When to Use Parametric versus Nonparametric Procedures in Statistics for Social Research

Using parametric procedures in statistics means you can generalize your findings from the sample to the population. You can use parametric procedures when you have a large sample size or when your sample meets certain assumptions about normality. If you have a small sample size or your sample cannot meet assumptions about normaltiy, you can still test your hypotheses with a nonparametric procedure. Using a nonparametric procedure means your findings only apply to the sample, not the population.

Parametric Procedures

  • Assumptions: Require data to follow a specific distribution, typically normal distribution.
  • Examples: t-Test, Pearson correlation.
  • Use When: You have a sufficiently large sample size, and your data meets the assumptions of normality, homogeneity of variances, and linearity.

Nonparametric Procedures

  • Assumptions: Do not require data to follow a specific distribution.
  • Examples: Wilcoxon test, Mann–Whitney U test, Spearman correlation.
  • Use When: Data does not meet the assumptions for parametric tests, with ordinal data, or when dealing with small sample sizes.

t-Test vs Wilcoxon Test vs Mann–Whitney U Test (Quasi-Experimental Hypotheses)

  • t-Test:
    • Use When: Comparing means of two groups.
    • Conditions: Normal distribution, similar variances, interval or ratio scale data.
    • Ideal For: Larger sample sizes.
  • Wilcoxon Test:
    • Use When: Non-normal or ordinal data; paired samples.
    • Conditions: Useful for smaller sample sizes; for matched or paired samples.
    • Ideal For: Situations where t-test assumptions are not met; paired data.
  • Mann–Whitney U Test:
    • Use When: Comparing two independent samples.
    • Conditions: Non-normal data or different sample sizes.
    • Ideal For: Situations similar to the t-test but without the normality assumption; unpaired data.

Pearson vs Spearman Correlation (Correlational Hypotheses)

  • Pearson Correlation:
    • Use When: Evaluating the linear relationship between two continuous, normally distributed variables.
    • Conditions: Variables on interval or ratio scale.
    • Ideal For: Expected linear relationships.
  • Spearman Correlation:
    • Use When: Data is ordinal or not normally distributed.
    • Conditions: Assessing monotonic relationships.
    • Ideal For: Non-linear relationships or data not meeting Pearson’s criteria.


  • Use parametric procedures (t-Test, Pearson) when your data adheres to normal distribution criteria and you have a large sample size.
  • Opt for nonparametric procedures (Wilcoxon for paired samples, Mann–Whitney U for independent samples, Spearman) in small sample sizes, ordinal data, or when parametric assumptions are not satisfied.
  • How to Conduct Normality Tests in PSPP in Statistics for Social Research

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