Shapiro-Wilk Normality Test Calculator
Check whether a variable is normally distributed before choosing a parametric test, with the two tests reviewers ask for and the plots that matter more than either.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
90 rows · example dataTests of normality
| Variable | n | Shapiro-Wilk W | p | K-S D | p | Skewness | z | Kurtosis | z |
|---|---|---|---|---|---|---|---|---|---|
| Hours_Study | 90 | .991 | .810 | .057 | .672 | 0.08 | 0.33 | -0.50 | -1.00 |
Note. K-S uses the Lilliefors correction. A significant result (p < .05) suggests a departure from normality. With large samples, |z| > 3.29 for skewness or kurtosis is a common cut-off.
Normal Q-Q plot
Histogram with normal curve
Interpretation
The Shapiro-Wilk test does not indicate a departure from normality for Hours_Study, W = .991, p = .810. Points close to the diagonal on the Q-Q plot support normality; curves at the ends indicate skew or heavy tails.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Shapiro-Wilk Normality Test Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/shapiro-wilk-test-calculator/
BibTeX
@software{xavier_normalitytest_2026,
author = {Xavier, Bibin},
title = {Shapiro-Wilk Normality Test Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/shapiro-wilk-test-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Shapiro-Wilk Normality Test Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is a normality test?
A normality test checks whether a variable could come from a normal distribution, an assumption of t-tests, ANOVA and Pearson correlation. This calculator runs the Shapiro-Wilk test (Royston’s algorithm, as in R and SPSS) and the Lilliefors-corrected Kolmogorov-Smirnov test, and draws the plots you need to judge the result.
When to use a normality test
Run a normality test on the dependent variable (or on residuals) before a t-test, ANOVA or Pearson correlation. Shapiro-Wilk is the most powerful test for samples up to a few thousand.
Assumptions
- Shapiro-Wilk becomes very sensitive in large samples (n > 300), so rely on the Q-Q plot and skewness there.
- For t-tests and ANOVA, check normality within each group using the split option.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the variable and split by group.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report a normality test in APA style
For example: “Exam scores were approximately normally distributed, W(90) = 0.98, p = .31.”
Frequently asked questions
How do I interpret the Shapiro-Wilk test?
The null hypothesis is that the data are normally distributed. A p-value below .05 suggests the data are not normal; a p-value of .05 or above means there is no evidence against normality.
Shapiro-Wilk or Kolmogorov-Smirnov: which should I report?
Shapiro-Wilk has more power for small and medium samples and is generally preferred. The Kolmogorov-Smirnov test needs the Lilliefors correction when the mean and SD are estimated from the data, which this tool applies.
My sample is large and the test is significant. Is that a problem?
With several hundred cases, normality tests flag tiny, harmless departures. Rely on the Q-Q plot and skewness and kurtosis, and remember that t-tests and ANOVA are robust to non-normality in large samples.
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