terça-feira, 10 de maio de 2016

Aula 11 (18/5/2016) - Finalizar Workshop - Arranjo Fatorial de Tratamentos - Interação

Finalizarmos Workshop: Uma apresentação para cada um dos alunos de ANOVA, Cluster e MANOVA

 Arranjo Fatorial de Tratamentos


Programa SAS


data fatorial;
input Genero $ Categ $ IMC;
cards;
F AT 19.7
F AT 20.3
F AT 19.3
F AT 20.9
F SEM 22.4
F SEM 21.9
F SEM 23.8
F SEM 24.1
F SED  26.3
F SED  23.5
F SED  24.8
F SED  26.6
F PR 26.2
F PR 24.2
F PR 25.4
F PR 24.9
M AT 20.2
M AT 21.3
M AT 19.3
M AT 21.1
M SEM 21.2
M SEM 20.1
M SEM 19.7
M SEM 21.1
M SED  27.3
M SED  23.4
M SED  25.2
M SED  26.4
M PR 22.3
M PR 22.2
M PR 22.1
M PR 23.3
;
proc print;
run;
Proc glm;
class Genero Categ;
model IMC = Genero Categ Genero*Categ;
lsmeans Genero*Categ / slice=Genero adjust=tukey PDIFF=all;
lsmeans Genero*Categ / slice=Categ adjust=tukey PDIFF=all;
run;
Variações do programa:
Proc glm;
class Genero Categ;
model IMC = Genero Categ Genero*Categ;

 lsmeans Genero*Categ / slice=Genero adjust=tukey PDIFF=all;
lsmeans Genero*Categ / slice=Categ adjust=tukey PDIFF=all;
/*
lsmeans Categ;
means Categ / Tukey lines;

 means Genero*Categ / tukey lines;
*/

run;

Para Calculo de Efeitos Principais:
Proc anova;
class Genero Categ;
model IMC = Genero Categ Genero*Categ;
means Categ / Tukey lines;
run;
Arquivo de Saida (Tipo Word) para download:


Fazer os gráficos no Excel utilizando tabela dinâmica.






Podemos ver que os gráficos são diferentes, e que as concussões estatísticas também o são.
Veja que no gráfico do gênero feminino professor e sedentário não diferem (as duas barras, medias aritméticas tem a letra A).
No gratifico do Gênero Masculino as categorias Sedentário Professor diferem (Sedentário tem letra A e Professor letra B).







Foto das Louças Onde Discutimos os Resultados








Exemplo Sem Interação Significativa

Autora: Ana Carolina Donofre (Dados simulados)

data fatorial;

input Linhagem $ Densidade $ GP;

cards;

C 10 2.44

C 10 2.39

C 10 2.42

C 10 2.45

C 14 2.03

C 14 1.99

C 14 2.05

C 14 2.07

C 18 1.78

C 18 1.83

C 18 1.81

C 18 1.73

R 10 2.37

R 10 2.30

R 10 2.34

R 10 2.38

R 14 1.88

R 14 1.90

R 14 1.87

R 14 1.92

R 18 1.65

R 18 1.69

R 18 1.70

R 18 1.67

;

proc print;

run;
Proc glm;
class Linhagem Densidade;
model GP = Linhagem Densidade Linhagem*Densidade;
lsmeans Linhagem*Densidade / slice=Linhagem adjust=tukey PDIFF=all;
lsmeans Linhagem*Densidade/ slice=Densidade adjust=tukey PDIFF=all;

means Linhagem / Tukey lines;
means Densidade / Tukey lines;

run;

Arquivo para Download Sem Interação:



Resultados SAS Sem Interação





Outro Exemplo Sem Interação
data consumo;
input Trat $ Imp $ Cons;
cards;
1 a 17.2
1 a 18.3
1 a 17.5
1 a 18.4
1 b 20.3
1 b 21.3
1 b 22.1
1 b 19.5
2 a 22.1
2 a 23.5
2 a 24.5
2 a 21.5
2 b 25.5
2 b 26.4
2 b 27.3
2 b 26.1
3 a 20.2
3 a 23.2
3 a 21.5
3 a 20.1
3 b 22.2
3 b 22.3
3 b 24.5
3 b 26.1
4 a 19.8
4 a 18.8
4 a 19.5
4 a 20.2
4 b 24.3
4 b 23.4
4 b 22.1
4 b 22.7
;
proc print;
run;
proc glm;
class Trat Imp;
model Cons = Trat Imp Trat*Imp;
lsmeans Trat*Imp / slice=Trat adjust=tukey PDIFF=all;
lsmeans Trat*Imp / slice=Imp adjust=tukey PDIFF=all;
run;


