Examining the Shapiro-Wilk Test: A Guide to Identifying Non-Normal Data

Understanding the Shapiro-Wilk Test

The Shapiro-Wilk test is a statistical hypothesis test used to assess whether a given dataset follows a normal distribution. By comparing the observed data to a theoretical normal distribution, the test helps researchers determine if the data deviates significantly from normality.

Null Hypothesis and Significance Level

The null hypothesis of the Shapiro-Wilk test assumes that the population from which the sample was drawn is normally distributed. If the p-value obtained from the test is less than the chosen alpha level (typically 0.05), the null hypothesis is rejected, indicating that the data is not normally distributed.

Using SPSS for Shapiro-Wilk Test

SPSS is a widely used statistical software that allows researchers to perform the Shapiro-Wilk test. To run the test in SPSS: 1. Input your data into a dataset. 2. Select "Analyze" > "Descriptive Statistics" > "Explore." 3. Choose the variables you want to test for normality. 4. Click on the "Options" button and select "Shapiro-Wilk test" under "Tests of Normality."

Interpreting the Results

The Shapiro-Wilk test produces a W-statistic and a p-value. A W-statistic close to 1 indicates that the data is close to normal distribution. A low W-statistic and p-value suggest that the data is not normally distributed.

Example in R

Using R, the Shapiro-Wilk test can be performed with the "shapiro.test" function: shapiro.test(data) The output will include the W-statistic and the p-value.

Conclusion

The Shapiro-Wilk test is a valuable tool for researchers to assess the normality of a dataset. Understanding its principles and how to perform the test in SPSS and R is crucial for ensuring accurate data analysis and reliable conclusions.