Repeated Measures ANOVA.doc

Repeated Measures Lecture - 361/17/2020Repeated Measures T&F Ch. 8The analyses considered here are those involving comparison of means in two or more research conditions when either the same people or matched people have participated in the conditions.Two major categories of design1. Participants as own controls design. (Also called Within Subjects designs.)Same people participant in all conditions of the research.Simplest: 2 conditions; Comparing performance of a group of people before treatment and after treatment. Called a Before-After or Pre-Post design. Longitudinal studies comparing performance of people over multiple time periods.So many repeated measures designs involve comparisons over time.Others use the same people in two difference experimental conditions.We gave participants the Big Five under instructions to respond Honestly.We gave the same participants the Big Five under instructions to fake good.We compared mean conscientiousness scores in the honest condition with mean C scores in the faking condition.The key advantage of repeated measures designs is the similarity of participants in the two or more conditions. For this reason, the maximum similarity is achieved by using the same people in all conditions. But there are many designs in which you cant use the same people. Learning designs are a good example. Once youve learned something, you cant unlearn it. The next design is a way around that.2. Matched participants designs.Different people experience the different conditions, but theyre matched with respect to one or more variables that are correlated with the dependent variable, making them “as if” they were the same people in each condition. Of course, you cant match on everything, so matched participants are not as nearly identical as participants matched with themselves.3. Cloned participants designs!?Having your cake and eating it to. This is a way of having nearly perfectly matched participants without having to use the same people in all conditions. The ultimate matching.Advantages of RM designs1. Absence of confounds from extraneous variables. Since the people in each condition are the same or are matched, differences found between conditions are more likely to be due to treatment differences rather than to participant differences on variables were not interested in.2. Increase in Power.Repeated measures designs offer increased power for the same or smaller samples when compared with between subjects designs.Consider the relationship between the independent groups t-test and the correlated groups t-test.The correlated-groups t-test is often expressed asX-bar1 X-bar2-S12 + S22 2rS1S2r is the correlation between matched participants.-NIf S1=S2=S, this can be rewritten asX-bar1 X-bar2t = - 2S2 (1-r) - NThe key to this is the (1-r) part. r is the correlation between the paired scores. In an independent groups design, r = 0. In a repeated measures design, r is usually 0.This means that for a given difference in means (X-bar1 X-bar2), the larger the value of r, the smaller the denominator and therefore the bigger the value of t. The bigger the value of t, the more likely it is to be a rejection t.That is, power to detect a difference is a positive function of r, the larger the correlation between paired scores, the greater the likelihood of detecting a difference, if there is a difference.So designs with a positive correlation between scores in the two conditions will be more powerful than designs with zero correlation, e.g., independent groups designs.Of course, if there is no difference between the means of the two populations, then power is not an issue. But if there IS a difference between the population mean, the correlated groups design will be more likely to detect it. The data matrix and repeated measures designsBetween Subjects Designs: Different conditions are represented in different rows of the data matrix.Condition 1Condition 2Repeated Measures Designs: Different conditions are represented in different columns of the data matrix.Condition 2Condition 1Data Matrix of Designs with 2 Repeated Measures FactorsThis example has two repeated measures factors, one with 2 levels and one with 3.Example: Two types of material are being taught material involving multiplication and material involving division. Three data collection time periods are used at equally spaced intervals.Levels of inner factorLevels of outer factorDivisionMultiplicationMultiplication Time 2Time 1Time 3Time 3Time 2Time 1Combination Designs: Between Subjects and Repeated Measures factors . . .1B 1W: In this example, the Between-subjects factor has two levels and the Repeated Measures factor has 3. For example, two ways of teaching statistics (with lab