## Chapter 5

### Query from Floris Hegger

In chapter 4, you discuss several types of graphs. One of them is the grouped scatterplot in which you show how men and women differ in terms of exam performance and exam anxiety. You literally say the following: “These lines (Figure 4.36) tell us that the relationship between exam anxiety and exam performance was slightly stronger in males (the line is steeper) indicating that men’s exam performance was more adversely affected by anxiety than women’s exam anxiety.” I have to (partly) disagree with this. The steepness of the line does not indicate how strong the relationship between the variables is; the strength of a relationship is usually displayed by r, the correlation coefficient. I think it is misleading, since the strength of the relationship is determined by ‘how close the dots are on the line’ and not by ‘the steepness of the line’.

This point is fair, stronger associations do reflect data that cluster more closely around the line, but as Floris also points out *the strength of a relationship is usually displayed by r, the correlation coefficient* and in the case of two variables, *r* has a direct relationship to *b* (the gradient of the line). Therefore, the gradient (slope of the line) provides information about strength but it is ‘contaminated’ by information about the spread of scores. The issue here (and the sense in which the point is a very good one) is that I’ve plotting the raw data not the standardized data. If I’d plotted the standardized data, *r* would be equal to the gradient. In this situation we could directly compare the male and female lines and use the gradient as information about the relative strength of the relationship in those two groups. However, because I’ve plotted the raw data, the statement in the book only holds if the standard deviations of both variables are the same for males and females, which they might not be.

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