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The null hypothesis of normality is rejected if the

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chi-square) distribution with 2 degrees of freedom. The null hypothesis of normality is rejected if the calculated test statistic exceeds a critical value from the 2 ) 2 ( χ distribution. Econ 325 – Normality Test 6 The critical values can be found from the Appendix Table for the chi-square distribution as: Significance Level α Critical Value 0.10 4.61 0.05 5.99 0.01 9.21 The presentation of this test of normality is valid for ‘large samples’. For ‘small samples’ the decision rule can be viewed as approximate.
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Econ 325 – Normality Test 7 Example: A stock market data set has daily percentage returns observed for the year 1997 for two companies – Barrick Gold and Bank of New York. The sample has observations for n = 253 trading days. For each company, an exercise is to test for normality of the daily returns. Various statistics are given in the table below. Both the ‘small sample’ and ‘large sample’ versions of the skewness and excess kurtosis statistics are presented to give emphasis to the methodology. Barrick Gold Bank of NY ‘Small sample’ statistics Skewness 1 g 0.01 - 0.14 Excess Kurtosis 2 g 1.38 0.41 ‘Large sample’ statistics Skewness S 0.01 - 0.14 Excess Kurtosis EK 1.33 0.38 Jarque-Bera test for normality – calculated with the ‘large sample’ statistics JB test statistic 18.73 2.31 p-value < 0.0005 0.315 Econ 325 – Normality Test 8 For Barrick Gold, the Jarque-Bera test statistic of 18.73 exceeds the critical values for any reasonable significance level to lead to the conclusion that the daily returns do not follow a normal distribution.
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