Normality Tests in SPSS: 5 Steps, Shapiro-Wilk, Skewness

Q: Do I test normality for every questionnaire item?

No. Single items on a 1-to-5 format are ordinal and are not expected to be normal. Run normality tests in SPSS on the scale scores that will enter the t-tests, ANOVAs, correlations and regressions.

Q: Is Shapiro-Wilk available for large samples in SPSS?

Yes. SPSS computes it in Explore for samples from 3 cases up to an upper limit of several thousand that depends on the version, so it appears for almost every thesis sample. In very large samples it is significant almost by construction, and the indices and plots carry the decision.

Q: Does Cronbach's alpha or factor analysis require normal data?

Cronbach's alpha does not. Exploratory factor analysis prefers approximate normality but tolerates moderate departures. Confirmatory factor analysis with maximum likelihood in AMOS does assume multivariate normality; with non-normal data use a Bollen-Stine bootstrap or a robust estimator and say so.

Q: My supervisor insists on t-tests and ANOVA although the data are not normal. What should I do?

Show the evidence. If every group exceeds 30 and the departure is moderate, the parametric tests are justified by robustness; add bootstrap confidence intervals. If the departure is severe or groups are small, present both analyses in an appendix, state which one the conclusions rest on, and keep a written record of the agreed decision.

By the Mastermind PhD team · Last updated: 3 November 2026 · Editorial policy

Is a Kolmogorov-Smirnov p value below .05 enough reason to abandon the t-test and switch to Mann-Whitney? This is the most common question students bring to a statistician after their first SPSS output, and acting on it is one of the most common mistakes. Normality tests in SPSS are one of three sources of evidence, and their meaning changes with sample size: with 400 cases they reject normality for deviations that have no effect on a t-test, and with 20 cases they miss deviations that do.

This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.

This guide explains which variable you should be testing in the first place, how Shapiro-Wilk differs from Kolmogorov-Smirnov, how to read skewness and kurtosis at different sample sizes, the exact steps for running normality tests in SPSS, the five accepted responses when the assumption fails, and how to report the check in your thesis.

What is a normality test? A normality test checks whether the values of a variable are distributed approximately like the symmetric, bell-shaped normal distribution. Parametric tests such as the t-test, ANOVA, Pearson correlation and linear regression assume this for the dependent variable within each group, or for the residuals of the model. The check combines formal tests (Shapiro-Wilk, Kolmogorov-Smirnov with the Lilliefors correction), numerical indices (skewness and kurtosis with their standard errors) and plots (histogram with normal curve, normal Q-Q plot).

normality tests in SPSS: What is a normality test? — In short – the Mastermind PhD team

Table of Contents

Which variable do you actually test?

The first error with normality tests in SPSS is testing every variable in the file, including single questionnaire items and demographic codes. The assumption concerns:

The dependent variable within each group for the independent t-test and one-way ANOVA (burnout scores for women, then for men), not the dependent variable as a whole.
The residuals in linear regression, not the predictors and not the outcome on its own.
The differences between the two measurements in a paired t-test, not each measurement separately.
Scale scores entering a Pearson correlation. Single Likert items are ordinal and are not expected to be normal.

Field (2018) notes that in large samples the sampling distribution of the mean tends toward normality whatever the shape of the data (the central limit theorem), which is why a group size of about 30 is often quoted as the point at which parametric tests become robust to moderate non-normality.

Shapiro-Wilk or Kolmogorov-Smirnov?

Among normality tests in SPSS, both appear in the Tests of Normality table produced by Explore. They are not equivalent.

Criterion	Kolmogorov-Smirnov (Lilliefors correction)	Shapiro-Wilk
Statistical power	Lower; misses real departures more often	Highest of the common tests across distributions and sample sizes (Razali & Wah, 2011)
Sample size	Traditionally quoted for larger samples	Designed for small and medium samples; SPSS computes it in Explore for samples from 3 cases up to several thousand, depending on version
Behavior in large samples	Rejects normality for trivial departures	Also rejects normality for trivial departures
What to report	Report it if your faculty expects it	Report it as the primary test, with skewness, kurtosis and plots

Two versions of Kolmogorov-Smirnov exist among the normality tests in SPSS. The one in Explore applies the Lilliefors correction, which is appropriate when the mean and standard deviation are estimated from the sample; this is the one to report. The one-sample K-S test under Nonparametric Tests assumes the population parameters are known and returns p values that are too large.

📱 Ask a statistician about your data — Send a short description of your instrument and sample size on WhatsApp and get a suitable analysis plan. Every analysis comes with the raw SPSS file and a results report.

Skewness and kurtosis: the numbers that matter in large samples

Because formal tests become oversensitive as the sample grows, the methodological literature relies on skewness and kurtosis. SPSS reports both with their standard errors; dividing the statistic by its standard error gives a z score.

Sample size	Rule	Source
Below 50	z for skewness and for kurtosis within ±1.96	Kim (2013)
50 to 300	z within ±3.29	Kim (2013)
Above 300	Absolute skewness below 2 and absolute kurtosis below 7	Kim (2013), citing West, Finch and Curran (1995)
Common shortcut	Skewness and kurtosis between −2 and +2 acceptable; ±1 as a stricter convention	George and Mallery (2010)

State the rule you adopt and its source in the methodology chapter, then apply it to every variable. Complete the normality tests in SPSS with plots: a histogram with the normal curve superimposed, and a normal Q-Q plot in which the points fall close to the diagonal when the distribution is acceptable.

