Nonparametric Testing

Question 1

What are nonparametric tests?

Answer 1

Statistical tests that do not assume a normal distribution; they use ranks or frequencies instead of raw scores.

Question 2

When are nonparametric tests used?

Answer 2

When data are ordinal, nominal, skewed, or when sample size is small (n < 30).

Question 3

How do nonparametric tests differ from parametric tests?

Answer 3

They analyze ranks or counts rather than means; less powerful but more flexible.

Question 4

What is the main advantage of nonparametric tests?

Answer 4

Fewer assumptions about the data; can analyze ordinal or categorical variables.

Question 5

What is the main disadvantage of nonparametric tests?

Answer 5

Reduced statistical power and limited ability to test complex designs.

Question 6

What type of data are analyzed with nonparametric tests?

Answer 6

Ordinal, nominal, or non-normally distributed continuous data.

Question 7

What is the Chi-Square (χ²) test used for?

Answer 7

To determine if there is a relationship between categorical variables (nominal data).

Question 8

What are the two types of Chi-Square tests?

Answer 8

Goodness-of-Fit and Test of Independence.

Question 9

What does the Chi-Square Goodness-of-Fit test assess?

Answer 9

Whether observed frequencies match expected frequencies in one categorical variable.

Question 10

What does the Chi-Square Test of Independence assess?

Answer 10

Whether two categorical variables are associated (related) or independent.

Question 11

Give an example of a Chi-Square test in PT.

Answer 11

Determine if gender is related to exercise preference (χ²(1) = 4.0, p = .046).

Question 12

What is Fisher’s Exact Test used for?

Answer 12

To test association between two categorical variables in small samples (n < 20, 2×2 tables).

Question 13

What is the Mann–Whitney U test?

Answer 13

Nonparametric alternative to the independent t-test; compares medians between two independent groups.

Question 14

Give a PT example of the Mann–Whitney U test.

Answer 14

Compare median pain scores between aquatic and land therapy groups.

Question 15

What is the Wilcoxon Signed-Ranks test?

Answer 15

Nonparametric alternative to the paired t-test; compares paired or matched samples.

Question 16

Give a PT example of the Wilcoxon Signed-Ranks test.

Answer 16

Compare fatigue ratings before and after a four-week strength program.

Question 17

What is the Kruskal–Wallis test?

Answer 17

Nonparametric alternative to one-way ANOVA; compares medians among three or more independent groups.

Question 18

Give a PT example of the Kruskal–Wallis test.

Answer 18

Compare balance ranks across three different rehab interventions.

Question 19

What is the Friedman test?

Answer 19

Nonparametric equivalent of repeated-measures ANOVA; compares ranks across repeated measures in one group.

Question 20

Give a PT example of the Friedman test.

Answer 20

Compare weekly pain ratings across four sessions of therapy for the same patients.

Question 21

What is Spearman’s rho (ρ)?

Answer 21

Correlation coefficient for ranked or ordinal data; nonparametric equivalent of Pearson’s r.

Question 22

What is Kendall’s tau (τ)?

Answer 22

Alternative to Spearman’s rho for small samples or many tied ranks.

Question 23

What is the Sign test?

Answer 23

Simplest paired nonparametric test; compares direction (+/–) of change between two related measures.

Question 24

When should you use the Sign test?

Answer 24

When only the direction of change is known, not magnitude.

Question 25

What is the Phi coefficient (φ)?

Answer 25

Measure of association between two dichotomous (binary) variables.

Question 26

What is Cramer’s V?

Answer 26

Measure of association between two nominal variables with more than two categories.

Question 27

What statistic is reported for Chi-Square tests?

Answer 27

χ²(df, N) and p-value.

Question 28

What does p < 0.05 in a Chi-Square test indicate?

Answer 28

A significant association between the categorical variables.

Question 29

What is meant by “distribution-free” in nonparametric testing?

Answer 29

No assumption about underlying data distribution (normality not required).

Question 30

What is a common tradeoff when choosing a nonparametric test?

Answer 30

Greater robustness but reduced power to detect small effects.

Question 31

What nonparametric test corresponds to an independent t-test?

Answer 31

Mann–Whitney U.

Question 32

What nonparametric test corresponds to a paired t-test?

Answer 32

Wilcoxon Signed-Ranks.

Question 33

What nonparametric test corresponds to one-way ANOVA?

Answer 33

Kruskal–Wallis.

Question 34

What nonparametric test corresponds to repeated-measures ANOVA?

Answer 34

Friedman.

Question 35

What nonparametric test corresponds to Pearson’s r?

Answer 35

Spearman’s rho.

Question 36

What is a key reporting element for nonparametric results?

Answer 36

Medians and interquartile ranges (IQR) instead of means and SDs.

Question 37

Why are nonparametric tests common in PT research?

Answer 37

Many PT outcome measures are ordinal (e.g., MMT, pain scale) or have small sample sizes.