METHOD GUIDE
Normality Test in SPSS
What the Tests Can and Cannot Tell You
A normality test in SPSS comes with two Q-Q plots and two formal tests, and in a large sample the tests flag departures that do not matter while in a small one they miss those that do. Plots lead, the tests follow, and the response is planned.
IN SHORT
What a Normality Check Is For and What It Is Not
A normality test asks whether a sample is compatible with a normal distribution, and it is a diagnostic, not a hurdle that has to be passed. What matters for a t-test, ANOVA or regression is the distribution of the difference scores, the residuals or the group outcomes, and not the raw variable pooled over groups. To run a normality test in SPSS, open Analyze, Descriptive Statistics, Explore, place the variable under Dependent List (and a grouping variable under Factor List), and under Plots tick Normality plots with tests. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
A normality check is only a step before the choice of test. That choice is made across the whole family of comparisons, and Mann-Whitney U Test is the rank-based option where an ordinal outcome or the research question calls for it.
Comparative & Hypothesis Testing
The family of group comparisons, where the choice between a mean-based test, a robust version and a rank-based test is made from the design and the question, not from a normality p-value.
Independent Samples t-Test
The comparison of two group means with Welch's version, an assessment of shape and outliers in each group, and the effect size reported with its interval.
BEFORE YOU RUN IT
Deciding What Needs to Be Normal
A normality test applied to the wrong quantity answers the wrong question, so four decisions are made before any p-value is requested.
The Right Quantity For a paired t-test the differences matter, for ANOVA and regression the residuals matter, and for a t-test the outcome within each group. Pooled raw scores can look skewed simply because groups differ.
Sample Size Small samples give tests with little power, and large ones flag departures too small to matter. In neither case is the p-value a verdict, so shape is judged from plots and the tests follow.
Robustness of the Method Means tolerate mild skew in moderate and large samples, but outliers and heavy tails in small groups are a real concern. How sensitive the method is to the departure matters more than a yes or no.
Plan for Departures Decide in advance what a clear departure would lead to: a robust or Welch procedure, a transformation, a bootstrap check or a model suited to the outcome. A rank test is one option, not the automatic one.
IN SPSS
How to Run a Normality Test in SPSS
The outline is for IBM SPSS. The same Explore dialog serves scores per group, difference scores and saved residuals, which is why the quantity is chosen first.
- Decide which quantity to check: scores per group, paired differences or model residuals, and compute or save it first.
- Open Analyze, Descriptive Statistics, Explore, and place that variable under Dependent List.
- Put the grouping variable under Factor List when the check should be done within each group.
- Under Plots, tick Normality plots with tests and a histogram, and keep the descriptives for skewness and kurtosis.
- Read the Q-Q plots and histograms first, then skewness and kurtosis with their standard errors, then the Tests of Normality table.
- Record what the plots showed, the sample size and the response that followed.
READING THE OUTPUT
Reading the Tests of Normality Table and the Plots Beside It
Q-Q plots in SPSS and the histogram carry more information than the p-values in the Tests of Normality table, so they are read first and the table last.
| Output element | What it tells you | What to check |
|---|---|---|
| Case Processing Summary | The valid and missing cases for each variable or group | That the N per group is seen, since the power of every test depends on it |
| Descriptives: Skewness and Kurtosis | The asymmetry and tail weight of the distribution, each with a standard error | That the values are read as descriptions with their standard errors, not as a pass or fail rule |
| Tests of Normality: Kolmogorov-Smirnov (Lilliefors Significance Correction) | A test against a normal curve with mean and spread estimated from the data | That it is not preferred to Shapiro-Wilk, which usually has more power in small and moderate samples |
| Tests of Normality: Shapiro-Wilk | A test of the sample’s compatibility with a normal distribution | That a small p-value is read with the sample size, since large samples reject trivial departures |
| Normal Q-Q Plot | Observed quantiles against those expected under normality | That points follow the line, and where they leave it, in the tails or the middle, and by how much |
| Detrended Normal Q-Q Plot | The distance of each point from the line, magnified | Whether the pattern of departure looks systematic or like random scatter |
| Histogram and Boxplot | The shape, skew and individual extreme values | That extreme values are checked for entry errors before any decision about the method |
REPORTING
Writing Up a Normality Assessment Honestly
A short note in the methods section is enough, and the frame below has blanks to be filled from your own output.
