4. Hence, a test can be developed to determine if the value of b 2 is significantly different from 3. D’Agostino (1990) describes a normality test based on the kurtosis coefficient, b 2. 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. The test statistics are shown in the third table. 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. Normality tests based on Skewness and Kurtosis. 3. This video demonstrates conducting the Shapiro-Wilk normality test in SPSS and interpreting the results. This test checks the variable’s distribution against a perfect model of normality and tells you if the two distributions are different. If it is, the data are obviously non- normal. The Kolmogorov-Smirnov and Shapiro-Wilk tests can be used to test the hypothesis that the distribution is normal. The hypotheses used in testing data normality are: Ho: The distribution of the data is normal Ha: The distribution of the data is not normal. 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. Data does not need to be perfectly normally distributed for the tests to be reliable. If the data are normal, use parametric tests. Here two tests for normality are run. The normal distribution peaks in the middle and is symmetrical about the mean. Checking normality for parametric tests in SPSS . 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: (SPSS recommends these tests only when your sample size is less than 50.) Just make sure that the box for “Normal” is checked under distribution. One of the assumptions for most parametric tests to be reliable is that the data is approximately normally distributed. Recall that for the normal distribution, the theoretical value of b 2 is 3. SPSS Statistics Output. In parametric statistical analysis the requirements that must be met are data that are normally distributed. If the data are not normal, use non-parametric tests. If you perform a normality test, do not ignore the results. 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. 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