I understand the contrasts from previous posts and I think I am doing the right thing but it is not giving me what I would expect.
x <- c(11.80856, 11.89269, 11.42944, 12.03155, 10.40744,
12.48229, 12.1188, 11.76914, 0, 0,
13.65773, 13.83269, 13.2401, 14.54421, 13.40312)
type <- factor(c(rep("g",5),rep("i",5),rep("t",5)))
type
[1] g g g g g i i i i i t t t t t
Levels: g i t
When I run this:
> summary.lm(aov(x ~ type))
Call:
aov(formula = x ~ type)
Residuals:
Min 1Q Median 3Q Max
-7.2740 -0.4140 0.0971 0.6631 5.2082
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.514 1.729 6.659 2.33e-05 ***
typei -4.240 2.445 -1.734 0.109
typet 2.222 2.445 0.909 0.381
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.866 on 12 degrees of freedom
Multiple R-squared: 0.3753, Adjusted R-squared: 0.2712
F-statistic: 3.605 on 2 and 12 DF, p-value: 0.05943
Here my reference is my type "g", so my typei is the difference between type "g" and type "i", and my typet is the difference between type "g" and type "t".
I wanted to see two more contrasts here, the difference between typei+typeg and type "t" and difference between type "i" and type "t"
so the contrasts
> contrasts(type) <- cbind( c(-1,-1,2),c(0,-1,1))
> summary.lm(aov(x~type))
Call:
aov(formula = x ~ type)
Residuals:
Min 1Q Median 3Q Max
-7.2740 -0.4140 0.0971 0.6631 5.2082
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.8412 0.9983 10.860 1.46e-07 ***
type1 -0.6728 1.4118 -0.477 0.642
type2 4.2399 2.4453 1.734 0.109
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.866 on 12 degrees of freedom
Multiple R-squared: 0.3753, Adjusted R-squared: 0.2712
F-statistic: 3.605 on 2 and 12 DF, p-value: 0.05943
When I try to do the second contrast by changing my reference I get different results. I am not understanding what is wrong with my contrast.
Answer
Refence: http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
mat <- cbind(rep(1/3, 3), "g+i vs t"=c(-1/2, -1/2, 1),"i vs t"=c(0, -1, 1))
mymat <- solve(t(mat))
my.contrast <- mymat[,2:3]
contrasts(type) <- my.contrast
summary.lm(aov(x ~ type))
my.contrast
> g+i vs t i vs t
[1,] -1.3333 1
[2,] 0.6667 -1
[3,] 0.6667 0
> contrasts(type) <- my.contrast
> summary.lm(aov(x ~ type))
Call:
aov(formula = x ~ type)
Residuals:
Min 1Q Median 3Q Max
-7.274 -0.414 0.097 0.663 5.208
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.841 0.998 10.86 1.5e-07 ***
typeg+i vs t 4.342 2.118 2.05 0.063 .
typei vs t 6.462 2.445 2.64 0.021 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.87 on 12 degrees of freedom
Multiple R-squared: 0.375, Adjusted R-squared: 0.271
F-statistic: 3.6 on 2 and 12 DF, p-value: 0.0594