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Paired t -test: t D

Paired t -test: t D. Introduction To The Repeated Measures Design:What is a repeated measure? Finding an Experimental Effect In a Single Group: Before vs. After Creating a new distribution t D . Reduces Sampling Error: It’s a more powerful test Limited Applicability. Before-After.

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Paired t -test: t D

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  1. Paired t-test: tD Introduction To The Repeated Measures Design:What is a repeated measure? Finding an Experimental Effect In a Single Group: Before vs. After Creating a new distribution tD. Reduces Sampling Error: It’s a more powerful test Limited Applicability

  2. Before-After Pre-Measure Post-Measure Manipulation Anthony Greene

  3. It doesn’t have to be “Before-After” Anthony Greene

  4. Matched Subject Design For a given study the two groups of subjects could be closely matched • Age • IQ • Blood Pressure • Income • Education Level Anthony Greene

  5. The Basic Idea • Standard t-test Anthony Greene

  6. The Basic Idea • Standard t-test Anthony Greene

  7. The Basic Idea • Standard t-test • Is 13 different than 17? Or 13-17 different than 0? Anthony Greene

  8. The Basic Idea • Repeated Measures t-test Anthony Greene

  9. The Basic Idea • Repeated Measures t-test • Create A New Variable, D Anthony Greene

  10. The Basic Idea • Repeated Measures t-test • Is 4 different than 0? Anthony Greene

  11. The Basic Idea The fundamental advantage? • The error term in the within subjects design is smaller • In the simplified example, the standard error terms would be higher in the two sample version versus the difference test (in this case the sMDis zero) • The advantage is that individual differences (2, 13, 24, and 5, 16, 27) are not part of the error in tD Anthony Greene

  12. The Basic Idea Are there limitations? • The repeated measure design (before – after) must be used cautiously used in many experimental designs • Memory Subjects learn • Medicine and Clinical Psych Substantial time passes • Social Psych Minor deceptions • Loss of half the degrees freedom Anthony Greene

  13. Distribution of the Paired t-Statistic Suppose x is a variable on each of two populations whose members can be paired. Further suppose that the paired-difference variable D is normally distributed. Then, for paired samples of size n, the variable has the t-distribution with df = n – 1. The normal null hypothesis is that μD = 0 Anthony Greene

  14. The paired t-test for two population means (Slide 1 of 3) Step 1 The null hypothesis is H0: D = 0; the alternative hypothesis is one of the following: Ha: D 0Ha: D< 0Ha: D> 0 (Two Tailed) (Left Tailed) (Right Tailed) Step 2 Decide on the significance level,  Step 3 The critical values are ±t/2 -t+t (Two Tailed) (Left Tailed) (Right Tailed) with df = n - 1. Anthony Greene

  15. The paired t-test for two population means (Slide 2 of 3) Anthony Greene

  16. The paired t-test for two population means(Slide 3 of 3) Step 4 Compute the value of the test statistic Step 5 If the value of the test statistic falls in the rejection region, reject H0, otherwise do not reject H0. Anthony Greene

  17. The number of doses of medication needed for asthma attacks before and after relaxation training. Anthony Greene

  18. x1 x2 A Direct Comparison Anthony Greene

  19. x1 x2 A Direct Comparison Anthony Greene

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