vs. without) measured across 3 tests.LabT1LabT2LabT3NoLabT1NoLabT2NoLabT3The simplest type of repeated measures analysis the paired samples t-test.The data editorThe paired sample t as an analysis of difference scores.Null hypothesis is that the mean of the difference scores is 0.GET FILE=G:MdbR0DataFilesWrensen_070114.sav.DATASET NAME DataSet1 WINDOW=FRONT.T-TEST /TESTVAL=0 /MISSING=ANALYSIS /VARIABLES=dcons /CRITERIA=CI(.95).T-TestDataSet1 G:MdbR0DataFilesWrensen_070114.savOne-Sample StatisticsNMeanStd. DeviationStd. Error Meandcons166.710.8431.0654One-Sample TestTest Value = 0 tdfSig. (2-tailed)Mean Difference95% Confidence Interval of the DifferenceLowerUpperdcons10.854165.000.7102.581.839One-way Repeated Measures ExampleData from Altman, D. G. Practical Statistics for Medical Research. (Data on next page.)Data are from Table 12.2, p. 327. Table 12.2 shows the heart rate of nine patients with congestive heart failure before and shortly after administration of enalaprilat, an angiotensin-converting enzyme inhibitor. Measurements were taken before and at 30, 60, and 120 minutes after drug administration.Presumably, the drug should lower heart rate. So this is a basic longitudinal study, although the intervals between measurements are not equal.SUBJECT TIME0 TIME30 TIME60 TIME120 1 96 92 86 92 2 110 106 108 114 3 89 86 85 83 4 95 78 78 83 5 128 124 118 118 6 100 98 100 94 7 72 68 67 71 8 79 75 74 74 9 100 106 104 102Analyze - General Linear Model - Repeated MeasuresName the repeated-measures factor, and enter the number of levels. Then click on Add.Mike demo this live.Move the names of the columns representing the levels of the repeated measures factor into the appropriate place under Within-Subjects Variables. (Note the change in terminology from Repeated Measures to Within-Subjects.)Check the usual set of optional statistics.Since the 1st measurement appears to be special, I specified a dummy variable repeated measures contrast in which the all levels were compared with level 1 of the RM factor.The syntax for the analysis.GLM time0 time30 time60 time120 /WSFACTOR = time 4 Simple(1) General Linear Model - Repeated Measures.The syntaxGLM ss_math_tot1 ss_math_tot2 ss_math_tot BY group0Vs1 /WSFACTOR=time 3 Polynomial /METHOD=SSTYPE(3) /PLOT=PROFILE(time*group0Vs1) /PRINT=DESCRIPTIVE ETASQ OPOWER PARAMETER /CRITERIA=ALPHA(.05) /WSDESIGN=time /DESIGN=group0Vs1.The cell means displayed in a 2 way tableGroupTime1Time2Time3Control234249261Bridge233250261Ive rarely seen such a striking affirmation of the null.Repeated Measures ANOVA -1 Between Groups Factor2 Repeated Measures FactorsThe data are from Myers & Well, p 313 although the story describing the data is different from theirs. Memory for two types of event, one of some interest to the persons (C1), the other of less interest to them (C2) is tested at three time periods (B1, B2, and B3). The tests are performed under two conditions of distraction, much distraction (A1) and little distraction (A2). The interest here is on the effects of interest on memory, the effects of distraction on memory, and the the interaction of interest and distraction whether the effect of distraction is the same for memory of interesting and uninteresting material. The data matrix looks as follows . . Specify two repeated-measures factors, each with the correct number of levels. Then make sure you put the correct column with the correct factor specification. Note that factor C is specified first in parentheses.UninterestingmaterialInterestingmaterialC1B1 C1B2 C1B3 C2B1 C2B2 C2B3 AEnter “Outer” factor 1st 80 48 45 76 45 41 1LittledistractionMuch distraction 46 37 34 42 34 33 1 51 49 36 45 38 30 1 72 57 50 66 51 42 1 68 40 33 58 38 30 1 65 44 36 56 37 28 1 70 55 52 68 57 56 2 88 69 66 91 74 70 2 58 60 54 50 41 38 2 63 57 52 61 58 56 2 78 81 75 79 78 74 2 84 82 80 80 73 76 2GLM c1b1 c1b2 c1b3 c2b1 c2b2 c2b3 BY a /WSFACTOR = c 2 Polynomial b 3 Polynomial /METHOD = SSTYPE(3) /PLOT = PROFILE( b*a*c )C is outer factor.B is inner factor /PRINT = DESCRIPTIVE ETASQ OPOWER HOMOGENEITY /CRITERIA = ALPHA(.05) /WSDESIGN = c b c*b /DESIGN = a .If this werent an example, wed look into this.Hypotheses testedThe C (Interest) - Repeated Measures Main EffectC1B1 C1B2 C1B3 C2B1 C2B2 C2B3 ASample is treated as one giant group for the repeated measures comparisonsMuch distractionLittledistraction 80 48 45 76 45 41 1 46 37 34 42 34 33 1Sample is treated as one giant group for the repeated measures comparisons 51 49 36 45 38 30 1 72 57 50 66 51 42 1 68 40 33 58 38 30 1 65 44 36 56 37 28 1 70 55 52 68 57 56 2 88 69 66 91 74 70 2 58 60 54 50 41 38 2 63 57 52 61 58 56 2 78 81 75 79 78 74 2 84 82 80 80 73 76 2C2C1The B (Time) - Repeated Measures Main EffectC1B1 C1B2 C1B3 C2B1 C2B2 C2B3 AMuch distr