Non-Parametric One-Way ANOVA

What is a non-parametric test?

A statistical test that does not assume the data follow a specific distribution such as the normal distribution.

Why are non-parametric tests used?

When parametric test assumptions are violated or when data are ordinal rather than continuous.

What type of data are non-parametric tests commonly used with?

Ordinal data or non-normally distributed continuous data.

What is the non-parametric equivalent of the one-way between-subjects ANOVA?

The Kruskal–Wallis test.

What does the Kruskal–Wallis test compare?

The distributions or median ranks of three or more independent groups.

When should the Kruskal–Wallis test be used?

When comparing three or more independent groups with ordinal data or when parametric assumptions are violated.

What is the non-parametric equivalent of the one-way within-subjects ANOVA?

The Friedman test.

What does the Friedman test compare?

Differences between three or more related conditions using ranked data.

When should the Friedman test be used?

When the same participants are measured across multiple conditions but parametric assumptions are not met.

What is the main principle behind non-parametric ANOVA tests?

Data are converted into ranks rather than analysed as raw scores.

Why do non-parametric tests rank the data?

Ranking reduces the influence of outliers and distribution shape.

What is a rank in non-parametric tests?

A position assigned to a value after ordering all scores from lowest to highest.

How are tied ranks handled?

Tied values receive the average of the ranks they would have occupied.

What assumption of parametric ANOVA is most commonly violated, requiring non-parametric tests?

Normality of the data.

What does the normality assumption mean?

Data should be approximately normally distributed within groups.

What assumption of ANOVA concerns similar variability between groups?

Homogeneity of variance.

What test is used to assess homogeneity of variance in ANOVA?

Levene’s test.

What does a significant Levene’s test indicate?

The assumption of equal variances is violated.

Why might researchers prefer parametric tests when assumptions are met?

Parametric tests generally have higher statistical power.

What is statistical power?

The probability of correctly detecting a true effect.

Why do non-parametric tests often have lower power?

They analyse ranks instead of full numerical information.

What type of independent variable is used in the Kruskal–Wallis test?

A categorical independent variable with three or more independent groups.

What type of dependent variable is used in the Kruskal–Wallis test?

Ordinal or continuous data that do not meet parametric assumptions.

What type of design is analysed using the Friedman test?

A repeated-measures design with three or more related conditions.

What is the null hypothesis of the Kruskal–Wallis test?

The distributions of scores are equal across all groups.

What is the alternative hypothesis of the Kruskal–Wallis test?

At least one group differs from the others.

What is the null hypothesis of the Friedman test?

The distributions of scores are equal across conditions.

What is the alternative hypothesis of the Friedman test?

At least one condition differs from the others.

What test statistic is produced by the Kruskal–Wallis test?

The H statistic.

What does a large H statistic suggest?

The ranks differ substantially between groups.

What test statistic is produced by the Friedman test?

The chi-square (χ²) statistic based on ranked data.

What does a significant Friedman test indicate?

At least one condition differs from the others.

Why are post-hoc tests needed after significant non-parametric ANOVA results?

Because the omnibus test only indicates that a difference exists, not which groups differ.

What type of post-hoc comparisons are used after Kruskal–Wallis?

Pairwise comparisons between groups with adjusted significance levels.

Why must multiple comparison corrections be applied in post-hoc tests?

To reduce the risk of Type I error when making multiple comparisons.

What is Type I error?

Incorrectly rejecting a true null hypothesis (false positive).

What is the main advantage of non-parametric tests?

They are robust to violations of distributional assumptions.

What is the main limitation of non-parametric tests?

They provide less statistical power when parametric assumptions are satisfied.

What does robustness mean in statistics?

A test’s ability to produce reliable results even when assumptions are violated.

What determines whether a researcher should use parametric or non-parametric tests?

The level of measurement and whether statistical assumptions are met.

Why are ranks useful when data contain extreme outliers?

Outliers only affect rank position rather than the magnitude of values.

What is the key conceptual difference between ANOVA and Kruskal–Wallis?

ANOVA compares means, while Kruskal–Wallis compares ranked distributions.

What is the key conceptual difference between repeated-measures ANOVA and the Friedman test?

Repeated-measures ANOVA compares means, while Friedman compares ranked scores across conditions.