[R] Anova Type II and Contrasts

[John Fox]

Dear Peter,

Because your model is additive, "type-II" and "type-III" tests are identical, and the t-tests for the linear and quadratic coefficients are interpretable.

I hope this helps,
 John

------------------------------------------------
John Fox
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox/

On Fri, 6 Jul 2012 16:06:26 +0100
 mails <mails00000 at gmail.com> wrote:
> the study design of the data I have to analyse is simple. There is 1 control group (CTRL) and 2 different treatment groups (TREAT_1 and TREAT_2). 
> The data also includes 2 covariates COV1 and COV2. I have been asked to check if there is a linear or quadratic treatment effect in the data. 
> 
> I created a dummy data set to explain my situation: 
> 
> df1 <- data.frame( 
> 
> Observation = c(rep("CTRL",15), rep("TREAT_1",13), rep("TREAT_2", 12)), 
> 
> COV1 = c(rep("A1", 30), rep("A2", 10)), 
> 
> COV2 = c(rep("B1", 5), rep("B2", 5), rep("B3", 10), rep("B1", 5), rep("B2", 5), rep("B3", 10)), 
> 
> Variable = c(3944133, 3632461, 3351754, 3655975, 3487722, 3644783, 3491138, 3328894, 
>                         3654507, 3465627, 3511446, 3507249, 3373233, 3432867, 3640888, 
> 
>                         3677593, 3585096, 3441775, 3608574, 3669114, 4000812, 3503511, 3423968, 
>                         3647391, 3584604, 3548256, 3505411, 3665138, 
> 
>                        4049955, 3425512, 3834061, 3639699, 3522208, 3711928, 3576597, 3786781, 
>                        3591042, 3995802, 3493091, 3674475) 
> ) 
> 
> plot(Variable ~ Observation, data = df1) 
> 
> As you can see from the plot there is a linear relationship between the control and the treatment groups. To check if this linear effect is statistical 
> significant I change the contrasts using the contr.poly() function and fit a linear model like this: 
> 
> contrasts(df1$Observation) <- contr.poly(levels(df1$Observation)) 
> lm1 <- lm(log(Variable) ~ Observation, data = df1) 
> summary.lm(lm1) 
> 
> >From the summary we can see that the linear effect is statistically significant: 
> 
> Observation.L  0.029141   0.012377    2.355    0.024 *   
> Observation.Q  0.002233   0.012482    0.179    0.859   
> 
> However, this first model does not include any of the two covariates. Including them results in a non-significant p-value for the linear relationship: 
> 
> lm2 <- lm(log(Variable) ~ Observation + COV1 + COV2, data = df1) 
> summary.lm(lm2) 
> 
> Observation.L  0.04116    0.02624   1.568    0.126     
> Observation.Q  0.01003    0.01894   0.530    0.600     
> COV1A2        -0.01203    0.04202  -0.286    0.776     
> COV2B2        -0.02071    0.02202  -0.941    0.354     
> COV2B3        -0.02083    0.02066  -1.008    0.320   
> 
> So far so good. However, I have been told to conduct a Type II Anova rather than a Type I. To conduct a Type II Anova I used the Anova() function 
>  from the car package. 
> 
> Anova(lm2, type="II") 
> 
> Anova Table (Type II tests) 
> 
> Response: log(Variable) 
>                     Sum Sq Df F value Pr(>F) 
> Observation 0.006253  2  1.4651 0.2453 
> COV1              0.000175  1  0.0820 0.7763 
> COV2              0.002768  2  0.6485 0.5292 
> Residuals      0.072555 34 
> 
> The problem here with using Type II is that you do not get a p-value for the linear and quadratic effect. 
> So I do not know if the treatment effect is statistically linear and or quadratic. 
> 
> I found out that the following code produces the same p-value for Observation as the Anova() function. However, the result also does not include 
> any p-values for the linear or quadratic effect: 
> 
> lm2 <- lm(log(Variable) ~ Observation + COV1 + COV2, data = df1) 
> lm3 <- lm(log(Variable) ~ COV1 + COV2, data = df1) 
> anova(lm2, lm3) 
> 
> 
> Does anybody know how to conduct a Type II anova and the contrasts function to obtain the p-values for the linear and quadratic effects? 
> 
> Help would be very much appreciated. 
> 
> Best Peter
> 	[[alternative HTML version deleted]]
> 
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