/*
means Trat / tukey lines;
means Imp / tukey lines;
*/

Saida:
The SAS System

Obs Trat Imp Cons
1 1 a 17.2
2 1 a 18.3
3 1 a 17.5
4 1 a 18.4
5 1 b 20.3
6 1 b 21.3
7 1 b 22.1
8 1 b 19.5
9 2 a 22.1
10 2 a 23.5
11 2 a 24.5
12 2 a 21.5
13 2 b 25.5
14 2 b 26.4
15 2 b 27.3
16 2 b 26.1
17 3 a 20.2
18 3 a 23.2
19 3 a 21.5
20 3 a 20.1
21 3 b 22.2
22 3 b 22.3
23 3 b 24.5
24 3 b 26.1
25 4 a 19.8
26 4 a 18.8
27 4 a 19.5
28 4 a 20.2
29 4 b 24.3
30 4 b 23.4
31 4 b 22.1
32 4 b 22.7

The SAS System

The ANOVA Procedure
Class Level Information
Class Levels Values
Trat 4 1 2 3 4
Imp 2 a b

Number of Observations Read 32
Number of Observations Used 32


The SAS System

The ANOVA Procedure
Dependent Variable: Cons
Source DF Sum of Squares Mean Square F Value Pr > F
Model 7 196.0700000 28.0100000 20.53 <.0001
Error 24 32.7500000 1.3645833
Corrected Total 31 228.8200000

R-Square Coeff Var Root MSE Cons Mean
0.856874 5.321885 1.168154 21.95000

Source DF Anova SS Mean Square F Value Pr > F
Trat 3 117.2475000 39.0825000 28.64 <.0001
Imp 1 77.5012500 77.5012500 56.79 <.0001
Trat*Imp 3 1.3212500 0.4404167 0.32 0.8088


The SAS System

The ANOVA Procedure



The SAS System

The ANOVA Procedure
Tukey's Studentized Range (HSD) Test for Cons


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 24
Error Mean Square 1.364583
Critical Value of Studentized Range 3.90126
Minimum Significant Difference 1.6112

Means with the same letter
are not significantly different.
Tukey Grouping Mean N Trat
A 24.6125 8 2
B 22.5125 8 3
B
B 21.3500 8 4
C 19.3250 8 1


The SAS System

The ANOVA Procedure



The SAS System

The ANOVA Procedure
Tukey's Studentized Range (HSD) Test for Cons


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 24
Error Mean Square 1.364583
Critical Value of Studentized Range 2.91879
Minimum Significant Difference 0.8524

Means with the same letter
are not significantly different.
Tukey Grouping Mean N Imp
A 23.5063 16 b
B 20.3938 16 a

The SAS System

Obs Trat Imp Cons
1 1 a 17.2
2 1 a 18.3
3 1 a 17.5
4 1 a 18.4
5 1 b 20.3
6 1 b 21.3
7 1 b 22.1
8 1 b 19.5
9 2 a 22.1
10 2 a 23.5
11 2 a 24.5
12 2 a 21.5
13 2 b 25.5
14 2 b 26.4
15 2 b 27.3
16 2 b 26.1
17 3 a 20.2
18 3 a 23.2
19 3 a 21.5
20 3 a 20.1
21 3 b 22.2
22 3 b 22.3
23 3 b 24.5
24 3 b 26.1
25 4 a 19.8
26 4 a 18.8
27 4 a 19.5
28 4 a 20.2
29 4 b 24.3
30 4 b 23.4
31 4 b 22.1
32 4 b 22.7

The SAS System

The GLM Procedure
Class Level Information
Class Levels Values
Trat 4 1 2 3 4
Imp 2 a b

