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Lecture 5

ADM2304 Lecture 5: 5

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University of Ottawa
Tony Quon

Comparing Two Population Proportions: The Distribution of the Difference between Two Sample Proportions Confidence Interval for the Difference —> Since we know the distribution of the difference of two proportions we can calculate the confidence interval in exactly the same way —> The general structure of a confidence interval is (estimate ± (z- or t-value)×(SD or SE of estimate) —> Thus for the difference in the proportions for two independent populations, a 100(1-α)% confidence interval is given by: ⎛ p (1− p ) ˆ p (1− p ) ˆ ⎞ ⎜(p − p )±z 1 1 + 2 2 ⎟ ⎜ 1 2 α/2 ⎟ ⎝ n 1 n 2 ⎠ Rule of Thumb —> When can we use the two sample proportion test? - If n1p1, n2p2, n1(1 - p1) and n2(1 - p2) are all greater than 10 —> Note that there is no need to restrict ourselves to testing p1 - p2 = 0. We can test for any non-zero difference, p1 - p2 = p0, as well in which case the test statistic is: (p − p )− p z = 1 2 0 ~ N(0,1) p (1− p ) p (1− p ) 1 1 + 2 2 n 1 n 2 Pooling: Under hypothesis H0: p1 - p2 = 0, we are assuming that the proportions are actually X + X (p − p )−0 the same thing. So in estimating the SE we can use a pool estimate of proportion:
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