Parametric vs nonparametric tests

Parametric tests assume your data follow a known distribution, usually the normal distribution, and they work with the mean and variance. Nonparametric tests make no such distributional assumption and typically work with ranks or the median instead. The choice between them in your dissertation comes down to whether your data meet the parametric assumptions, not to personal preference.

Why the choice matters for your dissertation results

Picking the wrong family weakens every claim that follows. A parametric test applied to badly skewed data can return a p-value you cannot trust, while a nonparametric test used when assumptions are met throws away statistical power you paid for in recruitment. Examiners read your methods chapterlooking for a justified decision, so you need to state which assumptions you checked and what the checks showed. The honest path is to test the assumptions first, then let the result of those checks decide the family, which is exactly the logic behind picking the right statistical test.

The assumptions that separate the two families

Parametric methods rest on a short list of conditions. The outcome should be measured on an interval or ratio scale, the residuals should be roughly normally distributed, the groups should show similar spread (homogeneity of variance), and the observations should be independent. When these hold, parametric tests are more efficient and detect real effects with smaller samples. When they fail, especially with small sample sizes or strong skew, the nonparametric alternative protects your conclusions. Confirm normality properly before you commit, as set out in checking your data for normality.

How to decide on your own data, step by step

Work through the decision in order rather than guessing. First, identify the measurement level of your outcome; if it is ordinal or clearly not continuous, you are already in nonparametric territory. Second, check the distribution shape with a histogram and a normality test, and check equal variances with Levene's test. Third, weigh your sample size, since very small samples make normality hard to confirm and tilt the choice toward rank-based methods. If the assumptions hold, run the parametric test for its greater power; if they do not, move to the matched nonparametric counterpart from the table above. This same reasoning extends to comparing several groups, where the contrast between an t-test and analysis of variance shapes which family you reach for.

When to use non-parametric tests

Move to a nonparametric test in four recurring situations. The first is when your outcome is ordinal, such as a single Likert item or a ranked preference, where means are not meaningful in the first place; the wider treatment of rating data is in analysing Likert-scale responses. The second is a small sample size, roughly under thirty per group, where normality cannot be established with any confidence. The third is clear skew or heavy tails that a transformation will not fix, and the fourth is the presence of stubborn outliers that the median tolerates but the mean does not. In each case the rank-based method trades a little power for results you can actually defend. What you should not do is choose nonparametric out of habit when the assumptions hold, since that discards power you funded through recruitment, the same trade-off behind sample size and power planning.

Common non-parametric test alternatives

Each parametric test has a recognised rank-based counterpart, and naming the right one is half the battle in your methods chapter. The Mann-Whitney U test replaces the independent-samples t-test for two unrelated groups, comparing the distribution of ranks rather than the means. The Wilcoxon signed-rank test stands in for the paired t-test when the same people are measured twice. For three or more independent groups the Kruskal-Wallis test takes the place of a one-way analysis of variance, and Friedman's test is the repeated-measures equivalent when the same participants pass through several conditions, paralleling a within-subjects ANOVA.

For associations, Spearman's rho replaces Pearson's correlation when the relationship is monotonic but not linear, or when the variables are ordinal. A significant Kruskal-Wallis or Friedman result still needs follow-up comparisons with a corrected alpha, just as an ANOVA does, so the reporting discipline does not relax simply because the test is rank-based. You can sanity-check the parametric versions of these comparisons in the browser with the t-test calculator before deciding whether the assumptions push you toward the nonparametric route.

Reporting the decision in your write-up

Whichever family you use, the write-up should make the logic visible. State the assumption checks and their outcomes, name the test, and report the result with an effect size rather than a bare significance verdict. Nonparametric results are still summarised with clear descriptive statistics, typically medians and interquartile ranges, so the reader sees the data behind the test; for the wider picture of summary versus inference, see summarising versus generalising from your sample. A clean, justified test choice tells your supervisor you understood the data, not just the software.