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

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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.

Summary

• 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