Suppose we have data on vitamin E intake (IU/day) (from both diet and vitamin E supplements) at baseline in four treatment groups in a clinical trial of nutritional supplements. It is important to establish that the vitamin E intakes of the four treatment groups are comparable at baseline. The data (baseline vitamin E intake) for the first 10 participants in each group are given below. | Subject | Group 1 | Group 2 | Group 3 | Group 4 | |--------:|----------:|----------:|----------:|----------:| | 1 | 15.92 | 5.22 | 4.33 | 5.37 | | 2 | 8.24 | 3.29 | 16.31 | 6.39 | | 3 | 17.27 | 3.67 | 6.19 | 4.90 | | 4 | 16.24 | 4.29 | 7.95 | 4.75 | | 5 | 15.21 | 109.17 | 4.02 | 3.07 | | 6 | 8.25 | 5.82 | 6.12 | 10.64 | | 7 | 18.33 | 7.17 | 5.60 | 6.50 | | 8 | 14.12 | 4.42 | 12.20 | 159.90 | | 9 | 16.27 | 5.29 | 3.33 | 6.00 | | 10 | 5.38 | 55.99 | 7.33 | 7.31 | ## Part a (4 points) We wish to assess whether there are significant overall group differences in vitamin E intake. Check the assumptions for a comparison based on normal theory (i.e. standard ANOVA method) ```{r, echo=FALSE, eval=FALSE} #load the data group <- c(rep("A",10),rep("B",10),rep("C",10),rep("D",10)) vitE <- c(c(15.92,8.24,17.27,16.24,15.21,18.25,8.33,14.12,16.27,5.38), c(5.22,3.29,3.67,4.29,109.17,5.82,7.17,4.42,5.29,55.99), c(4.33,16.31,6.19,7.95,4.02,6.12,5.60,12.20,3.33,7.33), c(5.37,6.39,4.90,4.75,3.07,10.64,6.50,159.90,6.00,7.31)) vitE.df <- as.data.frame(cbind(group,vitE)) vitE.df$vitE <- as.numeric(as.character(vitE.df$vitE)) ```