Repeated Measures ANOVA - - The University of … · Web viewThat is, power to detect a difference is a positive function of r - the larger the correlation between paired scores,

Repeated Measures Lecture - 1 5/7/2023

Traditional Repeated Measures: T&F Ch 8

The 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 design

1. Participants as their 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 several time periods.

So, many repeated measures analyses involve comparisons over time.

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 can’t use the same people. Learning designs are a good example. Once you’ve learned something, you can’t unlearn it. The next design is a way around that.

2. Matched participants designs. (Matched people)

Different people experience the different conditions, but they’re 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 can’t match on everything, so matched participants are not as nearly identical as participants matched with themselves.

3. Cloned participants designs!!!!!??? (Totally matched organisms)

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.

Repeated Measures Lecture - 2 5/7/2023Advantages of Repeated Measures designs

1. Eliminating Confounds. In Between-Subjects designs, an extraneous variable may affect one group, but not the other, creating a confound. Within-Subjects designs are largely free of such 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 we’re 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 as

X-bar1 – X-bar2

----------------------------------------------S1

2 + S22 – 2rS1S2 r is the correlation between matched participants.

------------------------N

If S1=S2=S, this can be rewritten as

X-bar1 – X-bar2

t = ------------------------ 2S2 (1-r) -------------- N

The 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 of the t statistic 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.

Repeated Measures Lecture - 3 5/7/2023 How should data be put in the data editor for repeated measures designs?

Between-subjects Designs: Different conditions are represented in different rows of the data matrix.

Traditional Repeated Measures Designs: Different conditions are represented in different columns of the data matrix with each row representing a person or matched persons.

Condition 1

Condition 2

Condition 1

Condition 2

Lab

T1

Lab

T2

Lab

T3

NoLab

T1

NoLab

T2

NoLab

T3

Repeated Measures Lecture - 4 5/7/2023Data Matrix of Designs with 2 Repeated Measures Factors

This 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.

Combination 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.

I need to point out, that these data structures are appropriate for traditional repeated measures analyses.

Analyses using multilevel modeling procedures require a different data structure. Argh!!

Time 1

Time 2

Time 3

Time 1

Time 2

Time 3

Multiplication Multiplication Division Levels of outer factor

Levels of inner factor


The simplest type of repeated measures analysis – the paired samples t-test.

Comparing conscientiousness under honest instructions with conscientiousness under faking instructions.The data editor

4.407 – 3.697d = ------------------------ = 1.04 .685

This is a HUGE effect size.


The paired sample t as an analysis of difference scores.

We’ll get the exact same result by analyzing the single column of f-h difference scores.

Null hypothesis is that the mean of the difference scores is 0.GET FILE='G:\MdbR\0DataFiles\Wrensen_070114.sav'.DATASET NAME DataSet1 WINDOW=FRONT.T-TEST /TESTVAL=0 /MISSING=ANALYSIS /VARIABLES=dcons /CRITERIA=CI(.95).

T-Test[DataSet1] G:\MdbR\0DataFiles\Wrensen_070114.sav

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

dcons 166 .710 .8431 .0654

One-Sample Test

Test Value = 0

t df Sig. (2-tailed) Mean Difference

95% Confidence Interval of the Difference

Lower Upper

dcons 10.854 165 .000 .7102 .581 .839

From above, for reference . . .

Many statistical procedures involving repeated measures make use of difference scores.


One-way Repeated Measures ANOVA ExampleData from Altman, D. G. Practical Statistics for Medical Research. 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 9 100 106 104 102

Analyze -> General Linear Model -> Repeated MeasuresMike – demo this live.

Name the repeated-measures factor, and enter the number of levels. Then click on [Add].

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 of the SPSS dialog boxes from Repeated Measures to Within-Subjects.)

REALLY!!???

Repeated Measures Lecture - 8 5/7/2023Using Dummary Variable coding of Time Points

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.

Dummy variable coding is called Simple coding in SPSS.

Since the times are not equally spaced – 30,60,120 – I can’t easily use orthogonal polynomial contrasts to look at the shape of change over time. Drat!!

Check the usual set of optional statistics.

Output for the Parameter Estimates has been erased below, since it was of no value to interpretation of these results.

Plots are a natural adjunct to repeated measures analyses.

Generally speaking you should always make Time the horizontal axis if Time is in your analysis.

Repeated Measures Lecture - 9 5/7/2023The syntax for the analysis.GLM time0 time30 time60 time120 /WSFACTOR = time 4 Simple(1) <<<<---- Specifies the RM factor and the contrast. /METHOD = SSTYPE(3) /PLOT = PROFILE( time ) /PRINT = DESCRIPTIVE ETASQ OPOWER PARAMETER /CRITERIA = ALPHA(.05) /WSDESIGN = time .

General Linear Model

Hypothesis Tested in the Analysis

The null hypothesis that is tested in the analysis can be viewed in two different and essentially equivalent ways.

Version 1 of the Null hypothesis: Equality of Means

The first is that the four means are all equal: H0: µTime0 = µTime30 = µTime60 = µTime120

Version 2 of the Null hypothesis: Means of Differences Equal 0

If the means are all equal then the differences between pairs of means are all 0.

