MANN-WHITNEY U TEST

MANN-WHITNEY U TEST

  • Use when assumptions of independent two-sample t-test are violated (e.g., non-normal distribution).

  • Results: group rank differences instead of group mean differences.

STEPS FOR CARRYING OUT MANN-WHITNEY

  • Define hypotheses:

    • Null (Ho): No difference between groups.

    • Alternative (H1): Some difference exists.

  • Check assumptions.

  • Compare medians of two groups.

  • Calculate:

    • t-statistic & effect size

    • Mean ranks

    • U value

    • z value

    • p-value

  • Interpret results.

HYPOTHESES

  • Null Hypothesis: Ho: No difference between treatment and control.

  • Alternative Hypothesis: H1: Some difference between treatment and control.

DATASET OVERVIEW

  • Treatment (Yoga) Group: n = 16

  • Control Group: n = 16

  • Number of Prison Incidents recorded for both groups.

ASSUMPTIONS

  • Data violated normality assumptions for t-test.

  • Presence of extreme outliers.

MEDIAN AND DESCRIPTIVE STATISTICS

  • Treatment Median = 2, Control Median = 3

  • Treatment Mean = 3.625, Control Mean = 5.125

  • Sample Variance for Treatment = 16.25, Control = 39.32

CALCULATING MANN-WHITNEY

  • Use external tools (e.g., Mann-Whitney U Test Calculator) for calculations.

RESULTS SUMMARY

  • U-value = 114, Z-Score = -0.5088, p-value = 0.610

  • No significant difference found (U = 114, z = -0.51, p = .610).

  • If significant, include effect size with the statement.

EFFECT SIZE

  • Formula: r = z/√n

  • Interpret effect size:

    • r < 0.3: small effect

    • 0.3 ≤ r < 0.5: medium effect

    • r ≥ 0.5: large effect

WRITING UP RESULTS

  • Example format:

    • "A Mann-Whitney U test was conducted to examine differences in prison incidents…"

    • Include effect size if significant.