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Unformatted text preview: Comparing two means, paired experiment many studies are comparative they compare outcomes from one group with outcomes from another (e.g. two different medical treatments) in the matched-pairs design each subject in one group is paired with a similar subject in the other group one treatment is randomly assigned to one member of the pair - the other treatment is given to the other example: to compare two treatments for a disease, pair subjects who are similarly affected, same sex, age, etc. in some cases, the two treatments are given to the same subject in random order - with a wash-out period between the difference between the two measurements in a pair should only reflect the different treatments or experimental conditions the between-pair source of variability is removed if we can assume the differences are normally distributed, they can be analyzed using the one-sample t test or confidence interval Example: Suppose we are comparing costs of auto repairs at two locations. We get an estimate at both places for the 6 same cars that have recently been involved in collisions: Car Cost at 1 Cost at 2 Difference 1 760 730 30 2 1020 910 110 3 950 840 110 4 130 150 20 5 300 270 30 6 630 580 50 Is there evidence that mean costs are different at the two locations? repair costs vary considerably between cars for each car, the first location tends to be more expensive than the second Hypotheses: H : d = 0 H a : d 6 = 0 for the column of differences, n = 6 , df = 5 , y = 51 . 667 , s = 50 . 761 so test statistic is t = y- s/ n = 51 . 667- 50 . 761 / 6 = 2 . 493 . 2.493 is between 2.015 and 2.571, so P ( T > 2 . 493) is between .025 and .05 P-value is between 2(0 . 025) and 2(0 . 05), that is, between 0.05 and 0.10 (double because two-sided alternative) there is only weak evidence of a difference in costs Example: Ten patients were randomly selected to take part in a nutritional program designed to lower blood...
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- Spring '12