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1. Chapter 20 t - Test for Two Matched Samples

2. Vodka & Whiskey The researcher randomly selected 10 Cranberry vodka drinkers and 7 Boilermaker drinkers. The vodka group had a mean drunkenness of 52 and the whiskey group had a mean drunkenness of 39 . Previous Experiment Previous Decision The drunkenness of vodka drinkers and whiskey drinkers is different Question : Who typically drinks Cranberry Vodkas and who drinks Boilermakers? 2nd Question Who typically weighs more? 3rd Question : Was the difference in the previous experiment due to different alcohol or different weights? Women Men Lighter Heavier

5. Matched Samples t -Test Reducing a Two-Sample test into a Single Sample Comparison (Single Sample t -Test)

12. Hypothesis Test 11 Vodka & Whiskey  Matched Samples t-Test

13. Vodka/Whiskey: Matched t -Test Are all types of alcohol the same, even if the proofs are the same? This question was raised by a researcher who had observed vodka drinkers and noticed that they seemed to get drunk faster than whiskey drinkers. To test whether whiskey is the same or different than vodka, the researcher decided to compare people who drank 3 Cranberry Vodka’s to people to drank 3 Boilermakers. Since weight is known to affect drunkenness, the researcher has matched the samples to make sure that weight is evenly distributed between the group (on next slide).What will the researcher conclude at a .01 level of significance.

14. Vodka/Whiskey: Matched t -Test Step 0) Convert to Difference Scores 19 25 210 20 24 190 31 30 170 36 34 150 42 47 130 63 52 110 Whiskey Vodka Weight +6 +4 -1 -2 + 5 - 11 D

15. Vodka/Whiskey: Matched t -Test Step 0) Convert to Difference Scores =  D / n dif =  / 6 = .16 +6 +4 -1 -2 + 5 - 11 D D   (D 2  s D =  D) 2 n dif n dif - 1

16. Vodka/Whiskey: Matched t -Test Step 0) Convert to Difference Scores =  D / n dif =  / 6 = .16 = 6.37 +6 +4 -1 -2 + 5 - 11 D D   (D 2  s D =  D) 2 n dif n dif - 1   s D =  ) 2 6 6 - 1 36 16 1 4 25 121 D 2

22. Why Matching Works! Why can we assume the standard error is reduced ( if the matching variable is correlated with the dependent measure )

23. Why Matching Works

24. When Matching Doesn’t Work

26. Repeated Measures The Ultimate Matching

28. To match, or not to match… That is the question……

29. Matched vs Independent Tests Which test is more sensitive? Smaller Larger Standard Error Less More Degrees of Freedom Matched Independent

30. Matched vs Independent Tests Which test is more sensitive? Brings in Critical Values Spreads out Critical Values Standard Error Spreads out Critical Values Brings in Critical Values Degrees of Freedom Matched Independent … has a much greater effect on critical scores?

31. Matched vs Independent Tests Which test is more sensitive? Brings in a lot Spreads out a lot Standard Error Spreads out a little Brings in a little Degrees of Freedom Matched Independent … has a much greater effect on critical scores? More Sensitive

32. Two Sample Tests Final Notes