Compute µDiff1 = µTime0 - µTime30

µDiff2 = µTime30 - µTime60 (Any other 3 nonredundant differences would work.)µDiff3 = µTime60 - µTime120

Then the 2nd version of the null hypothesis is: H0: µDiff1 = µDiff2 = µDiff3 = 0

Note that the = 0 at the end of the 2nd null is very important. The null is that every difference is 0.

Repeated Measures Lecture - 10 5/7/2023The Sequence of Tests performed by GLM

The Multivariate test that all mean differences are 0. The first tests performed by GLM are what are called Multivariate Tests. They're called that because they are a test of the hypothesis that the multiple difference variables (3 in our case) are all 0. So, they’re multivariate tests.

Four different multivariate tests are performed. Each is based on slightly different assumptions, and in some instances, the results for the four may be different. In this case, they are all equivalent.

The multivariate tests are the most robust tests of the null hypothesis. This means that they are less affected by nonnormality of the distributions than are the tests that follow. The price paid for that robustness is loss of power. The multivariate tests are less powerful than those that follow. This means that if you're worried about power and are hoping to reject the null, rejecting the null with the multivariate tests means you're home free. But if you fail to reject the null with the multivariate tests, then you have to hope that you meet the restrictions for the more powerful tests that follow.

In this case, we fail to reject the null using the multivariate tests.

The test of sphericity . When conducting a one-way repeated measures ANOVA, the values of variances and covariances should fall within specific ranges. If this is so, the matrix is said to meet the sphericity criterion. If the sphericity criterion is met, then the most powerful test of the null can be employed. If it not met, then either the multivariate test must be used, or one of the special tests devoted to getting around the failure to find sphericity must be employed. Fortunately, SPSS gives you all the tests, so you can pick the one which is appropriate. The null hypothesis in Mauchly's test is that the sphericity condition holds, so we generally hope to not reject the null.

In this instance, the condition of sphericity holds (the test is not significant).

Whew – the sphericity condition is met.

Repeated Measures Lecture - 11 5/7/2023The Univariate Tests. Since the sphericity condition is met, we can use the test of significance printed in the top line of the following box.

If sphericity didn't hold, then we would either report the multivariate F above or report one of the F's from the 2nd, 3rd, or 4th lines of the table below. Each of them performs an adjustment for lack of sphericity. The specifics of the adjustment vary across tests. Note that in the top three lines, the null is rejected. The last line reports the most conservative adjustment. But since sphericity holds, we can report the F in the top line and conclude that there are significant differences between mean heart rates across time periods.The difference between these results and those of the Multivariate tests shown above highlight the power differences between the two types of tests. If you want to detect small differences, use the tests shown below.

Tests of user-specified Contrasts The following tests are of the contrasts specified above on page 8. If no contrasts had been specified, it would not be printed. The individual contrasts compare the means of the 30-, 60-, and 120-minute measurements with the pre-measure. The means at the 60- and 120-minute intervals were significantly lower than the pre-measure mean as we might expect if it took time for the drug to take effect.

Tests of Between-Subjects Effects. What are between-subjects factors doing in a repeated measures analysis? The answer is that there is only a technical between-subjects factor here - the difference between the mean of all the scores and 0, known in regression parlance as the intercept. That's what's being tested in the box below. The null hypothesis is that the intercept is 0. Don’t let its presence confuse you.


The plot below is that printed by GLM.


Repeated Measures Profile AnalysisA 2 x 5 Repeated Measures Analysis

A profile is a collection of numbers defining the levels of variables within a group. (See following page.)

For example, the set of Big 5 Scale Scores for a person – Ext, Agr, Con, Sta, and Opn define the Big 5 profile for that person. The set of Big 5 scale scores for a group would define the profile for that group.

This example compares the Big 5 profile for a group of student in two conditions – when told to respond honestly and when given an incentive to fake good.

Since the profiles of the same people are being compared at two different times, the analysis will involve two repeated measures factors.

The first factor is the instructional condition factor – responding with simply instructions to do so honestly vs responding with instruction to do so honestly but with an incentive to fake good.. These will be called the Honest and Incentive Faking Conditions.

The second factor is the Big 5 dimension factor. It has 5 levels – E vs A vs C vs S vs O.

For this analysis, the data occupy 10 columns of the data editor – 5 columns of Big 5 scale scores for the Honest condition and 5 columns for the Incentive Condition. Here are the first 10 cases of the data editor . . .

Each cell contains the mean of responses to 10 items from the IPIP 50-item sample Big 5 questionnaire.

In the analysis, three major comparisons will be made . . .

1. The main effect of Faking Conditon – Mean of all responses in the Honest vs. Mean of all in the Incentive condition.

2. The main effect of Big 5 dimension – Mean of all responses in to Ext items vs mean of Agr items vs. mean of Con items vs mean of Sta items vs mean of Opn items.

3. The interaction of Faking Conditon and Big 5 Dimensions - A comparison of differences in hones and incentive in Ext vs the difference in Agr vs the difference in Con vs the differnce in Sta vs the difference in Opn.

