Shapiro-Wilk says your data are not normal. Do you have to switch tests?

Usually not. This is one of the most over-applied rules in applied statistics.

Three things most people get wrong

It is the residuals that must be normal, not your raw data. For t-tests, ANOVA and regression, the assumption is about the residuals. Raw data pooled across groups with genuinely different means will look non-normal even when every assumption holds perfectly.

Shapiro-Wilk is sample-size dependent. With n = 500 it will flag trivial, harmless departures. With n = 15 it will fail to detect serious ones. A significant result on a large sample tells you the deviation is detectable, not that it matters.

t-tests and ANOVA are robust to non-normality. Thanks to the central limit theorem, with reasonable group sizes (roughly 30 or more) these tests perform well even on clearly non-normal data. Unequal variances cause far more trouble than non-normality.

What to look at instead

A Q-Q plot of the residuals. It shows you the shape and size of the departure, which a p-value cannot. Mild curvature at the tails is normal and harmless. A pronounced S-shape or a handful of points far off the line is worth attention.

Skew and outliers specifically. Heavy skew and extreme outliers are what actually damage these tests, not mild departures from normality.

When to switch

Small samples with clear skew, ordinal outcomes, or a handful of extreme outliers you cannot justify removing. Then Mann-Whitney, Wilcoxon, Kruskal-Wallis or Friedman are appropriate. Remember they test a different hypothesis, about distributions and ranks rather than means.

In Plotara

Shapiro-Wilk sits in Diagnostics alongside residual diagnostics and Q-Q plots, so you can look at the shape rather than just the p-value.