada una. Con el procedimiento NPAR1WAY realizamos pruebas estadísticas no paramétricas, que son equivalentes a las que podemos realizar usando un ANOVA sobre los datos ranqueados. data afidos; do semana=1 to 6; do repet=1 to 40; input output; end; end; datalines; ; title 'Datos originales'; proc boxplot; plot recuento*semana; proc glm data=afidos; class semana; model recuento = semana; output out=b p=pred r=resid; proc univariate data=b normal; var resid; qqplot resid / normal; proc gplot data=b; plot resid*pred; data b; set b; absresid=abs(resid); proc glm data=b; class semana; model absresid = semana; title 'Prueba de Levene (puede generalizarse a cualquier modelo)'; data afidos; set afidos; logrec=log(recuento+1); title 'Datos transformados'; proc glm data=afidos; class semana; model logrec = semana; output out=d p=pred r=resid;

2 proc univariate data=d normal; var resid; qqplot resid / normal; proc gplot data=d; plot resid*pred; 01:43 Thursday, March 10, proc npar1way data=afidos wilcoxon; class semana; var recuento; title 'Datos ranqueados'; proc rank data=afidos out=ranks1; var recuento; ranks rankrec; proc glm data=ranks1; class semana; model rankrec=semana; run;

3 01:43 Thursday, March 10, Datos originales Class Level Information Class Levels Values semana Number of Observations Read 240 Number of Observations Used 240 Dependent Variable: recuento Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE recuento Mean Source DF Type I SS Mean Square F Value Pr > F semana <.0001 Source DF Type III SS Mean Square F Value Pr > F semana <.0001

4 01:43 Thursday, March 10, Datos originales The UNIVARIATE Procedure Variable: resid Moments N 240 Sum Weights 240 Mean 0 Sum Observations 0 Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation. Std Error Mean Tests for Normality Test Statistic p Value Shapiro-Wilk W Pr < W < Kolmogorov-Smirnov D Pr > D < Cramer-von Mises W-Sq Pr > W-Sq < Anderson-Darling A-Sq Pr > A-Sq <0.0050

5 Datos originales 01:43 Thursday, March 10,

6 01:43 Thursday, March 10, Prueba de Levene (puede generalizarse a cualquier modelo) Class Level Information Class Levels Values semana Number of Observations Read 240 Number of Observations Used 240 Dependent Variable: absresid Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE absresid Mean Source DF Type I SS Mean Square F Value Pr > F semana <.0001 Source DF Type III SS Mean Square F Value Pr > F semana <.0001

7 01:43 Thursday, March 10, Datos transformados Class Level Information Class Levels Values semana Number of Observations Read 240 Number of Observations Used 240 Dependent Variable: logrec Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE logrec Mean Source DF Type I SS Mean Square F Value Pr > F semana <.0001 Source DF Type III SS Mean Square F Value Pr > F semana <.0001

8 01:43 Thursday, March 10, Datos transformados The UNIVARIATE Procedure Variable: resid Moments N 240 Sum Weights 240 Mean 0 Sum Observations 0 Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation. Std Error Mean Tests for Normality Test Statistic p Value Shapiro-Wilk W Pr < W Kolmogorov-Smirnov D Pr > D < Cramer-von Mises W-Sq Pr > W-Sq < Anderson-Darling A-Sq Pr > A-Sq <0.0050

9 Datos transformados 01:43 Thursday, March 10,

10 01:43 Thursday, March 10, Datos ranqueados The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable recuento Classified by Variable semana semana N Sum of Scores Expected Under H0 Std Dev Under H0 Mean Score Average scores were used for ties. Kruskal-Wallis Test Chi-Square DF 5 Pr > Chi-Square <.0001

11 01:43 Thursday, March 10, Datos ranqueados Class Level Information Class Levels Values semana Number of Observations Read 240 Number of Observations Used 240 Dependent Variable: rankrec Rank for Variable recuento Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE rankrec Mean Source DF Type I SS Mean Square F Value Pr > F semana <.0001 Source DF Type III SS Mean Square F Value Pr > F semana <.0001

12 Ejemplo 3 01:43 Thursday, March 10, En este ejemplo realizamos una prueba no paramétrica (comparación de rangos) para un diseño en bloques. Los datos son la cantidad de ácido oxálico generado por distintas cepas de un hongo en un experimento llevado a cabo en cuatro semanas diferentes (bloques). data sclerot; do week=1 to 4; do strain=1, 5, 6, 7; input output; end; end; datalines; proc sort; by week; title 'Ejemplo 3'; proc rank out=ranks2; by week; var oxalic; ranks rankoxal; proc glm; class week strain; model rankoxal = week strain / ss3; means strain / tukey; run; Class Level Information Class Levels Values week strain Source DF Sum of Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE rankoxal Mean Source DF Type III SS Mean Square F Value Pr > F week strain

