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Jarque-Bera test is a Lagrange multiplier test for normality. Several tests in statistics such as the T-test and F-test have normality as one of the assumptions. However, a Jarque-Bera test should be performed ahead of these tests to make sure that normality indeed exists. The Jarque-Bera test is well-suited for large data sets. For this reason, it is often used in place of other normality tests that are not reliable with large data. For example, the Shapiro-Wilk test cannot be used with n more than 2000. The Jarque-Bera test aims to see if our data has a normal distribution by matching the kurtosis and skewness of the data.
This is a goodness of fit test that compares the data provided by the researcher with a distribution that is known to examine if both have the same distribution. The Kolmogorov-Smirnov test is nonparametric but is often used to check for a normal distribution. It examines the assumption of normality in ANOVA (Analysis of Variance). It compares your empirical distribution function to a known hypothetical probability distribution.
The Chi-Square Goodness of fit test
This is a type of nonparametric test. Its goal is to find out if the values observed for given phenomena are different from the value the researcher expects to get. This test tries to explain how theoretical distributions like normal, Poisson, and binomial fit well in an empirical distribution. When performing this type of goodness of fit test, the data samples should be broken down into intervals. The next step is to compare the number of points within the interval with the number of points expected in each interval.
A Lilliefors test is an improved Kolmogorov-Smirnov test for normality. It is also known as the K-S-D test and can be performed using statistical packages such as SPSS. Lilliefors allows you to check for normality even if you do not know the standard deviation or the population mean. The researcher can estimate these parameters from the sample. A Lilliefors test assumes that the researcher has a random sample.