Repeated Measures Lecture - 14 5/7/2023GET FILE='G:\MDBR\0DataFiles\IncentiveData110923 w wpt 150416.sav'.DATASET NAME DataSet2 WINDOW=FRONT.DATASET ACTIVATE DataSet2.DATASET CLOSE DataSet1.

Profile of New York building heights


GLM hext fext hagr fagr hcon fcon hsta fsta hopn fopn /WSFACTOR=dim 5 Polynomial faking 2 Polynomial /METHOD=SSTYPE(3) /PLOT=PROFILE(dim*faking) TYPE=LINE ERRORBAR=NO MEANREFERENCE=NO YAXIS=AUTO /PRINT=DESCRIPTIVE ETASQ OPOWER PARAMETER /CRITERIA=ALPHA(.05) /WSDESIGN=dim faking dim*faking.

Repeated Measures Lecture - 16 5/7/2023General Linear Model

Within-Subjects FactorsMeasure: MEASURE_1

dim fakingDependent

Variable1 1 hext

2 fext2 1 hagr

2 fagr3 1 hcon

2 fcon4 1 hsta

2 fsta5 1 hopn

2 fopn

Descriptive StatisticsMean Std. Deviation N

H Extraversion Scale score 4.50750 .973997 202fext 4.62157 1.010780 202hagr 5.25040 .822099 202fagr 5.35371 .811655 202hcon 4.79299 .805177 202fcon 5.02456 .853447 202hsta 3.97874 1.095128 202fsta 4.43952 1.133031 202hopn 4.72693 .729562 202F Openness Scale Score 4.82524 .749732 202

Multivariate Testsa

Effect Value FHypothesis

df Error df Sig.Partial Eta Squared

Noncent. Parameter

Observed Powerc

dim Pillai's Trace .514 52.294b 4.000 198.000 .000 .514 209.175 1.000Wilks' Lambda .486 52.294b 4.000 198.000 .000 .514 209.175 1.000Hotelling's Trace 1.056 52.294b 4.000 198.000 .000 .514 209.175 1.000Roy's Largest Root

1.056 52.294b 4.000 198.000 .000 .514 209.175 1.000

faking Pillai's Trace .173 42.095b 1.000 201.000 .000 .173 42.095 1.000Wilks' Lambda .827 42.095b 1.000 201.000 .000 .173 42.095 1.000Hotelling's Trace .209 42.095b 1.000 201.000 .000 .173 42.095 1.000Roy's Largest Root

.209 42.095b 1.000 201.000 .000 .173 42.095 1.000

dim * faking

Pillai's Trace .248 16.351b 4.000 198.000 .000 .248 65.402 1.000Wilks' Lambda .752 16.351b 4.000 198.000 .000 .248 65.402 1.000Hotelling's Trace .330 16.351b 4.000 198.000 .000 .248 65.402 1.000Roy's Largest Root

.330 16.351b 4.000 198.000 .000 .248 65.402 1.000

a. Design: Intercept Within Subjects Design: dim + faking + dim * fakingb. Exact statisticc. Computed using alpha = .05

Note that the interaction was significant, so we’ll have to leave it in the analyses.


Mauchly's Test of Sphericitya

Measure: MEASURE_1

Within Subjects Effect Mauchly's WApprox. Chi-

Square df Sig.

Epsilonb

Greenhouse-Geisser Huynh-Feldt Lower-bound

dim .738 60.461 9 .000 .875 .893 .250faking 1.000 .000 0 . 1.000 1.000 1.000dim * faking .827 37.962 9 .000 .924 .943 .250Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.a. Design: Intercept Within Subjects Design: dim + faking + dim * fakingb. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.

Tests of Within-Subjects EffectsMeasure: MEASURE_1

Source

Type III Sum of Squares df

Mean Square F Sig.

Partial Eta Squared

Noncent. Parameter

Observed Powera

dim Sphericity Assumed

265.660 4 66.415 57.909 .000 .224 231.638 1.000

Greenhouse-Geisser

265.660 3.501 75.886 57.909 .000 .224 202.729 1.000

Huynh-Feldt 265.660 3.570 74.405 57.909 .000 .224 206.762 1.000Lower-bound 265.660 1.000 265.660 57.909 .000 .224 57.909 1.000

Error(dim) Sphericity Assumed

922.089 804 1.147

Greenhouse-Geisser

922.089 703.658

1.310

Huynh-Feldt 922.089 717.659

1.285

Lower-bound 922.089 201.000

4.588

faking Sphericity Assumed

20.526 1 20.526 42.095 .000 .173 42.095 1.000

Greenhouse-Geisser

20.526 1.000 20.526 42.095 .000 .173 42.095 1.000

Huynh-Feldt 20.526 1.000 20.526 42.095 .000 .173 42.095 1.000Lower-bound 20.526 1.000 20.526 42.095 .000 .173 42.095 1.000

