April 18 - 1 – μ 2 It clusters around a mean of 0 as...

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April 18, 2008 IV. Steps for significance test o Write H 0 and H 1 o Select an alpha level, and find z critical or t critical o Calculate t or z; compare to the critical value of z or t o Decide to reject the null hypothesis or not, and interpret Significance testing for two population means (independent sample means) We use this test when we have: o A continuous dependent variable (either interval or ratio level) o We compare the mean of the dependent variable across two independent groups o Examples: Salaries for men vs. women Average re-arrest rate for youth in juvenile court and in adult court Begin with the null hypothesis o Assume that the two groups’ population means are equal – this is H0 H 0 : μ 1 – μ 2 = 0 Same as saying μ 1 = μ 2 μ = population average The sampling distribution again o We think of a sampling distribution of μ
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Unformatted text preview: 1 – μ 2 It clusters around a mean of 0, as predicted by H We calculate the standard error of the difference between means Calculating the standard error o There are 2 different formulas to use, depending on whether σ 1 2 (population variance for group 1) = σ 2 2 (population variance for group 2) o We will use only one – assume that σ 1 2 ≠ σ 2 2 Unequal standard deviations o For unequal population variances: σ 1 - 2 = ( (s 1 2 / n 1-1) + (s 2 2 / n 2-1)) o The formula for t is: t obt =( 1- 2 )/ ( (s 1 2 / n 1-1) + (s 2 2 / n 2-1)) Degrees of freedom o For unequal standard deviations, it can be more complicated o DF=n 1 +n 2-2 is still a good estimate (contrary to what your book says)...
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