how to test for normality spss

4 min read 17-01-2025

Testing for normality is a crucial step in many statistical analyses. Many parametric tests (like t-tests and ANOVAs) assume that your data is normally distributed. If your data significantly deviates from normality, using these tests could lead to inaccurate results. This guide will walk you through how to test for normality in SPSS using various methods.

Why Test for Normality?

Before diving into the how-to, let's briefly reiterate why normality testing is important. Many statistical tests rely on the assumption that your data follows a normal distribution (bell curve). If this assumption is violated, the results of your analysis might be unreliable. Specifically, violating normality assumptions can affect:

Type I Error Rate: The probability of rejecting a true null hypothesis (false positive).
Power of the Test: The probability of correctly rejecting a false null hypothesis.

Therefore, understanding how your data is distributed is paramount to conducting accurate statistical analyses.

Methods for Testing Normality in SPSS

SPSS offers several ways to assess the normality of your data. We'll explore the most common approaches:

1. Histograms and Q-Q Plots

Visual inspection is a good starting point. Histograms provide a graphical representation of your data's distribution. A perfectly normal distribution will resemble a bell curve. Q-Q plots (Quantile-Quantile plots) compare your data's quantiles to the quantiles of a normal distribution. If your data is normally distributed, the points on the Q-Q plot will fall approximately along a straight diagonal line.

How to create them in SPSS:

Go to Analyze > Descriptive Statistics > Explore.
Move your variable(s) into the Dependent List.
Click on Plots.
Select Histograms and Normality plots with tests.
Click OK.

Interpreting Histograms and Q-Q plots:

Histogram: Look for a bell-shaped curve. Significant deviations suggest non-normality.
Q-Q Plot: Points closely following the diagonal line indicate normality. Large deviations suggest non-normality. Remember, minor deviations are often acceptable.

2. Statistical Tests: Kolmogorov-Smirnov and Shapiro-Wilk

While visual inspection is helpful, it's subjective. Statistical tests provide objective measures of normality. The Kolmogorov-Smirnov test and the Shapiro-Wilk test are commonly used.

How to run them in SPSS:

(These tests are automatically generated when you select "Normality plots with tests" in the Explore procedure as described above.)

Kolmogorov-Smirnov Test: This test is more powerful with larger sample sizes (n > 50).
Shapiro-Wilk Test: This test is generally more powerful with smaller sample sizes (n < 50).

Interpreting the Tests:

Both tests provide a test statistic and a p-value. A p-value less than your significance level (commonly 0.05) indicates that your data is significantly different from a normal distribution. Reject the null hypothesis of normality.

Important Note: These tests can be sensitive to sample size. With very large samples, even minor deviations from normality might lead to a statistically significant result, even if the deviation is practically insignificant for your analysis.

3. Skewness and Kurtosis

Skewness and kurtosis are measures of the shape of your data's distribution.

Skewness: Measures the symmetry of the distribution. A value of 0 indicates perfect symmetry. Positive skewness means a tail extends to the right; negative skewness means a tail extends to the left.
Kurtosis: Measures the "tailedness" of the distribution. A value of 3 indicates a normal distribution. Higher kurtosis (leptokurtic) means a sharper peak and heavier tails. Lower kurtosis (platykurtic) means a flatter peak and lighter tails.

How to obtain these values in SPSS:

Go to Analyze > Descriptive Statistics > Descriptives.
Move your variable(s) into the Variable(s) box.
Check the box for Save standardized values as variables.
Click OK.
The output will include skewness and kurtosis values. There is also some debate on whether it is necessary to check the standardized values of skewness and kurtosis. However, some suggest to use the rule of thumb that if the standardized skewness or kurtosis are greater than |3.29| (for a sample size of 100), normality is violated.

Interpreting Skewness and Kurtosis:

There are different rules of thumb for interpreting skewness and kurtosis. Generally, absolute values greater than 1 or 2 suggest departures from normality. However, these are guidelines, and the importance of deviations will depend on your sample size and the specific analysis you're conducting.

What to do if your data is not normally distributed?

If your normality tests indicate a significant departure from normality, consider the following:

Data Transformation: Transform your data (e.g., using logarithmic, square root, or reciprocal transformations) to make it more normally distributed.
Non-parametric Tests: Use non-parametric tests, which do not assume normality. These tests are generally less powerful than parametric tests but are more robust to violations of normality assumptions. Examples include Mann-Whitney U test or Kruskal-Wallis test.
Robust Methods: Use robust statistical methods which are less sensitive to outliers and deviations from normality.

Conclusion

Testing for normality in SPSS is an essential step in many statistical analyses. This guide covers multiple methods, helping you choose the approach that best suits your data and research question. Remember that visual inspection, statistical tests, and considering the practical significance of deviations are all important components of evaluating normality. Always consider the implications of any deviations from normality on your statistical conclusions.