Error(faking) Sphericity Assumed

98.011 201 .488

Greenhouse-Geisser

98.011 201.000

.488

Huynh-Feldt 98.011 201.000

.488

Lower-bound 98.011 201.000

.488

dim * faking Sphericity Assumed

9.702 4 2.426 20.823 .000 .094 83.292 1.000

Greenhouse-Geisser

9.702 3.695 2.626 20.823 .000 .094 76.944 1.000

Huynh-Feldt 9.702 3.773 2.571 20.823 .000 .094 78.564 1.000Lower-bound 9.702 1.000 9.702 20.823 .000 .094 20.823 .995

Error(dim*faking)

Sphericity Assumed

93.652 804 .116

Greenhouse-Geisser

93.652 742.722

.126

Huynh-Feldt 93.652 758.359

.123

Lower-bound 93.652 201.000

.466

a. Computed using alpha = .05


Tests of Within-Subjects ContrastsMeasure: MEASURE_1

Source dim faking

Type III Sum of

Squares dfMean

Square F Sig.Partial Eta Squared

Noncent. Parameter

Observed Powera

dim Linear 18.126 1 18.126 15.944 .000 .073 15.944 .978Quadratic

12.098 1 12.098 10.839 .001 .051 10.839 .906

Cubic 232.202 1 232.202 171.318

.000 .460 171.318 1.000

Order 4 3.234 1 3.234 3.303 .071 .016 3.303 .440Error(dim) Linear 228.514 201 1.137

Quadratic

224.359 201 1.116

Cubic 272.432 201 1.355Order 4 196.785 201 .979

faking Linear

20.526 1 20.526 42.095 .000 .173 42.095 1.000

Error(faking) Linear

98.011 201 .488

dim * faking Linear Linear

1.073 1 1.073 10.434 .001 .049 10.434 .895

Quadratic

Linear

2.618 1 2.618 22.292 .000 .100 22.292 .997

Cubic Linear

5.392 1 5.392 42.427 .000 .174 42.427 1.000

Order 4 Linear

.618 1 .618 5.215 .023 .025 5.215 .623

Error(dim*faking)

Linear Linear

20.673 201 .103

Quadratic

Linear

23.610 201 .117

Cubic Linear

25.547 201 .127

Order 4 Linear

23.822 201 .119


Tests of Between-Subjects EffectsMeasure: MEASURE_1Transformed Variable: Average

SourceType III Sum of Squares df Mean Square F Sig.

Partial Eta Squared

Noncent. Parameter

Observed Powera

Intercept 45616.886 1 45616.886 16783.070 .000 .988 16783.070 1.000Error 546.324 201 2.718a. Computed using alpha = .05

There were no quantitative differences between Big 5 dimensions, so orthogonal polynomial contrasts are not appropriate.


Parameter Estimates

Dependent Variable

Parameter B

Std. Error t Sig.

95% Confidence Interval

Partial Eta Squared

Noncent. Parameter

Observed Powera

Lower Bound

Upper Bound

H Extraversion Scale score

Intercept 4.508 .069 65.774 .000 4.372 4.643 .956 65.774 1.000

fext Intercept 4.622 .071 64.984 .000 4.481 4.762 .955 64.984 1.000hagr Intercept 5.250 .058 90.770 .000 5.136 5.364 .976 90.770 1.000fagr Intercept 5.354 .057 93.747 .000 5.241 5.466 .978 93.747 1.000hcon Intercept 4.793 .057 84.604 .000 4.681 4.905 .973 84.604 1.000fcon Intercept 5.025 .060 83.675 .000 4.906 5.143 .972 83.675 1.000hsta Intercept 3.979 .077 51.636 .000 3.827 4.131 .930 51.636 1.000fsta Intercept 4.440 .080 55.689 .000 4.282 4.597 .939 55.689 1.000hopn Intercept 4.727 .051 92.086 .000 4.626 4.828 .977 92.086 1.000F Openness Scale Score

Intercept 4.825 .053 91.472 .000 4.721 4.929 .977 91.472 1.000


The above tests simply test significance of the difference between the mean of each variable and zero.

Profile Plots

Respondents gave more positive responses to all dimensions in the Incentive condition.

There were significant differences in mean response to the Five dimensions.

The effect of Incentive was greater for Dimensions 3 (Conscientiousness) and 4 (Stability).

HonestIncentive

Bridge Group

Control Group


Repeated Measures ANOVA – start here on 10/16/171 Between Groups Factor / 1 Repeated Measures Factor

The Learning to Play Bridge effectiveness study.

Situation: A school system provides middle and high school students a period for whatever intellectual activity they wish to engage in. Some choose chess; some choose reading, some choose programming, some choose to play the card game called bridge.

One of the people involved with the bridge classes was interested in whether playing bridge during the hour periods over a long period of time would lead to greater performance on standardized tests of school-related achievement than the other activities. The data here provide a test of that notion.

File: BridgeData1_3Periods_RM090208For595.sav

Key variables:

group0Vs1. Variable representing the research condition. 0=Control; 1=Bridge

ss_math_tot1 ss_math_tot2 ss_math_tot3 Standardized total scores on math achievement at time period 1, time period 2 and time period 3.

ss_comput1 ss_comput2 ss_comput3: Standardized “computational??” achievement

ss_lang_tot1 ss_lang_tot2 ss_lang_tot3: Standardized language achievement

(The names of the variables are idiosyncratic because of the way the data were given to me. I’ve just been too lazy to change them to something easier to follow.)

