12 Two-sample inference - Comparing means ! Tests with one...

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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. ( d = 0) H A : Work related injuries change during No Smoking Days. ( 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 one...

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