Quick Answer
How should you test normality in SPSS?
Use more than one piece of evidence. Inspect histograms and Q-Q plots, review skewness and kurtosis where relevant, and consider a formal test such as Shapiro-Wilk. Interpret all of these in relation to sample size and the assumptions of the specific statistical method you plan to use.
Why Normality Checks Matter
Many statistical procedures involve normality assumptions, but the exact assumption differs by test. For example, in linear regression the normality concern is usually about model residuals rather than requiring every raw predictor to be perfectly normal.
Before running a “normality test,” identify what actually needs to be approximately normal for your planned analysis. Testing the wrong variable can lead to unnecessary transformations or inappropriate changes in method.
Start With Visual Checks
| SPSS output | What to look for | Limitation |
|---|---|---|
| Histogram | Overall shape, skewness, multiple peaks and extreme tails | Bin choices can change appearance |
| Q-Q plot | Whether points roughly follow the reference line | Minor deviations are common, especially in tails |
| Boxplot | Extreme observations and asymmetry | Shows outliers but not the full distribution shape |
Visual inspection is especially useful because formal tests can become sensitive to very small departures from normality in large samples.
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How to Interpret Shapiro-Wilk
The Shapiro-Wilk test evaluates a null hypothesis that the data follow a normal distribution. A small p-value indicates evidence against that null model. However, the result should not be interpreted in isolation.
With a large sample, a statistically significant result can occur for a small departure that may not seriously affect the planned analysis. With a small sample, the test may have limited ability to detect non-normality. Combine it with plots, skewness, kurtosis and robustness of the intended test.
Use Skewness and Kurtosis as Descriptive Clues
Skewness describes asymmetry, while kurtosis relates to shape and tail behaviour. Values further from zero can signal departure from a normal shape, but there is no single cutoff suitable for every study.
Use conventions required by your discipline or supervisor and state them if they influence a decision. Do not declare data “normal” simply because values fall inside a memorised range.
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For Regression, Check Residuals Rather Than Only Raw Variables
In multiple linear regression, examine the residuals from the fitted model. A histogram or Q-Q plot of residuals can help assess whether the error distribution is approximately normal. You should also check linearity, homoscedasticity, independence and influential observations where relevant.
A predictor can be skewed while model residuals are still reasonably behaved. This is why assumption checking should match the statistical model rather than follow a generic checklist.
What Should You Do If Data Are Not Normal?
First determine whether the departure is severe enough to matter for the chosen analysis. Check whether one or two errors or extreme observations are creating the problem. Then consider robust methods, transformations or non-parametric alternatives only when they fit the research question and methodology.
Never remove valid cases merely to make a p-value non-significant. Any transformation or exclusion should have a clear statistical and substantive reason and should be documented.
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How to Write Normality Results
Report the evidence you actually used. A concise section might state that histograms and Q-Q plots were inspected and that a formal test was also reviewed. If the distribution was moderately skewed but the chosen analysis was considered robust for the sample, explain that reasoning rather than claiming perfect normality.
If assumption checks lead you to change the analysis, state what changed and why. Transparency is more useful than presenting a binary “normal/not normal” label with no context.
Common Normality Testing Mistakes
- Using only Shapiro-Wilk and ignoring sample size and plots.
- Testing every variable when the model assumption concerns residuals.
- Deleting outliers simply to obtain p > .05.
- Treating non-significant Shapiro-Wilk as proof of perfect normality.
- Using rigid skewness and kurtosis cutoffs without disciplinary justification.
- Changing to a non-parametric test automatically after any significant normality test.
Instead of applying one mechanical rule, combine statistical evidence with the robustness of the planned test and explain why the chosen analysis remains appropriate for the observed distribution.
Normality diagnostics behave differently across sample sizes. Formal tests can be overly sensitive in large datasets and underpowered in small ones, while plots can be difficult to judge with only a few observations.
Remember That Sample Size Changes the Evidence
Key Takeaways
- Identify the exact normality assumption for your planned analysis.
- Combine plots with numerical and formal checks.
- Interpret Shapiro-Wilk in light of sample size.
- For regression, focus on residual diagnostics.
- Do not remove valid cases simply to achieve a desired result.
- Report the evidence and reasoning behind your decision.