What outcome would be ideal here??

A. Groups start out at about the same level since the two groups should be equivalent at the start.

B. The Bridge group’s scores on standardized tests increase at a faster rate than the Control group scores.

C. The interaction term would be significant.

Pictorially, this is the ideal outcome of this research project . . .

Bridge

T1

Bridge

T2

Bridge

T3

NoBridge

T1

NoBridge

T2

NoBridge

T3


The data

The data structure, schematically is

Those of you who take the Spring course will analyze these data again, using a the “modern” repeated measures procedures. The data will be structured differently for those analyses.

Repeated Measures Lecture - 22 5/7/2023Analyze -> General Linear Model -> Repeated Measures.

Options.


The syntax – analysis of math_tot scores.

Red’d lines are those that are specific to this problem.

GLM 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.

Shape of change over time

Plots. Remember that Time should be on the horizontal axis for repeated measures designs.


The significant “time” effect reflects the fact that the scores for all kids changed over time – the means increased.

Alas, the nonsignificant “time*group0Vs1” effect means that neither group increased at a higher rate than the other.

The cell means displayed in a 2 way table

Group Time0 Time1 Time2Control 234 249 261Bridge 233 250 261


There is a Between-subjects effect in this analysis – the Bridge group vs Control group factor. The table below presents a test of the significance of difference between the overall mean of the Bridge group scores vs the overall mean of the Control group scores. The difference is not significant.


I’ve rarely seen such a striking affirmation of a null hypothesis.

The conversation with my brother-in-law was a bit awkward.

Repeated Measures Lecture - 27 5/7/2023 Policy Capturing using – skip in 2017

Repeated Measures Analyses

Those in the I-O program know that cognitive ability is the single best predictor of performance in a variety of situations, including academia.

Although we know that cognitive ability is a valid predictor, it’s possible that others do not have that knowledge. If those others are involved in selection of employees, that lack of knowledge could be a serious problem for the organization at which they are employed.

This is a hypothetical research project to investigate whether or not HR persons involved in selection understand these basic results. It uses a technique called policy capturing. In policy capturing, persons are given scenarios and asked to rate each scenario on one or more dimensions. The scenarios are created so that they differ in specific ways, although the raters are not told about these differences. After the ratings have been gathered, analyses of the ratings are conducted to determine if the differences in the scenarios affected the ratings. If the raters had specific, perhaps hidden, policies controlling their ratings of the scenarios, e.g., prejudice against Blacks or females, those policies would be revealed by differences in ratings of the different subgroups distinguished by the characteristics impacted by the policies.

Here is an (quickly-created, unedited) example of the type of scenarios that might be employed in such a study.

Jeremy Smith graduate from a mid-sized university in 2006. His cumulative grade point was 3.84 on a 4-point scale. He majored in psychology with a minor in criminal justice. He was a member of the university marching band. While at the university he worked in a part-time job as a customer service specialist at a local auto-parts store. He finished his university education in 4 years, including classes in two summer sessions.

Based on this short resume, how likely would you be to employ this candidate for a position as a mid-level manager in a medium-sized insurance company.

1 2 3 4 5 6 7Not at Neither Likely VeryAll likely nor unlikely Likely

Ronald Smith graduate from a mid-sized university in 2006. His cumulative grade point was 2.03 on a 4-point scale. He majored in psychology with a minor in criminal justice. He was a member of the university marching band. While at the university he worked in a part-time job as a customer service specialist at a local auto-parts store. He finished his university education in 4 years, including classes in two summer sessions.

Based on this short resume, how likely would you be to employ this candidate for a position as a mid-level manager in a medium-sized insurance company.

1 2 3 4 5 6 7Not at Neither Likely VeryAll likely nor unlikely Likely

Obviously, more than two such scenarios would have to be included in the questionnaire and the two scenarios would have to be less similar in wording than the examples above. Several “high cognitive ability” scenarios might be presented with differently-names participants as well as several “low cognitive ability” scenarios.

Repeated Measures Lecture - 28 5/7/2023In this example, the dependent variable, the ratings, will be of suitability for employment. Let’s suppose that we have a four-item scale of suitability, with reliability = .8. (The above examples give only one of the four items in the scale.)

We will have participants in the research rate applicants differing consistently in only cognitive ability – one group described as having lower cognitive ability than the other group. The key characteristics, i.e., GPA, would be presented along with “distractor” characteristics, e.g., gender, to hide the key difference between the two types of applicants – their cognitive ability, as indexed by their GPA. There will be no consistent differences in other aspects of the descriptions.

Cognitive Ability

Low High

Each person rated each type of applicant. The order in which each person saw the scenarios was randomized across participants along with “filler” descriptions.

If the participants understood contemporary validity research and implemented that knowledge in their policies regarding suitability for employment, we would expect a difference in suitability ratings of the two key types of scenarios, reflecting, presumably, respondents’ recognition of the relationship of job performance to cognitive ability – scenarios describing applicants with high cognitive ability will be rated higher than scenarios describing applicants with low cognitive ability.

