Section 9: Non-parametric Statistical Tests

Question 1

What are non-parametric statistical tests?

Answer 1

Statistical methods that don’t assume a specific data distribution (e.g., normality); AKA distribution-free methods.

Question 2

When are non-parametric tests used?

Answer 2

When data is:

• not normally distributed
• ordinal/ranked
• sample sizes are small.

Question 3

What are the main advantages of non-parametric tests?

Answer 3

• Make fewer assumptions
• More robust
• Applicability much wider than parametric methods

Question 4

What are the main disadvantages of non-parametric tests?

Answer 4

• Have less statistical power than parametric tests
• may require larger samples sizes to draw conclusions with same degree of confidence

Question 5

What non-parametric test replaces the Independent Samples t-test?

Answer 5

Mann–Whitney U test (a.k.a. Wilcoxon rank-sum test).

Question 6

What non-parametric test replaces the Paired Samples t-test?

Answer 6

Wilcoxon matched-pairs signed-rank test.

Question 7

What non-parametric test replaces the One-way ANOVA?

Answer 7

Kruskal–Wallis rank test.

Question 8

What non-parametric test is the equivalent of Pearson’s correlation?

Geen idee of dit klopt

Answer 8

Spearman’s rank correlation.

Question 9

What does the Mann–Whitney U test compare?

Answer 9

Used to compare two independent samples when:

• outcome is not normally distributed
• and/or the samples are small

Question 10

What are the hypotheses of the Mann–Whitney U test?

Answer 10

• H₀: H0: 2 populations (exposure groups) are equal with respect to outcome variable
• H₁: 2 populations (exposure groups) are not equal with respect to outcome variable

Question 11

What is the purpose of the Mann–Whitney U test?

Answer 11

To test whether distribution of DV differs between 2 independent groups when data are not normally distributed.

Question 12

What does it mean when we say the Mann–Whitney U test checks if “the distribution of the dependent variable differs between two exposure groups”?

Answer 12

It checks whether one group tends to have higher or lower values (ranks) of the outcome variable compared to the other group — i.e., whether the pattern of values differs between them.

Question 13

Example: What would the Mann–Whitney U test assess in a study comparing breastfeeding duration between women with and without breast cancer?

Answer 13

• It would test whether breastfeeding duration (the outcome) is distributed differently between women with breast cancer and those without
• i.e., whether one group tends to have longer or shorter breastfeeding durations.

Question 14

How does the Mann–Whitney U test work conceptually?

Answer 14

It ranks all observations and compares the rank sums between groups.

Question 15

What does the Mann Whitney U test depend on?

Answer 15

Ranking all observations (from smallest to largest) and then adding the ranks in each exposure group

• Tied ranks are averaged
• Under the null hypothesis, the sum of ranks would on average be similar between the two groups

Question 16

What Stata command runs the Mann–Whitney U test?

Answer 16

ranksum outcome, by(group)

Question 17

What does the Wilcoxon signed-rank test compare?

Answer 17

Two related or paired samples to test whether their medians differ.

Question 18

What is the Wilcoxon matched-pairs signed-rank test (also known as the Wilcoxon signed-rank test)?

Answer 18

It’s a non-parametric test used to compare two sets of observations from the same group when outcome is not normally distributed or the sample size is small.

Question 19

What does the Wilcoxon signed-rank test evaluate?

Answer 19

It tests whether distribution of DV differs between two related (paired) observations from the same sample.

Question 20

What is the key hypothesis behind the Wilcoxon signed-rank test?

Answer 20

It examines whether the median of the differences between paired observations is zero in the population — meaning no real change or effect between the two time points or conditions.

Question 21

When would you use the Wilcoxon signed-rank test?

Answer 21

When comparing before-and-after measures in the same subjects and data are not normal.

Question 22

What are the hypotheses of the Wilcoxon signed-rank test?

Answer 22

H₀: Median of the differences = 0.
H₁: Median of the differences ≠ 0.

Question 23

What Stata command runs the Wilcoxon signed-rank test?

Answer 23

signrank var1 = var2

Question 24

What is the first step in the Wilcoxon matched-pairs signed-rank test?

