On tests for normality for discrete and continuous data
Date of Publication
Bachelor of Science in Mathematics
College of Science
Mathematics and Statistics
In this paper, various tests for normality were extensively studied, and were applied on different sets of discrete and continuous data. Sets of data were generated from the computer using Microsoft Excel. For each set of data, samples of size 100 were randomly selected. These sets of sample data were then analyzed using the Lilliefors test for normality. Other tests for normality were also applied for the sets of data of discrete and continuous cases. The Chi-square goodness-of-fit test was used for data generated from the Binomial Distribution (2, 0.6) and the Poisson Distribution (5), while the Kolmogorov-Smirnov test was used for data generated from the, Normal Distribution (8, 2) and the Exponential Distribution. Results of the different tests were then analyzed and compared. For the Binomial and Poisson Distribution, it was found out that the null hypothesis of normality, using the Chi-Square Goodness-of-Fit test, was failed to be rejected. While with the use of the Lilliefors Test, both distributors rejected the false null hypothesis. For the continuous cases, the Lilliefors Test and the Kolmogorov-Smirnov Test have the same results for the two probability distributions. These two tests have both rejected the normality of the Exponentially distributed samples. While for the sample with Normal distributions, they have both failed to reject the null-hypothesis that the sample data follow a normal distribution.
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Quinanola, K. M., & Roxas, A. D. (2001). On tests for normality for discrete and continuous data. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/17172