# 4 - Comparing two means paired experiment • many studies...

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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 : μ d = 0 H a : μ d 6 = 0 • for the column of differences, n = 6 , df = 5 , ¯ y = 51 . 667 , s = 50 . 761 • so test statistic is t = ¯ y- μ 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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4 - Comparing two means paired experiment • many studies...

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