Answer 24

Calculate the difference between each pair of observations (e.g., After – Before) to measure change for each subject.

Question 25

What happens to differences that are exactly zero in the Wilcoxon signed-rank test?

Answer 25

They are excluded from the analysis because they show no change between the two measurements.

Question 26

How are the differences ranked in the Wilcoxon signed-rank test?

Answer 26

The absolute values of the non-zero differences are ranked from smallest to largest; tied values are given average ranks.

Question 27

What are T⁺ and T⁻ in the Wilcoxon signed-rank test?

Answer 27

* T⁺: Sum of ranks for positive differences (increases) * T⁻: Sum of ranks for negative differences (decreases)

Question 28

What does it mean under the null hypothesis when T⁺ and T⁻ are similar? | Wilcoxon signed rank test

Answer 28

It means there is no systematic difference between the two sets of observations — the changes are balanced, so H₀ (no difference) is not rejected.

Question 29

What are the main steps of the Wilcoxon matched-pairs signed-rank test? | Klopt dit?

Answer 29

1. Calculate the difference between each pair of observations. 2. Exclude zero differences. 3. Rank the absolute values of the remaining differences (average tied ranks). 4. Sum the ranks for positive (T⁺) and negative (T⁻) differences. 5. Compare T⁺ and T⁻ — large differences indicate a significant effect.

Question 30

What does a large difference between T⁺ and T⁻ indicate in the Wilcoxon signed-rank test?

Answer 30

It suggests a systematic change in one direction (either increase or decrease), meaning the difference between paired observations is statistically significant — reject H₀.

Question 31

What is the Kruskal–Wallis rank test used for?

Answer 31

Used to compare two or more independent samples when outcome variable: * isn't normally distributed and/or * when sample sizes are small.

Question 32

What is the Stata command for the Kruskal–Wallis test?

Answer 32

kwallis outcome, by(group)

Question 33

What test checks for normality before deciding between parametric and non-parametric tests?

Answer 33

Shapiro–Wilk test (swilk varname in Stata).

Question 34

What does a p-value < 0.05 indicate in non-parametric tests?

Answer 34

The result is statistically significant; reject the null hypothesis.

Question 35

In Stata, where can you find non-parametric tests in the menu?

Answer 35

Statistics → Nonparametric analysis → Tests of hypotheses.

Question 36

What does the Kruskal–Wallis test evaluate?

Answer 36

tests whether distribution of DV **differs** between two or more exposure groups.

Question 37

How is the Kruskal–Wallis test related to the Mann–Whitney U test?

Answer 37

It’s an extension of the Mann–Whitney U test that allows comparison of more than two independent groups

Question 38

How do we interpret the Kruskal–Wallis rank test?

Answer 38

* If p > 0.05 → no significant difference; all groups have similar distributions. * If p < 0.05 → at least one group differs significantly, but post-hoc Mann–Whitney tests are needed to identify which groups differ.

Question 39

What is the hypotheses for Kruskal-Wallis rank test?

Answer 39

* H0: The populations (exposure groups) are equal with respect to the outcome variable * H1: The populations (exposure groups) are not equal with respect to the outcome variable

Question 40

What are Post-hoc Mann–Whitney Pairwise Comparisons?

Answer 40

Follow-up tests performed after a significant Kruskal–Wallis test to identify which specific groups differ from each other.

Question 41

Why do we use Post-hoc Mann–Whitney tests after a Kruskal–Wallis test?

Answer 41

Because the Kruskal–Wallis test only shows that at least one group differs, not which groups are different — the post-hoc tests reveal this.

Question 42

How are Post-hoc Mann–Whitney Pairwise Comparisons performed?

Answer 42

By comparing each pair of groups separately using the Mann–Whitney U test, then checking which pairs show significant p-values.

Question 43

How do you run Post-hoc Mann–Whitney tests in Stata?

Answer 43

Use the ranksum command with an if condition to select two groups, e.g.: ranksum outcome if group != 2, by(group)

Question 44

How do you interpret Post-hoc Mann–Whitney test results?

Answer 44

* p < 0.05: The two groups differ significantly. * p > 0.05: No significant difference between those groups.