Related Samples t-testRelated Samples tHypothesesSlide 4Slide 5Slide 6T formula for Related SamplesFinding T criticalSPSS(cont.)Related Samples t-testWed, Apr 7thRelated Samples tUse 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 pairHypothesesNull hyp (Ho) indicates no difference (or no effect), so we’ll hypothesize the mean difference in the pop (D) = 0Ha 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 = 5Next, sum up the deviation scores (D)Then find squared deviation scores for each city (D2) – add a new columnThen sum up the squared deviation scores, (D2)Here, D = 20, D2 = 150Use the T observed formula:T formula for Related SamplesT 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) = -4.56T obs = (5-0) / -4.56 = -1.09Note: D always = 0Finding T criticalUse 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 effectiveSPSSGSS98 dataset example…Analyze Compare Means Paired Samples t-testPop-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 comparingIn 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 NullDraw a conclusion about the pre/post test
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