The Kolmogorov-Smirnov test is often to test the normality assumption required by many statistical tests such as ANOVA, the t-test and many others. Data does not need to be perfectly normally distributed for the tests to be reliable. While Skewness and Kurtosis quantify the amount of departure from normality, one would want to know if the departure is statistically significant. The formal normality tests including Shapiro-Wilk test and Kolmogorov-Smirnov test may be used from small to medium sized samples (e.g., n < 300), but may be unreliable for large samples. Hence, a test can be developed to determine if the value of b 2 is significantly different from 3. 3. Normal distributions can be divided up into the same proportions by the standard deviations, so 95% of the area under the curve lies within roughly plus or minus two standard deviations of the mean; In this video Jarlath Quinn demonstrates how to use the functions within the explore command in SPSS Statistics to test for normality. In parametric statistical analysis the requirements that must be met are data that are normally distributed. You can reach this test by selecting Analyze > Nonparametric Tests > Legacy Dialogs > and clicking 1-sample KS test. The following two tests let us do just that: The Omnibus K-squared test; The Jarque–Bera test; In both tests, we start with the following hypotheses: Normality tests based on Skewness and Kurtosis. The Kolmogorov-Smirnov and Shapiro-Wilk tests can be used to test the hypothesis that the distribution is normal. If the data are not normal, use non-parametric tests. Here two tests for normality are run. The test statistics are shown in the third table. Just make sure that the box for “Normal” is checked under distribution. However, it is almost routinely overlooked that such tests are robust against a violation of this assumption if sample sizes are reasonable, say N ≥ 25. D’Agostino (1990) describes a normality test based on the kurtosis coefficient, b 2. SPSS Statistics Output. How to Shapiro Wilk Normality Test Using SPSS Interpretation | The basic principle that we must understand is that the normality test is useful to find out whether a research data is normally distributed or not normal. (SPSS recommends these tests only when your sample size is less than 50.) This video demonstrates conducting the Shapiro-Wilk normality test in SPSS and interpreting the results. Recall that for the normal distribution, the theoretical value of b 2 is 3. If you perform a normality test, do not ignore the results. If the data are normal, use parametric tests. 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