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Related Samples t-test Wed, Apr 7 th

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Related Samples t wUse 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) wUses same basic t formula, but focus now on ‘difference’ scores –Differences in pre- and post-test or difference in each partner in a pair

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Hypotheses wNull hyp (Ho) indicates no difference (or no effect), so we’ll hypothesize the mean difference in the pop ( D ) = 0 wHa 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). wWe’ll reject Ho if | t obs | > | t critical| (t observed is in critical region)

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CityJuly 2001July 2002 Fresno92 Merced104 Bakersfld89 Stockton91 Ex: What is the effectiveness of a new program to reduce litter? Measured aver litter in 4 cities in ’01 and ‘02

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CityJuly 2001 July 2002 D Fresno927 Merced1046 Bakersfld89 Stockton918 Find D (difference score) for each city, and then the average D (D bar) D bar = 20/4 = 5

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wNext, sum up the deviation scores ( D ) wThen find squared deviation scores for each city (D 2 ) – add a new column wThen sum up the squared deviation scores, ( D 2 ) Here, D = 20, D 2 = 150 wUse the T observed formula:

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T formula for Related Samples wT observed = (Dbar - D) S Dbar Where S Dbar (std error) = sqrt (S D 2 / N) and S D 2 = [ D 2 – ( D) 2 ] / N-1 = 150 – (20) 2 / 3 = -83.33 S Dbar = sqrt (-83.33 / 4) = -4.56 wT obs = (5-0) / -4.56 = -1.09 Note: D always = 0

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Finding T critical wUse 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) wEx) use =.01, 1-tailed test (expected litter to decrease), Df= 3 T critical = -4.541 T observed = -1.09 So fail to reject Ho (|t obs| < |t critical|) There is no difference in litter before & after new system not effective

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SPSS wGSS98 dataset example… wAnalyze Compare Means Paired Samples t-test wPop-up window, select ‘wife…’ for var1, ‘children…’ for var2, then click arrow to put them in “Paired vars” box OK

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(cont.) wIn output, 1 st section is “Paired Samples Stats”, look for means for ‘wife…” and ‘children’ – this is what we’re comparing wIn 3 rd 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 wDraw a conclusion about the pre/post test scores.

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