Number of Observations Read 32
Number of Observations Used 32


The SAS System

The GLM Procedure
Dependent Variable: Cons
Source DF Sum of Squares Mean Square F Value Pr > F
Model 7 196.0700000 28.0100000 20.53 <.0001
Error 24 32.7500000 1.3645833
Corrected Total 31 228.8200000

R-Square Coeff Var Root MSE Cons Mean
0.856874 5.321885 1.168154 21.95000

Source DF Type I SS Mean Square F Value Pr > F
Trat 3 117.2475000 39.0825000 28.64 <.0001
Imp 1 77.5012500 77.5012500 56.79 <.0001
Trat*Imp 3 1.3212500 0.4404167 0.32 0.8088

Source DF Type III SS Mean Square F Value Pr > F
Trat 3 117.2475000 39.0825000 28.64 <.0001
Imp 1 77.5012500 77.5012500 56.79 <.0001
Trat*Imp 3 1.3212500 0.4404167 0.32 0.8088




The SAS System

The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
Trat Imp Cons LSMEAN LSMEAN Number
1 a 17.8500000 1
1 b 20.8000000 2
2 a 22.9000000 3
2 b 26.3250000 4
3 a 21.2500000 5
3 b 23.7750000 6
4 a 19.5750000 7
4 b 23.1250000 8

Least Squares Means for effect Trat*Imp
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable: Cons
i/j 1 2 3 4 5 6 7 8
1 0.0282 <.0001 <.0001 0.0080 <.0001 0.4493 <.0001
2 0.0282 0.2256 <.0001 0.9992 0.0263 0.8087 0.1378
3 <.0001 0.2256 0.0074 0.5036 0.9593 0.0099 1.0000
4 <.0001 <.0001 0.0074 <.0001 0.0803 <.0001 0.0141
5 0.0080 0.9992 0.5036 <.0001 0.0855 0.4853 0.3489
6 <.0001 0.0263 0.9593 0.0803 0.0855 0.0008 0.9923
7 0.4493 0.8087 0.0099 <.0001 0.4853 0.0008 0.0052
8 <.0001 0.1378 1.0000 0.0141 0.3489 0.9923 0.0052








The SAS System

The GLM Procedure
Least Squares Means
Trat*Imp Effect Sliced by Trat for Cons
Trat DF Sum of Squares Mean Square F Value Pr > F
1 1 17.405000 17.405000 12.75 0.0015
2 1 23.461250 23.461250 17.19 0.0004
3 1 12.751250 12.751250 9.34 0.0054
4 1 25.205000 25.205000 18.47 0.0002


The SAS System

The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Tukey
Trat Imp Cons LSMEAN LSMEAN Number
1 a 17.8500000 1
1 b 20.8000000 2
2 a 22.9000000 3
2 b 26.3250000 4
3 a 21.2500000 5
3 b 23.7750000 6
4 a 19.5750000 7
4 b 23.1250000 8

Least Squares Means for effect Trat*Imp
Pr > |t| for H0: LSMean(i)=LSMean(j)
Dependent Variable: Cons
i/j 1 2 3 4 5 6 7 8
1 0.0282 <.0001 <.0001 0.0080 <.0001 0.4493 <.0001
2 0.0282 0.2256 <.0001 0.9992 0.0263 0.8087 0.1378
3 <.0001 0.2256 0.0074 0.5036 0.9593 0.0099 1.0000
4 <.0001 <.0001 0.0074 <.0001 0.0803 <.0001 0.0141
5 0.0080 0.9992 0.5036 <.0001 0.0855 0.4853 0.3489
6 <.0001 0.0263 0.9593 0.0803 0.0855 0.0008 0.9923
7 0.4493 0.8087 0.0099 <.0001 0.4853 0.0008 0.0052
8 <.0001 0.1378 1.0000 0.0141 0.3489 0.9923 0.0052








The SAS System

The GLM Procedure
Least Squares Means
Trat*Imp Effect Sliced by Imp for Cons
Imp DF Sum of Squares Mean Square F Value Pr > F
a 3 56.621875 18.873958 13.83 <.0001
b 3 61.946875 20.648958 15.13 <.0001





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