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Chi-squared Test (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 i -th bin Test statistic:. Chi-squared Test (2).

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Chi-squared Test (1)

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  1. Chi-squared Test (1) • H0: population follows distribution • Divide the observations into k bins • Oi = observed frequency in i-th bin • Ei = expected frequency in i-th bin • Test statistic:

  2. Chi-squared Test (2) • 2follows (approx) a chi-square distribution with k-p-1 degrees of freedom where p is the number of estimated parameters • Reject H0 if 2 > 2,k-p-1 .

  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 • H0: birthdays follow a uniform distribution • Construct a chi-squared test for this hypothesis

  5. Contingency Table Test • Goal: to find out if two methods of classification are statistically indept • 2 follows a chi-squared • distribution with (r-1)(c-1) • degrees of freedom. • Reject the null hypothesis • if 2 exceeds 2,(r-1)(c-1)

  6. Example: Smoking & Gender • Test the hypothesis (at the 1% level) that whether a person smokes is independent of the person’s gender.

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