Before running most parametric tests (t-tests, ANOVA, Pearson correlation, regression), you need to check whether your data is approximately normally distributed. If it is not, you need to use a non-parametric alternative. This is called assumption testing, and your supervisor will expect to see it in your Chapter 4.
What is normality?
A normal distribution is the classic bell curve — symmetrical, with most values clustering around the mean and fewer values at the extremes. Many parametric tests assume your data follows this pattern.
In practice, data never follows a perfect normal distribution. The question is whether the deviation is large enough to matter. That is what normality tests assess.
The Shapiro-Wilk test
The Shapiro-Wilk test is the standard normality test for small to medium samples (n up to 50). It is more powerful than the older Kolmogorov-Smirnov test for detecting non-normality.
Null hypothesis (H0): The data is normally distributed
Alternative hypothesis (H1): The data is NOT normally distributed
If p > .05: fail to reject H0 — normality is not significantly violated, proceed with parametric test.
If p < .05: reject H0 — normality is violated, consider non-parametric alternative.
When to use Kolmogorov-Smirnov instead
For larger samples (n > 50), use the Kolmogorov-Smirnov test. ResearchScope automatically selects the appropriate test based on your sample size.
How to report normality in APA format
"Normality was assessed using the Shapiro-Wilk test. Results indicated that the assumption of normality was met for job satisfaction, W = .971, p = .142, and work performance, W = .963, p = .081."
When normality is violated: "The Shapiro-Wilk test revealed a significant departure from normality for the variable anxiety, W = .821, p = .003. Accordingly, the non-parametric Mann-Whitney U test was used in place of the independent samples t-test."
The Q-Q plot
Alongside the numerical test, use a Q-Q (quantile-quantile) plot for visual confirmation. A Q-Q plot shows your sample data quantiles against theoretical normal quantiles. If points fall on or near the diagonal line, your data is approximately normal. Deviations from the line indicate non-normality.
What to do when normality is violated
| Parametric test | Non-parametric alternative |
|---|---|
| Independent t-test | Mann-Whitney U |
| Paired t-test | Wilcoxon signed-rank |
| One-way ANOVA | Kruskal-Wallis |
| Pearson r | Spearman rho |
ResearchScope applies these alternatives automatically. When normality is violated, it switches to the non-parametric test and notes the reason in plain English — for example: "Normality was violated (W = .821, p = .003). Mann-Whitney U was used instead of the independent samples t-test."
Skewness and kurtosis as supplementary checks
Beyond the formal test, check your skewness and kurtosis values. Values outside ±2 for skewness or ±7 for kurtosis generally indicate meaningful departures from normality. ResearchScope reports both in the descriptive statistics table.