Test of Normality of Data in SPSS

Summary

This tutorial demonstrates how to test whether data is approximately normally distributed using SPSS, which is crucial for valid parametric tests. It covers both numerical methods (such as skewness, kurtosis, and Shapiro-Wilk test) and graphical methods (like histograms and QQ plots). The video also explains how to interpret results, using a dataset of student ages and gender as an example. It highlights when normality assumptions are met and how to proceed if they are violated, including data transformation or using non-parametric tests. The presenter emphasizes the importance of understanding normality for accurate statistical analysis.

Takeaways

• 😀 Parametric tests, such as correlation, t-tests, and ANOVA, require certain assumptions about the data to be valid.
• 😀 One key assumption is that the dependent variable should be approximately normally distributed.
• 😀 SPSS offers both numerical and graphical methods to test for normality in your data.
• 😀 Numerical methods for testing normality include skewness, kurtosis, the Kolmogorov-Smirnov test, and the Shapiro-Wilk test.
• 😀 Skewness and kurtosis values should be close to zero for data to be considered normally distributed.
• 😀 The Shapiro-Wilk test is preferred for smaller datasets (under 50 observations) and is the most sensitive normality test.
• 😀 Graphical methods include histograms and QQ plots, which help visually assess the normality of the data distribution.
• 😀 A histogram overlaid with a normal curve allows for easier judgment about the distribution's shape.
• 😀 In a QQ plot, if data points closely follow the straight line, the data is approximately normally distributed.
• 😀 When testing normality by groups (e.g., male vs. female), each group's normality should be tested separately, with similar interpretation criteria.
• 😀 If data fails the normality tests, transformations like square roots or logarithms can be applied, or non-parametric tests can be used as alternatives.

Q & A

What is the purpose of testing for normality in parametric tests?

Testing for normality ensures that the data is drawn from a population that follows a normal distribution. This assumption is critical for the validity of parametric tests like Pearson's correlation, t-tests, ANOVA, and regression analysis.

What are the two main methods to test for normality in SPSS?

The two main methods are numerical and graphical methods. The numerical methods include skewness and kurtosis, as well as the Kolmogorov-Smirnov and Shapiro-Wilk tests. The graphical methods involve the histogram and the QQ plot.

How do you perform a normality test in SPSS for a single variable?

To test normality in SPSS, go to the 'Analyze' menu, select 'Descriptive Statistics', then 'Explore'. Move the dependent variable to the 'Dependent List', and check the options for skewness and kurtosis under 'Statistics'. For graphical tests, select the histogram and QQ plot under the 'Plots' tab.

What does skewness measure in relation to normality?

Skewness measures the asymmetry of the data distribution. A skewness value close to zero indicates a symmetric distribution, which is a characteristic of normality.

What is kurtosis and how is it related to normality?

Kurtosis measures the 'tailedness' of the data distribution. A kurtosis value close to zero suggests that the distribution has a similar shape to a normal distribution, which typically has a kurtosis near zero.

What do the p-values in the Kolmogorov-Smirnov and Shapiro-Wilk tests indicate?

In these tests, a p-value greater than 0.05 indicates that the data is approximately normally distributed. A p-value less than 0.05 suggests that the data deviates significantly from normality.

Why is the Shapiro-Wilk test preferred for smaller datasets?

The Shapiro-Wilk test is more sensitive and accurate for small datasets (less than 50 observations), making it the recommended choice for testing normality in smaller samples.

How can you visually inspect normality in SPSS?

You can visually inspect normality by examining the histogram with an overlaid normal curve and the QQ plot. If the histogram's curve resembles a bell shape and the points on the QQ plot lie close to the straight line, the data can be considered approximately normally distributed.

What should you do if the normality assumption is violated in your data?

If the normality assumption is violated, you can either transform the data (e.g., using square roots or log transformations) to make it more normally distributed or choose non-parametric tests, which do not require normality assumptions.

How do you check normality for different groups (e.g., gender) in SPSS?

To check normality for different groups, move the categorical variable (e.g., gender) to the 'Factor List' in the 'Explore' dialog box. SPSS will then perform the normality tests for each group separately.