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12 Two-sample inference

12 Two-sample inference - Comparing means • Tests with...

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Unformatted text preview: Comparing means • ! Tests with one categorical and one numerical variable • ! Goal: to compare the mean of a numerical variable for different groups. Paired vs. 2 sample comparisons Paired comparisons allow us to account for a lot of extraneous variation 2-sample methods are sometimes easier to collect data Paired designs • ! Data from the two groups are paired • ! Each member of the pair shares much in common with the other, except for the tested categorical variable • ! There is a one-to-one correspondence between the individuals in the two groups Paired design: Examples • ! Before and after treatment • ! Upstream and downstream of a power plant • ! Identical twins: one with a treatment and one without • ! Earwigs in each ear: how to get them out? Compare tweezers to hot oil Paired comparisons • ! We have many pairs • ! In each pair, there is one member that has one treatment and another who has another treatment (“Treatment” can mean “group”) Paired comparisons • ! To compare two groups, we use the mean of the difference between the two members of each pair Paired t test • ! Compares the mean of the differences to a value given in the null hypothesis • ! For each pair, calculate the difference. The paired t-test is simply a one-sample t-test on the differences. Example: National No Smoking Day • ! Data compares injuries at work on National No Smoking Day (in Britain) to the same day the week before • ! Each data point is a year data Hypotheses H : Work related injuries do not change during No Smoking Days. ( μ d = 0) H A : Work related injuries change during No Smoking Days. ( μ d ! 0) Calculate differences Calculate t using d ’s d = 25 s d 2 = 1043.78 n = 10 t = 25 !...
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12 Two-sample inference - Comparing means • Tests with...

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