Related Sample

Hypothesis Tests: Two Related SamplesAKA Dependent Samples TestsAKA Matched-Pairs TestsCal State Northridge320Andrew Ainsworth PhDMajor Points2Related samples? Matched Samples?Difference scores?An examplet tests on difference scoresAdvantages and disadvantagesEffect sizePsy 320 - Cal State NorthridgeReview: Hypothesis Testing3State Null HypothesisAlternative HypothesisDecide on (usually .05)Decide on type of test (distribution; z, t, etc.)Find critical value & state decision ruleCalculate testApply decision rulePsy 320 - Cal State NorthridgeRelated/Dependent Samples4Samples can be related for 2 basic reasonsFirst, they are the same people in both samplesThis is usually called either repeated measures or within subjects designPsy 320 - Cal State NorthridgeRelated/Dependent Samples5Samples can be related for 2 basic reasonsSecond, individuals in the two sample are so similar they are essentially the same personOften called a matched-pairs designPsy 320 - Cal State NorthridgeRelated/Dependent SamplesRepeated MeasuresThe same participants give us data on two measurese.g. Before and After treatmentIQ levels before IQPLUS, IQ levels after IQPLUS

6Psy 320 - Cal State NorthridgeRelated/Dependent SamplesMatched-Pairs DesignTwo-separate groups of participants; but each individual in sample 1 is matched (on aspects other than DV) with an individual in sample 2

7Psy 320 - Cal State NorthridgeRelated/Dependent Samples8With dependent samples, someone high on one measure is probably high on other.Scores in the two samples are highly correlatedSince they are correlated cannot treat them as independent (next chapter)However the scores can be manipulated (e.g. find the differences between scores)Psy 320 - Cal State NorthridgeDifference Scores9Calculate difference between first and second scoree. g. Difference = Before - AfterBase subsequent analysis on difference scoresIgnoring Before and After dataPsy 320 - Cal State NorthridgeAn Example10Therapy for rape victimsFoa, Rothbaum, Riggs, & Murdock (1991)One group received Supportive CounselingMeasured post-traumatic stress disorder symptoms before and after therapyPsy 320 - Cal State Northridge10Foa, E.B., Rothbaum, B.O., Riggs, D.S., & Murdock, T.B. (1991). Treatment of posttraumatic stress disorder in rape victims: A comparison between cognitive-behavioral procedures and counseling. Journal of Consulting and Clinical Psychology, 59, 715-723.

Hypotheses?11H0: symptoms/before symptoms/after H1: symptoms/before > symptoms/afterORH0: symptoms/before - symptoms/after 0H1: symptoms/before - symptoms/after > 0ORH0: (symptoms/before - symptoms/after) 0H1: (symptoms/before - symptoms/after) > 0Psy 320 - Cal State NorthridgeSupportive Therapy for PTSD12

Supportive Therapy for PTSD13We want to compare the means to see if the mean after is significantly larger than the mean beforeHowever, we cant perform the test this way (reasons Ill explain in the next chapter)Since scores in the 2 conditions come from the same people we can use that to our advantage (subtract post from pre)Psy 320 - Cal State NorthridgeCalculating a difference score14

Psy 320 - Cal State NorthridgeSupportive Therapy for PTSD15

We now have a single sample problem identical to chapter 12.These are change scores for each person.Psy 320 - Cal State NorthridgeResults16The Supportive Counseling group decreased number of symptomsWas this enough of a change to be significant?Before and After scores are not independent.See raw data (subjects high stayed high, etc.)Scores are from the same person measured twice so obviously dependent samplesPsy 320 - Cal State NorthridgeResults17If no change, mean of differences should be zeroSo, test the obtained mean of difference scores (well call D) against m = 0.Then, use same test as in Chapter 12.We dont know s, so use s and solve for tPsy 320 - Cal State NorthridgetD test18df = n - 1 = ___ - 1 = ___

Psy 320 - Cal State Northridget test198 df, = .05, 1-tailed tcrit = _____We calculated t = _____Since ____ > ____, reject H0Conclude that the mean number of symptoms after therapy was less than mean number before therapy.Supportive counseling seems to help reduce symptomsPsy 320 - Cal State NorthridgeSPSS Printout20

Psy 320 - Cal State NorthridgeRelated/Dependent Samples21AdvantagesEliminate subject-to-subject variabilityControl for extraneous variablesNeed fewer subjectsDisadvantagesOrder effectsCarry-over effectsSubjects no longer naiveChange may just be a function of timeSometimes not logically possiblePsy 320 - Cal State NorthridgeEffect Size Again22We could simply report the difference in means.Difference = 8.22But the units of measurement have no particular meaning to us - Is 8.22 large?We could scale the difference by the size of the standard deviation.Psy 320 - Cal State NorthridgeEffect Size23

Note: This effect size d is not the same thing as D (difference)Its called d here because it is in reference to Cohens dPsy 320 - Cal State NorthridgeEffect Size24The difference is approximately 2 standard deviations, which is very large.Why use standard deviation of Before scores?Notice that we substituted statistics for parameters.Psy 320 - Cal State NorthridgeSample #1Pre-Treatment

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Sheet1PersonPre - TreatmentPost - Treatment12115224153211742620532176272072188251991810Mean23.88915.667SD4.1974.243

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Sheet1PersonPre - TreatmentPost - TreatmentDifference (Pre - Post)12115___22415___32117___42620___5321715627207721813825196918108Mean23.88915.6678.222SD4.1974.2433.598

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Sheet1PersonDifference (Pre - Post)1___2___3___4___515677138698Mean8.222SD3.598

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