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# slide9 - Chi-squared Test(1 H0 population follows...

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1 Chi-squared Test (1) ± H 0 : population follows distribution ± Divide the observations into k bins ± O i = observed frequency in i -th bin ± E i = expected frequency in -th bin ± Test statistic: χ 2 = O i E i () 2 E i i = 1 k 2 Chi-squared Test (2) ± χ 2 follows (approx) a chi-square distribution with k-p-1 degrees of freedom where p is the number of estimated parameters ± Reject H 0 if χ 2 > χ 2 α , .

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3 How many categories? ± Expected frequency in each bin should be at least 3. Can be as small as 1 or 2 if other bins are at least 5. If number is too small, lump with adjacent bin. 4 Example: Uniform Birthdays ± H 0 : birthdays follow a uniform distribution ± Construct a chi-squared
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slide9 - Chi-squared Test(1 H0 population follows...

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