If the Sig. value of the Shapiro-Wilk Test is greater than 0.05, the data is normal. If it is below 0.05, the data significantly deviate from a normal distribution.

Normality is the assumption that the underlying residuals are normally distributed, or approximately so. While a residual plot, or normal plot of the residuals can identify non-normality, you can formally test the hypothesis using the Shapiro-Wilk or similar test.

Shapiro-Wilks Normality Test. The Shapiro-Wilks test for normality is one of three general normality tests designed to detect all departures from normality. It is comparable in power to the other two tests. The test rejects the hypothesis of normality when the p-value is less than or equal to 0.05.

For reporting a Shapiro-Wilk test in APA style, we include 3 numbers:

1. the test statistic W -mislabeled “Statistic” in SPSS;
2. its associated df -short for degrees of freedom and.
3. its significance level p -labeled “Sig.” in SPSS.

The Prob < W value listed in the output is the p-value. If the chosen alpha level is 0.05 and the p-value is less than 0.05, then the null hypothesis that the data are normally distributed is rejected. If the p-value is greater than 0.05, then the null hypothesis is not rejected.

Power is the most frequent measure of the value of a test for normality—the ability to detect whether a sample comes from a non-normal distribution (11). Some researchers recommend the Shapiro-Wilk test as the best choice for testing the normality of data (11).

Conducts the Shapiro-Wilk test of normality on the (deviance) residuals of a Regression output.

In order to make valid inferences from your regression, the residuals of the regression should follow a normal distribution. The residuals are simply the error terms, or the differences between the observed value of the dependent variable and the predicted value.

When the residuals are not normally distributed, then the hypothesis that they are a random dataset, takes the value NO. This means that in that case your (regression) model does not explain all trends in the dataset. Thus, your predictors technically mean different things at different levels of the dependent variable.

The two well-known tests of normality, namely, the Kolmogorov–Smirnov test and the Shapiro–Wilk test are most widely used methods to test the normality of the data. Normality tests can be conducted in the statistical software “SPSS” (analyze → descriptive statistics → explore → plots → normality plots with tests).

The Shapiro-Wilk test still indicates that the residuals are not normally distributed. We stated early that small departures from normality are okay. From the QQ plot, the residuals are not as skewed as before the transformation. Therefore, this transformation helped and we can perform the inferences assuming normality.

The normality assumption can be tested visually thanks to a histogram and a QQ-plot, and/or formally via a normality test such as the Shapiro-Wilk or Kolmogorov-Smirnov test.

Choosing the appropriate test depending on whether assumptions are met may be confusing so here is a brief summary: Check that your observations are independent. If variances are equal, use ANOVA. If variances are not equal, use the Welch ANOVA. If normality is not assumed, use the Kruskal-Wallis test.

The null hypothesis is that the residuals are normally distributed. We stated before that no “real-world” data are perfectly normally distributed. Thus, the null hypothesis is not correct. We just want to know if there is enough evidence against normality. The more data you have, the more likely that you have enough evidence to reject the null.