How do you run normality tests in SPSS?

Analyze, then Descriptive Statistics, then Explore.
Move the dependent variable to Dependent List. If the planned test is a t-test or ANOVA, move the grouping variable to Factor List so that the output is split by group.
Click Plots, tick Normality plots with tests and Histogram, and untick Stem-and-leaf if you do not need it.
Under Statistics make sure Descriptives is ticked; this produces skewness and kurtosis with their standard errors.
Click OK and read, in this order: the Descriptives table (skewness, kurtosis), the Tests of Normality table (Shapiro-Wilk, Kolmogorov-Smirnov), the histogram and the Normal Q-Q plot.

For regression, normality tests in SPSS are run on the residuals: run the model first and save the standardized residuals (Save, then Standardized under Residuals). SPSS creates a variable named ZRE_1; examine it with the same Explore steps and add the normal probability plot from the regression Plots dialog.

normality tests in SPSS: what this guide covers - Which variable do you actually test?، Shapiro-Wilk or Kolmogorov-Smirnov?، Skewness and kurtosis: th — What this guide covers – the Mastermind PhD team

How do you decide? The two-out-of-three rule

Treat the distribution as acceptable when two of three conditions hold: (1) skewness and kurtosis are within the adopted threshold, (2) the histogram and Q-Q plot show no marked asymmetry, heavy tails or second peak, and (3) Shapiro-Wilk is not significant. With more than about 100 cases, give the first two conditions more weight than the third, and say so in the text with a citation. The purpose of normality tests in SPSS is to decide whether the planned parametric test will give trustworthy p values, not to prove that the data are perfectly normal; no real data set is.

What do you do if normality fails? Five responses in order

Check for outliers and data-entry errors first. A value of 55 among scores from 1 to 5 destroys any distribution. The histogram and boxplot reveal it; correct the entry, or document the exclusion with an explicit criterion such as a standardized score beyond ±3.29.
Rely on robustness when the departure is moderate and the groups are large. Report the indices and plots, cite the robustness argument, and use the parametric test, with Welch’s correction if variances differ.
Use the non-parametric alternative. Mann-Whitney U instead of the independent t-test, Wilcoxon signed-rank instead of the paired t-test, Kruskal-Wallis instead of one-way ANOVA, Spearman instead of Pearson. This is the response examiners accept most readily because it requires the least argument.
Transform the variable. A logarithm or square root for positive skew, a square for negative skew. Suitable for genuine ratio variables such as income or response time, not for Likert scale means, and the results must then be interpreted on the transformed scale or converted back.
Bootstrap. Available in most SPSS procedures through the Bootstrap button, it estimates confidence intervals without the normality assumption and is accepted in current journals.

When normality tests in SPSS fail, choose one response per variable and document it. Do not run both the parametric and the non-parametric test and keep whichever supports your hypothesis; examiners recognize this as selective reporting.

Worked example: two contrasting cases

Case 1. Burnout scores of 180 teachers. Shapiro-Wilk W = .981, p = .012, which rejects normality. Skewness = −0.52 (SE = 0.18, z = −2.9) and kurtosis = 0.38 (SE = 0.36, z = 1.1), both within the ±3.29 rule for samples between 50 and 300. The histogram is close to bell-shaped with a slight tail to the left, and the Q-Q points sit on the diagonal. Decision: normality is acceptable on two of three criteria and the sample exceeds 100, so the independent t-test is used, with a note that the significant test reflects sample size.

Case 2. Burnout scores of 22 school principals. Shapiro-Wilk p = .003, skewness = 1.86 (SE = 0.49, z = 3.8, beyond ±1.96 for a sample under 50), and the histogram shows scores piled at the low end with a long right tail. Decision: the distribution is not normal and the sample is small, so principals are compared with other groups using Mann-Whitney U, and medians are reported.

In both cases the normality tests in SPSS were significant. What separated the decisions was sample size, the indices and the plots, and that is what the results chapter has to show.

How do you report the normality check in your thesis?

A model sentence when the assumption holds: “Normality of the job satisfaction scores was assessed within each group. Shapiro-Wilk tests were non-significant for men (W = .987, p = .21) and women (W = .990, p = .34); skewness ranged from −0.42 to 0.37 and kurtosis from −0.61 to 0.55, within the ±1 convention, and normal Q-Q plots showed points close to the diagonal. Parametric tests were therefore retained.”

When it fails: “… skewness of 1.86 (z = 3.8) and a right-skewed histogram indicated marked non-normality in the small principal group (n = 22), so the Mann-Whitney U test was used in place of the independent t-test.”

Place the full table of tests in the results chapter before the hypothesis tests, or in an appendix with a cross-reference.

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Frequently asked questions

Kolmogorov-Smirnov gives p = .000 with 450 cases. Must I switch to non-parametric tests?

Not necessarily. First, write *p* < .001, never .000. Second, with 450 cases the test rejects normality for trivial departures. Check skewness and kurtosis against the rule for samples above 300 (absolute skewness below 2, kurtosis below 7) and look at the histogram; if they are acceptable, parametric tests are defensible with a citation.

Do I test normality for every questionnaire item?