How to Test Normality in SPSS: A Step-by-Step Guide

Before you run a t-test, ANOVA, or Pearson correlation, you need to know how to test normality in SPSS. Many parametric procedures rest on a normality assumption, but the assumption does not always apply to your raw scores: what exactly needs to be normal depends on the analysis you plan to run. This guide explains what the assumption really covers, shows you the two built-in normality tests in SPSS, where to click, how to read the output, and what to do if the assumption is not met.

Why Check Normality Before Running Parametric Tests in SPSS

Normality means scores cluster symmetrically around the mean and taper off evenly on both sides, forming the familiar bell curve. But "the data must be normal" is too simple, and it is worth being precise about what each procedure actually assumes:

Independent-samples t-test: the assumption concerns the distribution of scores within each group. It matters most when group sizes are small; with larger, balanced samples the test is fairly robust to moderate departures.
ANOVA and linear regression: for conventional significance testing, normality applies to the model errors (residuals), not to the raw variables themselves. A predictor does not need to be normally distributed, and neither does the outcome variable on its own.
Pearson correlation: the significance test assumes bivariate normality, but in practice linearity and the absence of extreme outliers usually matter more.

So before testing anything, identify which assumption your planned analysis actually makes. Checking takes about two minutes in SPSS, so there is no reason to skip it, but check the right thing.

Shapiro-Wilk vs Kolmogorov-Smirnov: Which Normality Test to Use in SPSS

SPSS gives you two tests of normality side by side: Shapiro-Wilk and Kolmogorov-Smirnov. Here is how they differ:

Shapiro-Wilk: Generally the more powerful test for detecting departures from normality. Razali and Wah (2011), in a large simulation study comparing four normality tests, found that Shapiro-Wilk had the highest statistical power across the conditions they examined.
Kolmogorov-Smirnov: A general-purpose test that works at any sample size but is less sensitive than Shapiro-Wilk, particularly to deviations in the tails of the distribution. In the SPSS Explore procedure, it is reported with the Lilliefors significance correction (you will see this footnote under the table).

You will often see a rule that says: read Shapiro-Wilk when n is 50 or smaller and Kolmogorov-Smirnov when n is larger than 50 (this convention appears in university SPSS guides such as Newcastle University's statistics FAQ). Treat this as a teaching convention, not a statistical requirement. The "50" traces back to the original Shapiro and Wilk (1965) paper, whose tables covered samples up to 50; modern software is not bound by it, and SPSS computes Shapiro-Wilk for samples far larger than 50. Because Shapiro-Wilk is the most powerful of the common tests (Razali & Wah, 2011), many researchers use it at any sample size. The better practice is to interpret whichever test you report alongside a histogram, a Q-Q plot, your sample size, and the analysis you are planning. One caution at the other extreme: Kim (2013) warns that formal normality tests become unreliable for very large samples (n > 300), because trivial departures get flagged as statistically significant even when the data look approximately normal.

How to Run a Normality Test in SPSS: Step by Step

Follow these steps:

Click Analyze → Descriptive Statistics → Explore…
Move the continuous variable you want to test into the Dependent List box. (If you want to test normality separately for each group of a categorical variable, move that variable into the Factor List box.)
Click the Plots… button.
Under the Plots section, tick Normality plots with tests. It is also a good idea to tick Histogram under the Descriptive section so you can see the shape of your data.
Click Continue, then OK.

SPSS now produces a Tests of Normality table, descriptives (including skewness and kurtosis), a histogram, and Normal Q-Q plots. If you prefer syntax, the equivalent command is:

EXAMINE VARIABLES=anxiety_score /PLOT HISTOGRAM NPPLOT /STATISTICS DESCRIPTIVES /MISSING LISTWISE.

How to Interpret the Normality Test Output in SPSS

To show what the output looks like, here is a completely illustrative example with made-up numbers (not real study results). Suppose a researcher collected test-anxiety scores from 30 students and wants to check the distribution of scores before running a t-test.

Reading the Tests of Normality table

The table has two rows, one for Kolmogorov-Smirnov and one for Shapiro-Wilk. We read the Shapiro-Wilk row because it is the more powerful test (Razali & Wah, 2011), and this choice is common for small samples like this one. In this hypothetical output, the Shapiro-Wilk statistic W = .962, df = 30, and Sig. (the p-value) = .345.

The rule: if Sig. is greater than .05, you fail to reject the null hypothesis of normality, meaning your data are consistent with a normal distribution. Here, .345 is greater than .05, so we can proceed with the t-test. Important: a non-significant result is not proof that the data are perfectly normal. It only means there is no statistically significant evidence of non-normality.

You will notice a footnote under the table: a. Lilliefors Significance Correction. That correction applies only to the Kolmogorov-Smirnov row, so do not let it confuse you when you read the Shapiro-Wilk result.

Checking skewness, kurtosis, and the Q-Q plot

Do not rely on the significance test alone. In the Descriptives table, look at skewness and kurtosis divided by their standard errors to form z-scores. In our made-up example: skewness = −0.42 with a standard error of 0.427, so z = −0.42 / 0.427 = −0.98; kurtosis = 0.51 with a standard error of 0.833, so z = 0.51 / 0.833 = 0.61.

