Psy 420 – Midterm 2 Part 2 (Version A) – In lab (50 points total)A researcher wants to know if memory is improved by repetition (Duh!). So he shows a group of five participants a list of 30 words at for different time points. At each time point the participants are given a free recall task. The number of words recalled at each trial is recorded below for each participant. Time 1 Time 2 Time 3 Time 4 S1 10 18 20 26 S2 16 24 26 31 S3 10 18 19 28 S4 16 24 24 30 S5 13 21 21 29 Memory over time study Within-Subjects FactorsMeasure: MEASURE_1TIME1TIME2TIME3TIME4TIME1234DependentVariable Descriptive Statistics13.00003.00000521.00003.00000522.00002.91548528.80001.923545TIME1TIME2TIME3TIME4MeanStd. DeviationN Tests of Within-Subjects EffectsMeasure: MEASURE_1628.4003209.467276.220.000.986628.4001.704368.875276.220.000.986628.4002.838221.407276.220.000.986628.4001.000628.400276.220.000.9869.10012.7589.1006.8141.3359.10011.353.8029.1004.0002.275Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSourceTIMEError(TIME)Type III Sumof SquaresdfMean SquareFSig.Partial EtaSquaredTests of Within-Subjects ContrastsMeasure: MEASURE_1585.6401585.640525.238.000.9921.80011.8002.667.178.40040.960140.96084.454.001.9554.46041.1152.7004.6751.9404.485TIMELinearQuadraticCubicLinearQuadraticCubicSourceTIMEError(TIME)Type III Sumof SquaresdfMean SquareFSig.Partial EtaSquared Tests of Between-Subjects EffectsMeasure: MEASURE_1Transformed Variable: Average8988.80018988.800321.891.000.988111.700427.925SourceInterceptErrorType III Sumof SquaresdfMean SquareFSig.Partial EtaSquared 1. Based on the output is (Time1 and Time 4) vs. (Time 2 and Time 3) a significant comparison? How do you know (it’s right in front of you so think about it)? And how much percent of variance is accounted for by this comparison? No calculations involved. (2 points) 2. Perform a comparison of (Time 1 and Time 2) vs. (Time 3 and Time 4) by hand and test it for significance. Show all work. (6 points)The pharmaceutical companies are trying to figure out which is the best medication to treat erectile dysfunction (ED), Viagra (Drug 1) and Levitra (Drug 2). An independent company conducts clinical trials to test the treatments using three trials per treatment with 10 participants. Scores indicate the number of hours that the “treatment” lasted. Viagra Levitra T1 T2 T3 T1 T2 T3 S1 11 14 15 23 22 19 S2 7 11 12 19 18 14 S3 6 11 11 19 19 14 S4 6 10 11 20 19 14 S5 8 13 13 21 21 16 S6 7 11 10 20 20 16 S7 16 20 21 28 28 23 S8 7 12 13 22 21 16 S9 9 14 14 22 22 18 S10 12 15 17 24 23 19 Output for Drug by Trial Study Within-Subjects FactorsMeasure: MEASURE_1VT1VT2VT3LT1LT2LT3TRIAL123123DRUG12DependentVariable Mauchly's Test of SphericitybMeasure: MEASURE_11.000.0000.1.0001.0001.000.5464.8402.089.688.771.500.4286.7852.034.636.694.500Within Subjects EffectDRUGTRIALDRUG * TRIALMauchly's WApprox.Chi-SquaredfSig.Greenhouse-GeisserHuynh-FeldtLower-boundEpsilonaTests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables isproportional to an identity matrix.May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in theTests of Within-Subjects Effects table.a. Design: Intercept Within Subjects Design: DRUG+TRIAL+DRUG*TRIALb.Tests of Within-Subjects EffectsMeasure: MEASURE_1984.1501984.1501152.800.000.992984.1501.000984.1501152.800.000.992984.1501.000984.1501152.800.000.992984.1501.000984.1501152.800.000.9927.6839.8547.6839.000.8547.6839.000.8547.6839.000.85446.900223.45095.211.000.91446.9001.37634.09495.211.000.91446.9001.54230.41795.211.000.91446.9001.00046.90095.211.000.9144.43318.2464.43312.381.3584.43313.877.3194.4339.000.493235.3002117.650394.602.000.978235.3001.272184.919394.602.000.978235.3001.388169.546394.602.000.978235.3001.000235.300394.602.000.9785.36718.2985.36711.452.4695.36712.490.4305.3679.000.596Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSourceDRUGError(DRUG)TRIALError(TRIAL)DRUG * TRIALError(DRUG*TRIAL)Type III Sumof SquaresdfMean SquareFSig.Partial EtaSquared Tests of Within-Subjects Contrasts Measure: MEASURE_1 Source DRUG TRIAL SS df MS F Sig. Partial Eta Squared TRIAL Trial 1 vs. Trial 2 68.450 1 68.450 101.826 .000 .919 Trial 2 vs. Trial 3 72.200 1 72.200 112.034 .000 .926 Error(TRIAL) Trial 1 vs. Trial 2 6.050 9 .672 Trial 2 vs. Trial 3 5.800 9 .644 Tests of Between-Subjects EffectsMeasure: MEASURE_1Transformed Variable: Average5088.05015088.050295.425.000.970155.006917.223SourceInterceptErrorType III Sumof SquaresdfMean SquareFSig.Partial EtaSquaredEstimated Marginal Means 1. DRUGMeasure: MEASURE_111.900.9859.67114.12920.000.88318.00221.998DRUG12MeanStd. ErrorLower BoundUpper Bound95% Confidence Interval 2. TRIALMeasure: MEASURE_115.350.93113.24417.45617.200.90415.15419.24615.300.96113.12617.474TRIAL123MeanStd. ErrorLower BoundUpper Bound95% Confidence Interval 3. DRUG * TRIALMeasure: MEASURE_18.9001.0166.60211.19813.100.92411.00915.19113.7001.04411.33816.06221.800.86719.83923.76121.300.89519.27523.32516.900.91214.83618.964TRIAL123123DRUG12MeanStd. ErrorLower BoundUpper Bound95% Confidence Interval Profile Plots Estimated Marginal Means of MEASURE_1TRIAL321Estimated Marginal Means24222018161412108DRUG123. Did we meet the sphericity assumption for all variables? How do you know? Why isn’t sphericity test for the Drug variable? (2 points) 4. Create an ANOVA summary table that looks a little more like we’re used to. Include all sources of variance. (3 points) Source SS DF MS F Total 5. Why is there a main effect for trial (where are the differences?)? When describing it include the directionality of the comparison. (4 points). 6. Base on the line graph why is there a significant interaction (in words)? (2 points)7. Based on the significant effects what other follow-up analysis(es) would you perform (in words)? (1 point) An experimenter is doing a study where variable A is a between groups variable and variables B and C are within