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# Psych 2220 Psych 2220

OSU

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This 5 page Class Notes was uploaded by MadsSwart on Sunday March 13, 2016. The Class Notes belongs to Psych 2220 at Ohio State University taught by Joseph Roberts in Winter 2016. Since its upload, it has received 21 views.

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Date Created: 03/13/16

Psych 2220 – Chapter 10: Paired Samples t tests - Related samples t test - Repeated measures t test - Dependent samples t test Paired samples - A design where two observations are related to each other, and the difference between observations is the focal dependent measure. o Correlation also deals with paired variables – try to determine strength and direction of relationship o Related-samples tests capitalize on a known association [without indepence] between paired observations A and B. with that knowledge, we increase our power to detect differences between paired observations. Regular t test vs. paired samples - Earlier t test compares one sample to a population, testing the null hypothesis that there’s no difference between the mean sampled from and the mean we hypothesized. - Paired samples gather paired observations and compute difference for each pair. Compare one sample of differences to the population of possible differences for which µ =0Dif there is no difference between observations o Null hypothesis still contains zero difference; µ -0 D Paired samples t test approach Gather your paired observations Difference scores- your data are the difference scores for each pair of related observations. So… - N number of pairs of observations D - Mean (M or µ) mean difference scores ( or µD) - SD (s) standard deviation of difference scores (S ) D - SM Standard error of difference scores of (s orM SD ) Possible use of paired samples - Most common: same people, measured twice [two conditions or different times] - Less common but equally valid: different people bound by a clear one- to-one relationship [spouses, siblings, interaction partners, etc.] or even unrelated people matched on some extra variable that correlates with the DV. Study design examples: • Measure depression, then give CBT, then measure depression. • Measure parent's intent to quit smoking BEFORE and AFTER an educational intervention presenting their child’s biochemical SHS exposure data to the parent. The t Statistic for Differences Difference scores compared to population of difference scores • (one-sample t test: scores compared to population of scores) Null hypothesis: no difference between means, i.e. the mean difference is zero. H0: μ1= μ2 OR μ1 - μ2 = 0 OR μD = 0 (Above is two-tailed; one-tailed is possible but not shown) The Formula We compare an average difference between means to the null hypothesis prediction of zero difference. ´ t =D−μ D paired S´ D S sD´ D √ N M−μ M tM= sM SX M−μ M S MS =X = √ N √N Example mean(test1) = 62.6 sd(test1) = 30.26 mean(test2) = 89.4 sd(test2) = 7.83 N = 5 Test Test Dif 1 2 50 85 35 30 80 50 89 97 8 100 98 -2 44 87 43 One (bad) approach using one-sample procedures: Treat one mean as if it were a population mean. • mean(Test2) = 89.4 • Compare Test1 to a hypothetical population with μ = 89.4. • What’s the critical t value for this one-sample t test? Instead, conduct a one-sample t test on the Difference: • di ff = test2 - test1 • mean(di ff) = 26.8 • sd(di ff) = 22.64 • What’s the critical t value for a one-sample t test of Diff scores? • This is the same as a paired samples t test. Why is the second approach better? • A sample mean is not a population mean. Treating it as such will sometimes obscure a true difference and sometimes make sampling error look like a real effect. • If there is any predictive relationship between the score pairs, then computing differences cuts down on random variation. Advantages to Repeated Measures Variability between subjects not a problem, b/ce each participant serves as his/her own control • If you have a very heterogeneous sample (lots of variation in scores between different people), that variability is chopped out of the calculation with a paired-samples approach. ´ t = D−μ D≈ Signawithinisebetween D SD Noisewithinisebetween Same statistical power with fewer total people, or much greater statistical power with the same number of people as a non-repeated design • Cutting out the between-participants “noise” from your measurements leads to much higher capacity for detecting any “signal.” • More statistically powerful studies are less costly studies in implementation. (Would you rather record 100 measurements, or 20, if you get the same info either way?) In which group is the difference most apparent? • The visual “noise” that interferes with identifying the direction of difference (on the left) is analogous to the statistical “noise” that using a paired- samples approach removes (right side). • Removing that noise increases statistical power Test 1 Test 2 Test 1 Test 2 0 5 0 5 -41 -27 0 14 19 43 0 24 100 88 0 -12 44 36 0 -8 Disadvantages to Repeated Measures Order effects: Taking one observation can affect later observations recorded from same individuals. • The presence of order effects poses a threat to internal validity. Even if we detect some difference, we can’t appropriately claim that our intended manipulation is the cause of the difference. One solution: counterbalancing Effect Sizes for paired samples Recall that we use Cohen’s d as a way of describing the extent of difference between a sample mean and some target value (a hypothesized mean, a zero-point, etc.). Cohen’s d is the standardized indicator of effect size, because it describes that difference in the units of observed variation: standard deviations. d = 1.5 means a 1.5 standard deviation difference. A simple extrapolation from Ch.9 material is to develop the formula for a paired-samples Cohen’s d using the standard deviation of the di fference,DS . ^ MD−μ D (M 1M )20 d= = sD SD When we have paired samples, we no longer want to compare one sample mean to an arbitrary target value. Instead, we compare one sample mean to the other sample mean (which is formally the same as comparing the mean difference to zero). Cohen’s d should still describe that effect size in a standardized way, but we want it to be descriptively useful. • It’s often NOT useful to present effect size in terms of the standard deviation of difference scores, because we don’t directly perceive difference scores. • It often IS descriptively useful to present effect size in terms of observed variation among individual observations: the sample standard deviation. Alternate ways of calculating Cohen’s d for paired samples Use the denominator that’s most descriptively useful and appropriate to your data. How do you want people to understand this effect size? • Use SD of control group, of pre-intervention scores, or the mean of two groups’ SDs. M −M M −M d= 1 2 d= 1 2 S Time 1 Scontrol ^ M1−M 2 d= s Confidence Intervals How do you think these work? Just need to know where to get your s & sM from. Confidence Intervals for Repeated Measures Just like other intervals, we want to build these such that we can be confident they’ll overlap the population mean difference. Center the CI on sampled mean difference, M . D Extend outward by t criticalndard errors of the difference, s ofMthe difference. t (¿¿crit x MD) M Upper±¿ Dlower D

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