Stat 217 – Day 26Last Time – Analyzing Paired DataExample: Marriage agesSlide 4Paired vs. Independent SamplesSlide 6Slide 7Sign TestSlide 9To DoStat 217 – Day 26More on Matched PairsLast Time – Analyzing Paired DataHave two observations per observational unitNot independent samples!Examine the differencesRandomization = which firstIf the differences follow a normal distribution or sample size is large, can apply one-sample t-procedures on the differencesOr JMP: Matched Pairs menuExample: Marriage agesMean = 35.71 yearsSD = 14.56 yearsMean = 33.83 yearsSD = 13.56 yearsExample: Marriage agesAge differences:Mean = 1.875 years, SD = 4.81 yearsPaired vs. Independent SamplesHow test two strategies for rounding third base?Want to “adjust” for person-to-person variability to better compare running strategiesWill helpful is long as slow/fast runners are slow/fast both timesPaired vs. Independent SamplesIf given 2 columns of data, must first ask whether or not they are pairedRandom assignmentAre the values related (e.g., same person, married couple, same shopping item)?Can we mix up the values in one column and not really change things?Example: Marriage agesAge differences:Another way to analyze these data?Sign Test24 couples: 6 with wife older, 2 same age, 16 with husband olderIs it surprising to have as many as 16 of the husband’s older for the spouses are equally likely to be older?Let represent the probability the husband is olderH0: = .5 (equally likely)Ha: > .5 (husband tends to be older)Sign TestCan we apply our normal approximation?Risky, sample size is fairly smallCoin Tossing applet22 tossesTo DoHave a nice 3 day weekend!Investigation 6 due TuesdayAsk about typos!Will be readings/practice problems posted, will be a review handout posted this
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