wk5 IRM - nonparametric data test

Nonparametric alternatives in IRM: Spearman correlation and Wilcoxon test

• • Use non-parametric test when normality assumptions are violated (e.g., data are not normal or there are outliers you don’t want to remove).

  • Parametric tests generally have more statistical power, but nonparametric tests are important when assumptions don’t hold.

  • Nonparametric tests have very few or sometimes no assumptions, making them very flexible.

Spearman correlation

• Spearman correlation is an alternative to Pearson when data is nonparametric

  • Spearman is denoted as $r_s$ or rho (p)

  • Assumptions for spearman correlations are:

  • At least one variable needs to be continuous; the other can be continuous or dichotomous.

  • The relationship between the two variables should be monotonic, not necessarily linear.

    • Monotonic means the relationship consistently increases or decreases

    • It can plateau; the rate of incline/decline can change but the trend must be consistently up or down.

    • Visualize monotonicity with a scatter plot
      

      

• What Spearman measures

  • It assesses the strength of a monotonic relationship between two variables.

  • Pearson correlation looks at the actual values of your data and measures a straight-line (linear) relationship.

  • Spearman correlation ignores the exact values and instead looks at the order or rank of the data — who’s first, second, third, etc. — and measures if the order is consistent between the two variables.

  • The coefficient can be interpreted using the same qualitative cutoffs as Pearson
    

    

  • It is an effect size measure, report just $r_s$ and a p-value

  • e.g. $r_s$ (38) = .34, p = .009

    

Wilcoxon tests (nonparametric alternative to t-tests)

• Wilcoxon test comes in two forms, one-sample(within-subjects) and two-sample(between-subjects)

  • Wilcoxon tests can handle any type of dependent variable data in two-group comparisons when assumptions of parametric tests are not met

  • The Wilcoxon test for two groups is often referred to as the Mann–Whitney U Wilcoxon test.

  • Wilcoxon test statistic is denoted by W in reporting;
    note that there is also a Shapiro–Wilk statistic denoted W in a different test, so be careful with context: "W" from Wilcoxon test vs "W" from Shapiro–Wilk test.

• Reporting examples

  • w = 110, \, p < 0.001.

    

• Quick mental model

  • Spearman: ranks data, tests monotonic association, robust to nonnormality.

  • Wilcoxon: compares distributions between two independent groups without assuming normality; provides a test statistic and p-value to determine if groups differ.