norTestPRN - A Test of Normality Textbook Reference Chapter...

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A Test of Normality Textbook Reference: Chapter 14.2, pages 624–26. The calculation of p-values for hypothesis testing typically is based on the assumption that the population distribution is normal. Therefore, a test of the normality assumption may be useful to inspect. A variety of tests of normality have been developed by various statisticians. One of these tests will be described here. To start, the calculation of descriptive statistics is reviewed. A data set has the numeric observations: , , . . . , . 1 x 2 x n x Familiar descriptive statistics are the sample mean: ¦ n 1 i i x n 1 x and the sample variance: ¦ 0 0 n 1 i 2 i 2 ) x x ( 1 n 1 s Econ 325 – Normality Test 1 Now introduce two new statistics. The sample skewness is defined as: 2 3 2 n 1 i 3 i ) ~ ( ) x x ( n 1 S V 0 ¡ ¦ where ¦ 0 V n 1 i 2 i 2 ) x x ( n 1 ~ Skewness gives a measure of how symmetric the observations are about the mean. For a normal distribution the skewness is 0 . A distribution skewed to the right has positive skewness and a distribution skewed to the left has negative skewness. The sample kurtosis is defined as: 2 2 n 1 i 4 i ) ~ ( ) x x ( n 1 K V 0 ¡ ¦ Kurtosis gives a measure of the thickness in the tails of a probability density function. For a normal distribution the kurtosis is 3 .
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