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ISU PSY 138 - Related Samples t-test

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Related Samples t-testRelated Samples tHypothesesSlide 4Slide 5Slide 6T formula for Related SamplesFinding T criticalSPSS(cont.)Related Samples t-testWed, Apr 7thRelated Samples tUse when:–1 group of subjects is tested more than once (e.g., pre-test / post-test)…or–2 groups of related (or matched) subjects are measured once (e.g., twins)Uses same basic t formula, but focus now on ‘difference’ scores–Differences in pre- and post-test or difference in each partner in a pairHypothesesNull hyp (Ho) indicates no difference (or no effect), so we’ll hypothesize the mean difference in the pop (D) = 0Ha indicates there will be a difference (2-tailed, D not = 0) or there will be a difference in a specific direction (1-tailed, D > 0 or D < 0).We’ll reject Ho if | t obs | > | t critical| (t observed is in critical region)City July 2001 July 2002Fresno 9 2Merced 10 4Bakersfld 8 9Stockton 9 1 Ex: What is the effectiveness of a new program to reduce litter? Measured aver litter in 4 cities in ’01 and ‘02City July 2001July 2002DFresno 9 2 7Merced 10 4 6Bakersfld 8 9 -1Stockton 9 1 8Find D (difference score) for each city, and then the average D (D bar)D bar =20/4 = 5Next, sum up the deviation scores (D)Then find squared deviation scores for each city (D2) – add a new columnThen sum up the squared deviation scores, (D2)Here, D = 20, D2 = 150Use the T observed formula:T formula for Related SamplesT observed = (Dbar - D)SDbarWhere SDbar (std error) = sqrt (SD2/ N) andSD2 = [D2 – (D)2] / N-1= 150 – (20)2 / 3 = -83.33SDbar = sqrt (-83.33 / 4) = -4.56T obs = (5-0) / -4.56 = -1.09Note: D always = 0Finding T criticalUse the t table as before,–Need alpha level & 1 or 2-tailed test?–Need Df = N-1 (here N=pairs of scores or total # participants if repeated measures)Ex) use  = .01, 1-tailed test (expected litter to decrease), Df= 3T critical = -4.541T observed = -1.09So fail to reject Ho (|t obs| < |t critical|)There is no difference in litter before & after new system  not effectiveSPSSGSS98 dataset example…Analyze  Compare Means  Paired Samples t-testPop-up window, select ‘wife…’ for var1, ‘children…’ for var2, then click arrow to put them in “Paired vars” box  OK(cont.)In output, 1st section is “Paired Samples Stats”, look for means for ‘wife…” and ‘children’ – this is what we’re comparingIn 3rd section, “Paired Samples Test”, note mean difference score, t observed, df, and ‘sig (2-tail)’.–Mean difference score is compared to 0–Sig (2 tail) should be compared to alpha level (e.g., .05). If ‘sig’ value < alpha  reject NullDraw a conclusion about the pre/post test


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ISU PSY 138 - Related Samples t-test

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