Parametric vs non-parametric tests: how to choose (in R)

When to use a t-test vs a Mann–Whitney, ANOVA vs Kruskal–Wallis, Pearson vs Spearman. A clear R example shows when non-parametric tests earn their keep.

“Parametric or non-parametric?” comes up in almost every analysis. The short answer: parametric tests assume a distribution (usually normal); non-parametric tests don’t, trading a little power for robustness. Here’s how to choose, with R. (Not sure which test at all? Try our which-test tool.)

The pairings

Parametric	Non-parametric equivalent
One/two-sample t-test	Wilcoxon signed-rank / Mann–Whitney
One-way ANOVA	Kruskal–Wallis
Pearson correlation	Spearman correlation

Non-parametric tests work on ranks, so they shrug off skew and outliers.

When it matters

On clean, roughly normal data, the two agree closely. The gap opens with skew or outliers:

library(ggplot2)
set.seed(4)
a <- rlnorm(30, 0, 1)         # right-skewed
b <- rlnorm(30, 0.6, 1)

data.frame(value = c(a, b), group = rep(c("A", "B"), each = 30)) |>
  ggplot(aes(group, value, fill = group)) +
  geom_boxplot(alpha = 0.7, show.legend = FALSE) +
  scale_fill_manual(values = c("#2f6fed", "#17a2b8")) +
  labs(title = "Skewed data: means are pulled by the long tail",
       x = NULL, y = "Value") +
  theme_minimal(base_family = "sans") +
  theme(plot.title = element_text(face = "bold", colour = "#1b2a4a"))

Figure 1

t.test(a, b)$p.value          # parametric (compares means)

[1] 0.394317

wilcox.test(a, b)$p.value     # non-parametric (compares ranks)

[1] 0.7191489

Both may agree here, but on heavily skewed data the Wilcoxon test is often the more trustworthy call — the mean isn’t a good summary when the distribution has a long tail.

How to decide

• Roughly normal, no wild outliers, decent n → parametric (more power, familiar effect sizes).
• Skewed, small samples, ordinal data, or clear outliers → non-parametric.
• Check first, don’t guess — see checking normality in R. And remember non-parametric tests answer a slightly different question (ranks/medians, not means).

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