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Non-parametric

Friedman Test — Non-parametric Repeated Measures

Non-parametric alternative to repeated-measures ANOVA. 8 participants rank 3 study techniques by recall; rank sums, chi-square statistic, and Dunn post-hoc comparisons.

📊 χ²(2) = 6.25, p = .044, N = 8
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🔢 31 · Friedman Test — Non-parametric Repeated Measures

Ranking 3 Study Techniques by Word-List Recall
Non-parametric
Research Question: The same 8 participants tried three study techniques — re-reading, practice testing, and spaced practice — and recalled a 20-word list after each. With only 8 participants and a bounded recall score, the repeated-measures ANOVA's normality assumption is shaky, so the Friedman test (its non-parametric counterpart) is used instead.
Participant Re-reading Practice Testing Spaced Practice
1121517
2141618
3101416
4161819
5131517
6171416
7151714
8121517
Friedman's chi-square (N subjects, k conditions, R_j = rank sum of condition j)
χ 2 = 12 N k ( k + 1 ) ∑ j = 1 k R j 2 − 3 N ( k + 1 ) , d f = k − 1
  1. 1
    Rank the 3 scores within each participant (1 = lowest recall): Most participants rank Re-reading lowest and Spaced Practice highest — but participants 6 and 7 break that pattern, which is exactly the kind of noise real data has.
  2. 2
    Sum the ranks per technique:
    R Re-reading = 11 , R Practice Testing = 16 , R Spaced Practice = 21
  3. 3
    χ²:
    χ 2 = 12 8 ( 3 ) ( 4 ) ( 11 2 + 16 2 + 21 2 ) − 3 ( 8 ) ( 4 ) = 0.125 ( 818 ) − 96 = 6.25 , d f = 2
  4. 4
    Decision rule and post-hoc: p = .044 < .05 → reject H₀ → the techniques differ. A Dunn post-hoc test (with Bonferroni-Holm correction) shows Spaced Practice beats Re-reading (p_adj < .001), but the other two pairs are not significant after correction.
6.25
χ²(2)
.044
p
8
N
🔴 Significant — χ²(2) = 6.25, p = .044. Study technique affects recall; Spaced Practice beats Re-reading on post-hoc.
APA-7
A Friedman test showed a significant difference in recall across the three study techniques, χ²(2) = 6.25, p = .044, N = 8. Dunn's post-hoc comparisons indicated that spaced practice produced significantly higher recall than re-reading (p_adj < .001); no other pairwise difference reached significance.

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