If the policy of a participant was to ignore cognitive ability when rating suitability for employment, that policy would be reflected by a nonsignificant difference in mean suitability ratings between the low and high cognitive ability scenarios.

Whatever the results, we can say that our analysis has captured the policies of the raters.

Repeated Measures Lecture - 29 5/7/2023The Analysis

The analysis could be a simple paired-sample t-test, but I’ll do it using the GLM Repeated Measures procedure, since I want to expand the example following this analysis.

Here are some of the data . . .



NotesOutput Created 23-SEP-2015 10:18:01Comments

Input Filter <none>Weight <none>Split File <none>N of Rows in Working Data File 80

Missing Value Handling Definition of Missing User-defined missing values are treated as missing.Cases Used Statistics are based on all cases with valid data for all variables in

the model.Syntax GLM lowca highca

/WSFACTOR=ca 2 Polynomial /METHOD=SSTYPE(3) /PLOT=PROFILE(ca) /PRINT=DESCRIPTIVE ETASQ OPOWER /CRITERIA=ALPHA(.05) /WSDESIGN=ca.

Resources Processor Time 00:00:00.14Elapsed Time 00:00:00.14

Within-Subjects FactorsMeasure: MEASURE_1ca Dependent Variable1 lowca2 highca


Descriptive Statistics

Mean Std. Deviation Nlowca .1536 .91630 80highca .4583 .86124 80

Multivariate Testsa

Effect Value F Hypothesis df Error df Sig.Partial Eta Squared

Noncent. Parameter

Observed Powerc

ca Pillai's Trace .176 16.872b 1.000 79.000 .000 .176 16.872 .982Wilks' Lambda .824 16.872b 1.000 79.000 .000 .176 16.872 .982Hotelling's Trace .214 16.872b 1.000 79.000 .000 .176 16.872 .982Roy's Largest Root .214 16.872b 1.000 79.000 .000 .176 16.872 .982

a. Design: Intercept Within-subjects Design: cab. Exact statisticc. Computed using alpha = .05


Measure: MEASURE_1

Within-subjects Effect Mauchly's WApprox. Chi-

Square df Sig.

Epsilonb


ca 1.000 .000 0 . 1.000 1.000 1.000Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.a. Design: Intercept Within-subjects Design: cab. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.


SourceType III Sum of Squares df Mean Square F Sig.

Partial Eta Squared

Noncent. Parameter

Observed Powera

ca Sphericity Assumed 3.714 1 3.714 16.872 .000 .176 16.872 .982Greenhouse-Geisser 3.714 1.000 3.714 16.872 .000 .176 16.872 .982Huynh-Feldt 3.714 1.000 3.714 16.872 .000 .176 16.872 .982Lower-bound 3.714 1.000 3.714 16.872 .000 .176 16.872 .982

Error(ca) Sphericity Assumed 17.390 79 .220

Greenhouse-Geisser 17.390 79.000 .220

Huynh-Feldt 17.390 79.000 .220

Lower-bound 17.390 79.000 .220



Source caType III Sum of

Squares df Mean Square F Sig.Partial Eta Squared

Noncent. Parameter

Observed Powera

ca Linear 3.714 1 3.714 16.872 .000 .176 16.872 .982Error(ca) Linear 17.390 79 .220


Tests of Between-Subjects Effects (beware – nothing of value is tested here)Measure: MEASURE_1Transformed Variable: Average

SourceType III Sum of


Noncent. Parameter Observed Powera

Intercept 14.978 1 14.978 11.004 .001 .122 11.004 .906Error 107.535 79 1.361


Mauchly’s test is not applicable when the repeated measures factor has only 2 levels.


Profile Plots


Policy Capturing usingFactorial Repeated Measures

(Pardon the repetition from the previous example.)

Those in the I-O program know that cognitive ability is the single best predictor of performance in a variety of situations, including academia. Many also know that conscientiousness is also a valid, though less efficacious predictor of performance, also including performance in academia.

Although we know that these two characteristics are valid predictors, it’s possible that others do not have that knowledge. If those others are involved in selection of employees, that could be a serious problem for the organization at which they are employed.

This is a hypothetical research project to investigate whether or not HR persons involved in selection understand these basic results. It uses a technique called policy capturing. In policy capturing, persons are given scenarios and asked to rate each scenario on one or more dimensions. The scenarios are created so that they differ in specific ways, although the raters are not told about these differences. After the ratings have been gathered, analyses of the ratings are conducted to determine if the differences in the scenarios affected the ratings. If the raters had specific policies regarding the differences in the scenarios, e.g., prejudice against Blacks or females, those policies would be revealed by differences in ratings of the different subgroups distinguished by those policies.

In this example, the dependent variable, the ratings, will be of suitability for employement. Let’s suppose that we have a four-item scale of suitability, with reliability = .8.

We will have persons rate four different types of hypothetical applicant. The four types of applicants will be described as having different combinations of cognitive ability and conscientiousness – four combinations arranged factorially as shown in the following table . . .