State what was checked (scores per group, paired differences or model residuals), the sample size, and the evidence used: Q-Q plots and histograms, skewness and kurtosis and, if reported, the Shapiro-Wilk statistic as W(df) = ___, p = ___. Describe what the plots showed in words, such as mild right skew without extreme values, and say what response followed and why: the method kept, a robust or Welch procedure, a transformation or a different model. Avoid wording such as the data were normal. Write that no clear departure was seen, because a test cannot show that data are normal. Where a sensitivity analysis used another method, report both results.
COMMON MISTAKES
Normality Checks That Point to the Wrong Method
These errors lead to a wrong choice of method more often than the output itself does, and the first three concern what a p-value is taken to mean.
Failed Test, Automatic Rank Test A small p-value in the normality table does not require a rank-based test. Many methods tolerate the departure, and a Welch or robust procedure, a transformation or a better-suited model are options.
Passed Test Read as Proof A large p-value shows only that the test found no departure at this sample size. With few cases the test has little power, so a clear plot matters more than the number beside it.
Large Sample Rejected for Nothing With hundreds of cases the tests flag departures too small to affect the analysis. The size and shape of the departure is judged from the plot, not from the p-value alone.
Whole Variable Instead of Residuals Testing the pooled outcome ignores what the model assumes. Residuals for a regression or ANOVA, differences for paired data and each group for a t-test are the quantities to check.
Outliers Mistaken for Skew A single extreme value can fail the test while the rest of the data look normal. Check it for an entry error or a different population before choosing a method for the whole sample.
Checks Repeated Until One Passes Running several tests, transformations and subsets until one gives a large p-value is an undeclared analytic path. Plan the check, report what was done and keep the first assessment.
Already run this analysis? Independent Statistical Review checks which quantity was tested, the response to any departure and the wording before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About Normality Output
Choosing between Shapiro-Wilk and Kolmogorov-Smirnov, a large sample that fails despite a clean plot and the response to a real departure are the questions this output raises, along with a review of the data shape.
Should I use the Shapiro-Wilk test in SPSS or the Kolmogorov-Smirnov test?
Shapiro-Wilk usually has more power than the Lilliefors-corrected Kolmogorov-Smirnov test in small and moderate samples, and it is the one most often reported. Either way, the p-value supplements the plots and is never a rule. Report the plots and the descriptives with it, and name the sample size, because both tests depend on it.
Why does my large sample fail the normality test when the plot looks fine?
Tests gain power as the sample grows, so they detect departures too small to affect the analysis. In a large sample the Q-Q plot, the size of the skew and the robustness of the planned method decide, and a significant test alone is not a reason to change the method. A small sample shows the opposite problem, a clear departure with a large p-value.
What should I do if the Q-Q plot shows a real departure?
Match the response to the method and the kind of departure. Mild skew in moderate samples often needs no change, perhaps with a sensitivity analysis. Strong skew or outliers in small groups point to a Welch or robust procedure, a transformation or a model suited to the outcome. A bootstrap interval can serve as a check, though it does not rescue very small samples. A rank test fits an ordinal outcome or a question about distributions.
Can a statistician judge the shape of my data and the response?
Yes. An in-house PhD-level statistician can examine the plots and output for the quantity your method makes its assumption about, recommend a response that fits your design, and carry out the analysis or review one you have run. For the tables and the wording alone, Results Reporting & Interpretation covers that stage. The interpretation remains yours.
How do you protect my research data and confidentiality?
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What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
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