Shapiro-Wilk Test in SPSS: Step-by-Step Guide for Normality Testing
In the realm of quantitative research, ensuring the validity of statistical analyses hinges on meeting certain assumptions—one of the most critical being the assumption of normality. The Shapiro-Wilk test, available in IBM SPSS Statistics, is a powerful and commonly used method for assessing whether a dataset is normally distributed.
This comprehensive guide explains the concept, application, and interpretation of the Shapiro-Wilk test in SPSS. Whether you are a psychology student, social science researcher, or data analyst, this article will equip you with the necessary knowledge to perform and understand this test accurately.
What is the Shapiro-Wilk Test?
The Shapiro-Wilk test is a statistical procedure designed to test the null hypothesis that a sample x1,x2,…,xnx_1, x_2, …, x_nx1,x2,…,xn comes from a normally distributed population. Introduced by Samuel Shapiro and Martin Wilk in 1965, it remains one of the most robust tools for normality testing, especially for small to moderate sample sizes (n < 2000).
Key Characteristics:
- Type of Test: Normality test
Hypotheses:- H₀: The data are normally distributed.
H₁: The data are not normally distributed.
- H₀: The data are normally distributed.
- Output: W statistic and p-value
If the p-value is less than or equal to 0.05, you reject the null hypothesis, concluding that the data deviate significantly from a normal distribution.
Why Normality Matters in SPSS Analysis
In SPSS, many statistical techniques (e.g., t-tests, ANOVA, regression) assume that the residuals or variables are normally distributed. If the data violate this assumption, the validity of the statistical inference is compromised, potentially leading to Type I or Type II errors.
For Example:
- Independent-samples t-test requires the dependent variable to be normally distributed within each group.
- Linear regression assumes normality of residuals for accurate parameter estimation.
Thus, checking for normality is a critical preliminary step in any parametric analysis.
How to Perform the Shapiro-Wilk Test in SPSS (Step-by-Step)
Follow these detailed steps to conduct the Shapiro-Wilk test in SPSS:
- Step 1: Open SPSS and Load Your Dataset
Start by opening your SPSS data file or importing your dataset from Excel or CSV. - Step 2: Navigate to the Explore Function
Click: Analyze > Descriptive Statistics > Explore - Step 3: Define the Variable(s)
Move the dependent variable(s) into the “Dependent List” box.
If your dataset includes groupings (e.g., gender, condition), you can specify them under “Factor List” for subgroup analysis. - Step 4: Select the Normality Test
Click the “Plots” button:
Check “Normality plots with tests”
Optionally, select “Histogram” and “Stem-and-leaf”
Click Continue, then OK to run the analysis.
SPSS Output Interpretation: Shapiro-Wilk Test
After running the test, SPSS will generate multiple tables. Focus on the “Tests of Normality” table. The table presents the results of both:
- Kolmogorov-Smirnov Test
- Shapiro-Wilk Test
For sample sizes n < 50, Shapiro-Wilk is the preferred choice.
Key Values in Output:
| Statistic | df | Sig. (p-value) |
|---|
| 0.972 | 30 | 0.215 |
Interpretation:
If p > 0.05: Fail to reject H₀ → Data is normally distributed.
If p ≤ 0.05: Reject H₀ → Data is not normally distributed.
Shapiro-Wilk Test: Examples
Let’s consider two scenarios:
Example 1: Normal Distribution
- Sample size: 30
- Variable: Anxiety Score
- Shapiro-Wilk p = 0.172 → Data follows a normal distribution
Example 2: Non-Normal Distribution
- Sample size: 20
- Variable: Income Level
- Shapiro-Wilk p = 0.012 → Data is not normally distributed
In the second case, you may consider data transformation (e.g., log, square root) or non-parametric alternatives (e.g., Mann-Whitney U test).
Advantages of Shapiro-Wilk Test
- More powerful than Kolmogorov-Smirnov, especially for small samples
- Detects subtle deviations from normality
- Integrated within SPSS for easy access
Limitations of the Shapiro-Wilk Test
- Sensitive to outliers
- For large samples (n > 2000), it may flag insignificant deviations as significant
- Cannot be used for categorical data or ordinal variables
Shapiro-Wilk vs Kolmogorov-Smirnov Test
| Feature | Shapiro-Wilk | Kolmogorov-Smirnov |
|---|---|---|
| Sample size suitability | n < 2000 | n > 50 |
| Power | Higher | Lower |
| Default in SPSS | Yes | Yes |
| Handles ties/outliers | Less robust | More robust |
Conclusion: Use Shapiro-Wilk for small samples; reserve K-S for large or complex datasets.
What to Do If Data Is Not Normal?
If your dataset fails the Shapiro-Wilk test:
- Apply data transformation: log, square root, inverse
- Use non-parametric tests: Mann-Whitney, Kruskal-Wallis
- Report the violation and justify your choice of analysis in your research
Real-World Applications of the Shapiro-Wilk Test
- In psychological research, to assess the normality of scale scores (e.g., depression, anxiety)
- In social sciences, for verifying assumptions before regression or ANOVA
- In medical statistics, to validate biomarker distributions before modeling
FAQs
Q: When should I use the Shapiro-Wilk test?
A: Use it when testing the normality of a continuous variable, especially in small to mid-sized samples (n < 2000).
Q: What if the p-value is less than 0.05 in the Shapiro-Wilk test?
A: It indicates that the data significantly deviate from normality. Consider using non-parametric tests or data transformation.
Q: Can I use Shapiro-Wilk for categorical variables?
A: No, it is only applicable for continuous, interval, or ratio-level data.
Q: Is the Shapiro-Wilk test available in SPSS?
A: Yes, it is available under Analyze > Descriptive Statistics > Explore, under “Normality plots with tests.”
Final Thoughts
The Shapiro-Wilk test in SPSS is a critical tool for any researcher who needs to validate the assumption of normality before performing parametric analyses. With this guide, you should be well-equipped to not only run the test in SPSS but also to interpret its results confidently and apply them appropriately in your research context.