13 The SAS System 01:43 Thursday, March 10, Dependent Variable: diametro Note: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square Critical Value of Studentized Range Minimum Significant Difference Means with the same letter are not significantly different. Tukey Grouping Mean A A A N strain B B B

14 The SAS System 01:43 Thursday, March 10, Dependent Variable: diametro Análisis de la varianza (III). Experimentos factoriales Los siguientes datos provienen de un experimento para comparar los efectos del ph del suelo y de los aditivos de calcio sobre el crecimiento de árboles de naranja. El experimento se condujo según un diseño en bloques completos al azar. data arboles; input bloque ph calcio datalines; ; proc glm data=arboles; class bloque ph calcio; model diametro=bloque ph calcio ph*calcio; lsmeans ph calcio ph*calcio / slice=ph pdiff adjust=tukey; ods output diff=diferencias lsmeans=medias; *ods listing exclude lsmeans diff; run; %include 'i:\pdglm800.sas'; %pdglm800(diferencias, medias,alpha=.05,sort=yes); run; proc gplot data=medias; where effect='ph_calcio'; symbol i=join value=dot; plot lsmean*ph=calcio; run; Class Level Information Class Levels Values bloque ph calcio

15 The SAS System 01:43 Thursday, March 10, Dependent Variable: diametro Number of Observations Read 36 Number of Observations Used 36 Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE diametro Mean Source DF Type III SS Mean Square F Value Pr > F bloque ph <.0001 calcio ph*calcio

16 The SAS System 01:43 Thursday, March 10, Least Squares Means Adjustment for Multiple Comparisons: Tukey ph diametro LSMEAN LSMEAN Number Least Squares Means for effect ph Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: diametro i/j <.0001 < < < calcio diametro LSMEAN LSMEAN Number Least Squares Means for effect calcio Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: diametro i/j

17 The SAS System 01:43 Thursday, March 10, Least Squares Means Adjustment for Multiple Comparisons: Tukey ph calcio diametro LSMEAN LSMEAN Number Least Squares Means for effect ph*calcio Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: diametro i/j < <.0001 <.0001 <.0001 <.0001 < < < < < < < < <

18 01:43 Thursday, March 10, Ejemplo 3 Tukey's Studentized Range (HSD) Test for rankoxal ph DF ph*calcio Effect Sliced by ph for diametro Sum of Squares Mean Square F Value Pr > F < SALIDA DE LA MACRO PDGLM800 Obs Dependent ph BYGROUP=1 Effect=calcio LSMean calcio LetterGroup 1 diametro A 2 diametro B 3 diametro B Obs Dependent ph BYGROUP=2 Effect=ph LSMean calcio LetterGroup 4 diametro A 5 diametro AB 6 diametro B 7 diametro C Obs Dependent ph BYGROUP=3 Effect=ph_calcio LSMean calcio LetterGroup 8 diametro A 9 diametro AB 10 diametro AB 11 diametro AB 12 diametro AB 13 diametro AB 14 diametro AB 15 diametro ABC 16 diametro ABC 17 diametro BCD

19 Ejemplo 3 01:43 Thursday, March 10, Tukey's Studentized Range (HSD) Test for rankoxal Obs Dependent ph LSMean calcio LetterGroup 18 diametro CD 19 diametro D

20 Ejemplo 3 01:43 Thursday, March 10, Tukey's Studentized Range (HSD) Test for rankoxal Diferencia entre medias no ajustadas y medias marginales en factoriales no balanceados data factor; input variedad $ fungic $ repet rendim; datalines; a no 1 14 a no 2 15 a si 1 14 a si 2 16 b no 1 13 b no 2 12 b si 1 19 b si 2 20 b si 3 20 proc glm data=factor; class variedad fungic; model rendim = variedad fungic variedad*fungic; means variedad fungic variedad*fungic; lsmeans variedad fungic variedad*fungic / stderr; run; Dependent Variable: rendim

21 Ejemplo 3 01:43 Thursday, March 10, Tukey's Studentized Range (HSD) Test for rankoxal Source DF Sum of Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE rendim Mean Source DF Type I SS Mean Square F Value Pr > F variedad fungic variedad*fungic Source DF Type III SS Mean Square F Value Pr > F variedad fungic variedad*fungic Means Level of variedad N Mean rendim Std Dev a b Level of fungic N Mean rendim Std Dev no si

22 Ejemplo 3 01:43 Thursday, March 10, Tukey's Studentized Range (HSD) Test for rankoxal Level of variedad Level of fungic N Mean rendim Std Dev a no a si b no b si Least Squares Means variedad rendim LSMEAN Standard Error Pr > t a <.0001 b <.0001 fungic rendim LSMEAN Standard Error Pr > t no <.0001 si <.0001 variedad fungic rendim LSMEAN Standard Error Pr > t a no <.0001 a si <.0001 b no <.0001 b si <.0001