Low Cons Low Consc High Consc High ConscRespondent Low CA High CA Low CA High CA

12

Assume that the order in which each person saw the scenarios was randomized across participants. Don’t ask me for examples of the scenarios. That would be a difficult, though I believe achievable task.

If the participants understood contemporary validity research, we would expect

1. A positive relationship of suitability to cognitive ability – scenarios describing applicants with high cognitive ability will be rated higher than scenarios describing applicants with low cognitive ability.2. A positive relationship of suitability to conscientiousness – scenarios describing applicants with high conscientiousness will be rated higher than scenarios describing applicants with low conscientiousness.3. No interaction between the effects of cognitive ability and conscientiousness on ratings – the effect of cognitive ability will be the same across conscientiousness levels and the effect of conscientiousness will be the same across levels of cognitive ability.

Repeated Measures Lecture - 34 5/7/2023The data would be analyzed using a repeated measures factorial design.

The data would be conceptualized in the data editor as 4 columns

Low C Low C High C High CID Low CA High CA Low CA High CA1 rating rating rating rating2 rating rating rating rating3 . . . .4 . . . .5 . . . .Etc etc etc etc etc

1

Here’s part of the actual hypothetical data . . .

Note that one of the repeated measures has already been defined.



General Linear ModelNotes

Output Created 23-SEP-2015 10:27:13Comments

Input Filter <none>Weight <none>Split File <none>N of Rows in Working Data File 80

Missing Value Handling Definition of Missing User-defined missing values are treated as missing.Cases Used Statistics are based on all cases with valid data for all variables in

the model.Syntax GLM lowC_lowCA lowC_highCA highC_lowCA highC_highCA

/WSFACTOR=C 2 Polynomial CA 2 Polynomial /METHOD=SSTYPE(3) /PLOT=PROFILE(CA*C) /EMMEANS=TABLES(C*CA) /PRINT=DESCRIPTIVE ETASQ OPOWER /CRITERIA=ALPHA(.05) /WSDESIGN=C CA C*CA.

Resources Processor Time 00:00:00.17Elapsed Time 00:00:00.16

Within-Subjects Factors

Measure: MEASURE_1

C CA Dependent Variable1 1 lowC_lowCA

2 lowC_highCA2 1 highC_lowCA

2 highC_highCA


Mean Std. Deviation NlowC_lowCA .0213 .98327 80lowC_highCA .3186 1.00520 80highC_lowCA .2859 1.10178 80highC_highCA .5980 .95945 80

Multivariate Testsa

Effect Value F Hypothesis df Error df Sig.Partial Eta Squared

Noncent. Parameter

Observed Powerc

C Pillai's Trace .135 12.288b 1.000 79.000 .001 .135 12.288 .934Wilks' Lambda .865 12.288b 1.000 79.000 .001 .135 12.288 .934Hotelling's Trace .156 12.288b 1.000 79.000 .001 .135 12.288 .934Roy's Largest Root .156 12.288b 1.000 79.000 .001 .135 12.288 .934

CA Pillai's Trace .176 16.872b 1.000 79.000 .000 .176 16.872 .982Wilks' Lambda .824 16.872b 1.000 79.000 .000 .176 16.872 .982Hotelling's Trace .214 16.872b 1.000 79.000 .000 .176 16.872 .982Roy's Largest Root .214 16.872b 1.000 79.000 .000 .176 16.872 .982

C * CA Pillai's Trace .000 .009b 1.000 79.000 .923 .000 .009 .051Wilks' Lambda 1.000 .009b 1.000 79.000 .923 .000 .009 .051Hotelling's Trace .000 .009b 1.000 79.000 .923 .000 .009 .051Roy's Largest Root .000 .009b 1.000 79.000 .923 .000 .009 .051

a. Design: Intercept Within-subjects Design: C + CA + C * CAb. Exact statisticc. Computed using alpha = .05


Measure: MEASURE_1

Within-subjects Effect Mauchly's WApprox. Chi-

Square df Sig.

Epsilonb


C 1.000 .000 0 . 1.000 1.000 1.000CA 1.000 .000 0 . 1.000 1.000 1.000C * CA 1.000 .000 0 . 1.000 1.000 1.000Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.

Repeated Measures Lecture - 37 5/7/2023a. Design: Intercept Within-subjects Design: C + CA + C * CAb. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.


SourceType III Sum of Squares df

Mean Square F Sig.

