05) suggests that the distribution is not normal and interpretations may be affected. SPSS provides the Shapiro-Wilk test output for interpretation. 05, the normality assumption may be violated, which can be problematic.To obtain the Shapiro-Wilk test in SPSS, follow the step-by-step guide for t tests that is provided in the Unit 8 assignment. When the Shapiro-Wilk test indicates a p value less than. The null hypothesis of the Shapiro-Wilk test is that the distribution is normal. Values less than 1.00 indicate an increasing departure from a perfect normal shape. A perfect normal distribution will have a Shapiro-Wilk value of 1.00.

In addition to a visual inspection of histograms and calculation of skewness and kurtosis values, SPSS provides a formal statistical test of normality referred to as the Shapiro-Wilk test.

The variance of Y scores is approximately equal across groups (homogeneity of variance assumption).

The outcome variable Y is normally distributed.

Recall from Unit 7 that two assumptions of the t test are that: Dallal GE and Wilkinson L (1986), 'An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality,' The American Statistician, 40, 294-296.Testing Assumptions: The Shapiro-Wilk Test and the Levene Test RB D'Agostino, 'Tests for Normal Distribution' in Goodness-Of-Fit Techniques edited by RB D'Agostino and MA Stephens, Macel Dekker, 1986.ģ.

Journal of the Royal Statistical Society. P Royston, Remark AS R94: A Remark on Algorithm AS 181: The W-test for Normality. In case you encounter any discrepancies, you should know that we fixed a bug in this test many years ago in Prism 4.01 and 4.0b.ġ. Since that method is only accurate with small P values, Prism simply reports “P>0.10” for large P values. To compute the P value, therefore, Prism uses the Dallal and Wilkinson approximation to Lilliefors' method (3). You only know the mean and SD of your sample. When analyzing data, you rarely know the overall population mean and SD. The Kolmogorov-Smirnov method as originally published assumes that you know the mean and SD of the overall population (perhaps from prior work). The distinction is that Anderson-Darling considers the discrepancies at all parts of the curve, and Kolmogorov-Smirnov only look at the largest discrepancy. Note that both this test and the Anderson-Darline test compare the actual and ideal cumulative distributions. This is not a very sensitive way to assess normality, and we now agree with this statement 1 : ' The Kolmogorov-Smirnov test is only a historical curiosity. It computes a P value from a single value: the largest discrepancy between the cumulative distribution of the data and a cumulative Gaussian distribution. We still offer this test (for consistency) but no longer recommend it. Prism uses the method of Royston (1).Įarlier versions of Prism offered only the Kolmogorov-Smirnov test. There are several ways to compute the Shapiro-Wilk test. The other reason is that the basis of the test is hard to understand. One reason is that, while the Shapiro-Wilk test works very well if every value is unique, it does not work as well when several values are identical.

We prefer the D'Agostino-Pearson test for two reasons. It takes into account the discrepancies at all parts of the cumulative distribution curve (unlike the Kolmogorov-Smirnov test, see below).Īnother alternative is the Shapiro-Wilk normality test. It computes the P value by comparing the cumulative distribution of your data set against the ideal cumulative distribution of a Gaussian distribution. The one used by Prism is the 'omnibus K2' test.Īn alternative is the Anderson-Darling test. Note that D'Agostino developed several normality tests. It is a versatile and powerful normality test, and is recommended. It then calculates how far each of these values differs from the value expected with a Gaussian distribution, and computes a single P value from the sum of these discrepancies. It first computes the skewness and kurtosis to quantify how far the distribution is from Gaussian in terms of asymmetry and shape. We recommend the D'Agostino-Pearson normality test. Why is there more than one way to test normality? There are many ways a distribution can deviate from a Gaussian distribution, so different normality tests give different results.

Shapiro wilk test