Kim (2013) suggests the following bands for judging these z-scores: for small samples (n < 50), absolute z-scores below 1.96; for medium samples (50 < n < 300), absolute z-scores below 3.29; and for n > 300, skip z-scores and inspect the histogram plus the absolute values instead, treating skewness above 2 or kurtosis above 7 as reference points for substantial non-normality. Be clear about what these numbers are: approximate guidelines from one author's recommendations, not universal standards. Other textbooks use different conventions (some apply 1.96 or 3.29 regardless of sample size; others judge the raw skewness and kurtosis values directly). Our example (n = 30, |z| = 0.98 and 0.61) sits comfortably within Kim's bands either way. Whatever bands you use, give the plots priority: look at the histogram and the Normal Q-Q plot (points hugging the diagonal line support normality, while systematic curves or S-shapes warn of skew), and weigh everything against your sample size and research context.

What to Do If Your Data Fail the Normality Test in SPSS

If Shapiro-Wilk is significant (Sig. < .05) and your plots confirm real non-normality, you have three standard options, and none of them should be automatic:

Transform the data: a log or square-root transformation can reduce right-skew. But a transformation changes the scale on which your results are interpreted, so it needs a substantive justification, not just a disappointing p-value. Some variables are naturally right-skewed (reaction times and income are classic examples) and are routinely analysed on a transformed scale for that reason. If you transform, say what you did and why, and re-check the distribution afterwards.
Use a non-parametric alternative: these rank-based tests do not assume normality, but they do not test exactly the same thing as their parametric counterparts. Mann-Whitney U, for example, compares the rank distributions of two groups; it can be read as a test of median difference only when the two distributions have similar shapes. Wilcoxon signed-rank (for paired data) and Kruskal-Wallis (for several groups) carry the same caution. Choose the alternative based on your research question, study design, group sizes, outliers, and the shape of your distributions, and report the statistic the test actually produces.
Keep the parametric test anyway: with balanced designs and moderate sample sizes, the t-test and ANOVA are reasonably robust to moderate departures from normality (Kim, 2013). This is a judgment call, and you must be transparent about it when reporting.

How should you report the result in your thesis? Something like this: A Shapiro-Wilk test was conducted to assess the normality of test-anxiety scores. The test was non-significant, W(30) = .96, p = .345, indicating no significant departure from normality.

Frequently Asked Questions

Can I use Shapiro-Wilk with a large sample?

Yes. The old "only up to 50" idea comes from the tables in the original 1965 paper, not from any limit of the test itself, and SPSS computes it for much larger samples. The real caution is the opposite one: with very large samples (n > 300), Shapiro-Wilk can flag tiny, harmless departures as significant (Kim, 2013), so give the histogram and Q-Q plot more weight there.

My normality test is significant but my sample is large. What should I do?

Do not panic and do not switch tests automatically. Look at the histogram, Q-Q plot, and skewness and kurtosis values. If the departure is mild, your planned parametric test is usually robust enough, especially with balanced groups; note the violation and your reasoning in your methodology chapter.

Should I test the raw variable or the residuals?

It depends on the analysis. For a t-test, check the scores within each group. For regression and ANOVA models, the normality assumption applies to the residuals, so test those (SPSS can save residuals from the regression procedure for this purpose).

Common Mistakes When Testing Normality in SPSS

Testing a categorical variable. Normality tests only make sense for continuous (scale) variables.
Testing the wrong thing. Running a normality test on a raw predictor before a regression answers the wrong question; the assumption there concerns the residuals.
Treating the n = 50 convention as a law. Shapiro-Wilk is not "for" small samples and Kolmogorov-Smirnov is not "for" large ones; power and your plots should guide you.
Treating p > .05 as proof of normality. It is only an absence of evidence against normality.
Ignoring the plots. The histogram and Q-Q plot often tell you more than a single p-value, especially in large samples where tests are oversensitive.
Switching to a non-parametric test without thinking. Rank-based tests answer a somewhat different question; check that it is the question you actually want answered.

Key Takeaways

First, know what your analysis assumes: within-group distributions for a t-test, residuals for regression and ANOVA.
Run the test via Analyze → Descriptive Statistics → Explore… → Plots… → Normality plots with tests.
Shapiro-Wilk is the more powerful test (Razali & Wah, 2011); the n ≤ 50 / n > 50 split is a teaching convention, not a rule.
Sig. > .05 means no significant departure from normality; support it with skewness/kurtosis (Kim, 2013, as approximate guidelines) and Q-Q plots.
If normality fails, weigh transformations (with a substantive reason), non-parametric alternatives (knowing they test something slightly different), or the robustness of your parametric test.

References

Kim, H.-Y. (2013). Statistical notes for clinical researchers: Assessing normal distribution (2) using skewness and kurtosis. Restorative Dentistry & Endodontics, 38(1), 52–54. https://doi.org/10.5395/rde.2013.38.1.52

Razali, N. M., & Wah, Y. B. (2011). Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. Journal of Statistical Modeling and Analytics, 2(1), 21–33.

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3–4), 591–611. https://doi.org/10.2307/2333709

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