Normality Tests
Many statistical tests in SPSS assume that data follows a normal distribution. Before applying these tests, it is essential to verify whether this assumption is reasonable.
Normality tests help determine whether a dataset is approximately normally distributed or whether alternative (non-parametric) methods should be used instead.
What Is Normal Distribution?
A normal distribution is a symmetric, bell-shaped curve where most values cluster around the mean and extreme values are rare.
Key characteristics of a normal distribution:
- Mean, median, and mode are approximately equal
- Data is symmetrically distributed
- Most observations fall near the center
Many real-world variables such as height, test scores, and measurement errors often follow this pattern.
Why Normality Matters in SPSS
Several statistical tests rely on the assumption of normality, including:
- t-tests
- ANOVA
- Linear regression
If data violates the normality assumption, test results may be unreliable. In such cases, non-parametric tests are preferred.
Example Dataset
Consider the following exam score data:
| Student_ID | Score |
|---|---|
| 1101 | 65 |
| 1102 | 70 |
| 1103 | 72 |
| 1104 | 75 |
| 1105 | 88 |
Before comparing means or running hypothesis tests, we must check whether these scores are approximately normally distributed.
Graphical Methods for Checking Normality
Visual inspection is often the first step. SPSS provides graphical tools such as:
- Histogram with normal curve
- Normal Q-Q plot
If data closely follows the normal curve and points lie near the diagonal in Q-Q plots, normality is likely satisfied.
Statistical Tests for Normality
SPSS provides formal tests to assess normality:
- Shapiro-Wilk Test (recommended for small samples)
- Kolmogorov-Smirnov Test
These tests produce a p-value used to evaluate normality.
Interpretation rule:
- p > 0.05 → data is approximately normal
- p ≤ 0.05 → data deviates from normality
Running Normality Tests in SPSS (Menu)
To run normality tests using the SPSS menu:
- Go to Analyze → Descriptive Statistics → Explore
- Move the variable into the Dependent List
- Click Plots → check Normality plots with tests
- Click OK
SPSS outputs both graphical and statistical normality results.
Using SPSS Syntax
Normality tests can also be run using syntax.
EXAMINE VARIABLES=Score
/PLOT=NONE
/STATISTICS=NONE
/CINTERVAL=95
/NORMALITY.
This command produces Shapiro-Wilk and Kolmogorov-Smirnov tests for the selected variable.
Interpreting the Output
When reviewing normality output:
- Focus on Shapiro-Wilk for small samples
- Check p-value first
- Confirm visually using histograms or Q-Q plots
Do not rely on statistical tests alone. Combine statistical results with visual inspection.
Common Mistakes
Common errors when assessing normality include:
- Ignoring sample size effects
- Relying only on p-values
- Forgetting visual inspection
Balanced judgment leads to better analytical decisions.
Quiz 1
What does normality testing evaluate?
Whether data follows a normal distribution.
Quiz 2
Which test is preferred for small samples?
Shapiro-Wilk test.
Quiz 3
What does p > 0.05 suggest?
Data is approximately normally distributed.
Quiz 4
Why use graphical methods along with tests?
To visually confirm distribution shape.
Quiz 5
Which SPSS menu provides normality plots?
Analyze → Descriptive Statistics → Explore.
Mini Practice
Create a dataset with a numeric variable called Test_Score containing at least 15 values.
Check normality using:
- Histogram with normal curve
- Shapiro-Wilk test
Interpret whether the data meets the normality assumption.
Use Explore → Plots → Normality plots with tests, and interpret p-values with visual inspection.
What’s Next
In the next lesson, you will learn about reliability analysis using Cronbach’s Alpha, which evaluates consistency in survey and scale data.