RQ-week4.Rmd

# Week 4 - Reading questions

```{r include=FALSE}
knitr::opts_chunk$set(warning=FALSE, message=FALSE)
config <- yaml::yaml.load_file("config.yml")
```

#### Reference {-}

[Miller, G. A., & Chapman, J. P. (2001). Misunderstanding 
analysis of covariance. Journal of Abnormal Psychology, 110(1), 40-48.](https://pdfs.semanticscholar.org/e6d5/8a8a0dd660f6bbaba8d88137735d40124b05.pdf)

#### Questions: {-}

1. What was the original purpose of ANCOVA?
1. In the intro two problems are mentioned which may arise when ANCOVA is 
used in the context of existing groups. Which problems are these, and why are 
these problems?
1. On p. 44 a hypothetical statistician is discussed (introduced by Lord) who uses 
ANCOVA to compare the weight of boys and girls, while using initial weight as a 
covariate. How does this statistician use ANCOVA exactly, and why is this wrong?
1. Why is comparing young women to old men problematic (p. 44)?
1. In the example discussed on p. 46 (first column), what is the DV, the 
covariate(s) and the grouping variable? Is this a good example of the problem the 
authors try to point out, and why do you think it is/is not?

```{r echo=FALSE, results = 'asis', eval = config$show_text}
cat("#### Answers {-}

1. ANCOVA was developed to improve the power of the test of the independent 
variable, not to “control” for anything.
1. In the intro two problems are mentioned which may arise when ANCOVA is 
used in the context of existing groups. Which problems are these, and why are 
these problems? 
    * Removal of variance related to the covariate might also remove variance 
related to the factor of interest, therefore deflating the effect of the factor 
on the DV. 
    * Additional problem is that preexisting groups might differ on more than 
one covariate (not all might be measured) and therefore differences 
remain intact. 
1. The statistician selects two groups, one with boys and one with girls that have 
identical frequency distributions of initial weight. By selecting these groups the 
statistician wants to look at the effect of a certain diet on the increase in weight 
by taking out the effect of initial weight (when you were heavier to start with, you 
are probably heavier later on). But by selecting a group of boys that is equal in 
weight as a group of girls, you will select girls that are heavier that the average 
girl, and boys that are lower in weight than the average boy. By regression to the 
mean, these boys will regress to the mean of the boys (and therefore increase 
more than other boys), and girls will increase less than other girls. 
1. Because all the women are young (in this example) and all men are old, you 
cannot conclude whether an effect is related to age or gender, because they are 
entwined.  
1. DV = performance on reading test  
Grouping variable = district (White vs. Black)  
Covariates = poverty, parent education, class size  
What is Quality in teaching staff? Also covariate, but treated as important 
predictor.  
They want to point out that you cannot separate the effects of district, poverty, 
parent education etc. on the performance, because these IVs are highly 
correlated. I don’t think this is a very good example, because the way the results 
are formulated does not clearly imply what kind of analysis is done. Besides that,
the point that numerous variables are correlated and therefore the effects (on the 
DV) cannot easily be separated, is true.
")
```