# Answers to the checkpoints of chapter 9

**Checkpoint 1**

- To test the association between two nominal variables or to test the distribution of a single variable.
- A nominal measurement level.
- That it is a skewed distribution, with a long tail, and so you don’t differentiate between one-tailed and two-tailed tests.
- (4-1)(3-1) = 6 degrees of freedom.
- In principle, you can use a chi-square test from nominal measurement level onwards. However, it is not a suitable test for analyzing the relationship between years of education and income, because these two variables are both at minimal interval level. There are better tests for this, which will tell you not only whether there is an association, but also how strong the association is. It would be better to use a correlation test.

**Checkpoint 2**

- The Wilcoxon rank-sum test.
- You order your observations, then you give them a rank number and then you add all the rank numbers together.
- You’ll get a tie in your ranking if a few consecutive rank numbers in the ranking are the same. That’s when you take the average rank number.
- The results are standardized using a
*z*score, which is interpreted according to the standard normal table.

**Checkpoint 3**

- The signed rank test is an alternative for the paired
*t*test on differences between two dependent populations. - The “plusses” and “minuses” (signs) indicate the difference in the observations between two measurements in the same group.
- They are not counted.

**Checkpoint 4**

- The Kruskal-Wallis test
- The test statistic has a chi-square distribution.
- Only a one-tailed test. You can’t do a two-tailed test because the chi-square distribution is asymmetrical.

**Checkpoint 5**

- You interpret the Spearman rank correlation in the same way as you would the Pearson correlation coefficient; the Spearman rank correlation produces slightly more conservative values.
- An alternative is the tau test.