Partial Eta Squared

Noncent. Parameter

Observed Powera

C Sphericity Assumed 5.916 1 5.916 12.288 .001 .135 12.288 .934Greenhouse-Geisser 5.916 1.000 5.916 12.288 .001 .135 12.288 .934

Huynh-Feldt 5.916 1.000 5.916 12.288 .001 .135 12.288 .934Lower-bound 5.916 1.000 5.916 12.288 .001 .135 12.288 .934

Error(C) Sphericity Assumed 38.034 79 .481


Huynh-Feldt 38.034 79.000 .481

Lower-bound 38.034 79.000 .481

CA Sphericity Assumed 7.428 1 7.428 16.872 .000 .176 16.872 .982Greenhouse-Geisser 7.428 1.000 7.428 16.872 .000 .176 16.872 .982

Huynh-Feldt 7.428 1.000 7.428 16.872 .000 .176 16.872 .982Lower-bound 7.428 1.000 7.428 16.872 .000 .176 16.872 .982

Error(CA) Sphericity Assumed 34.780 79 .440


Huynh-Feldt 34.780 79.000 .440

Lower-bound 34.780 79.000 .440

C * CA Sphericity Assumed .004 1 .004 .009 .923 .000 .009 .051Greenhouse-Geisser .004 1.000 .004 .009 .923 .000 .009 .051

Huynh-Feldt .004 1.000 .004 .009 .923 .000 .009 .051Lower-bound .004 1.000 .004 .009 .923 .000 .009 .051

Error(C*CA) Sphericity Assumed 36.940 79 .468


Huynh-Feldt 36.940 79.000 .468

Lower-bound 36.940 79.000 .468



Source C CAType III Sum of Squares df Mean Square F Sig.

Partial Eta Squared

Noncent. Parameter

Observed Powera

C Linear 5.916 1 5.916 12.288 .001 .135 12.288 .934

Error(C) Linear 38.034 79 .481

CA Linear 7.428 1 7.428 16.872 .000 .176 16.872 .982

Error(CA) Linear 34.780 79 .440

C * CA Linear Linear .004 1 .004 .009 .923 .000 .009 .051Error(C*CA) Linear Linear 36.940 79 .468


Tests of Between-Subjects EffectsMeasure: MEASURE_1Transformed Variable: Average

SourceType III Sum of


Noncent. Parameter Observed Powera

Intercept 29.956 1 29.956 11.004 .001 .122 11.004 .906Error 215.070 79 2.722




Estimated Marginal Means

C * CAMeasure: MEASURE_1

C CA Mean Std. Error95% Confidence Interval

Lower Bound Upper Bound1 1 .021 .110 -.197 .240

2 .319 .112 .095 .5422 1 .286 .123 .041 .531

2 .598 .107 .384 .812

Profile Plots

The CA difference indicates that the hypothetical raters value persons with high CA more than those with low CA.

The C difference indicates that the hypothetical raters value persons high in C more than those with low C.

There is no interaction of the effectsof CA and C on ratings.

Mike,

Why?


Repeated Measures Skipped in 20161 Quantitative Between Subject Factor

1 Repeated Measures FactorNhung Nguyen’s dissertation data.

Nhung’s dissertation

1. Gave the Big 5 to 200 persons under two instruction conditions- once to respond honestly (Honest instruction) and again to respond in a “way that would best guarantee that you would get a customer service representative job.” (Instructed Faking).2. Gave the Wonderlic test – a test of cognitive ability that correlates very highly with standard IQ tests.3. Computed a faking ability score for each Big 5 dimension. This score was computed as the difference between the score under the Faking instruction and the score under the Honest instruction standardized so that faking ability scores on the Big Five dimensions were comparable. Called faking ability because participants were instructed to fake in the Instructed Faking condition.

Questions: 1. The Repeated Measures Main Effect:

Are there differences in the mean faking amounts of the different Big 5 Personality dimensions? That is, are the Big Five dimensions equally fakable?

2. The Between-subjects Main Effect:Are there differences in overall average faking between the various levels of cognitive ability? Did people who scored high on cognitive ability fake more than those who score low? Put another way: is there a relationship between faking ability and cognitive ability?

3. The Interaction of the Between-subjects and Repeated Measures Effects:Are differences in faking between the Big 5 measures the same across levels of cognitive ability?

orIs the relationship of faking ability to cognitive ability the same for different Big 5 dimensions.

The analysis is a repeated measures ANOVA with a Quantitative Between-subjects factor (the Wonderlic scores).

Because the Between-subjects Factor is quantitative, it will be specified differently than a nominal factor and the effects associated with it will be interpreted and presented differently than those in the previous example, which involved a nominal (group0vs1) between-subjects factor.

GET FILE='E:\MdbR\Nhung\SJTPaper\ThesisPaperFile030907.sav'.GLM dsurg dagree dcons des dopen WITH gscore /WSFACTOR = persdim 5 Polynomial /METHOD = SSTYPE(3) /PLOT = PROFILE( persdim ) /EMMEANS = TABLES(persdim) WITH(gscore=MEAN) /PRINT = DESCRIPTIVE ETASQ OPOWER /CRITERIA = ALPHA(.05) /WSDESIGN = persdim /DESIGN = gscore .

The syntax generated by the pull down menus shown below.

Repeated Measures Lecture - 41 5/7/2023Specification of Factors: Analyze -> General Linear Model -> Repeated Measures

Quantitative between-subjects factors must be put in the covariates box in GLM.


Hypotheses Tested

The Repeated Measures Main Effect (Surgency is extraversion)

µdsurg µdagree µdcons µdes µdopen


H0: Equality of means of population of faking scores on the 5 personality dimensions.

Repeated Measures Lecture - 44 5/7/2023The Between-subjects Main Effect

H0: The correlation of gscore with the average difference scores in population is 0.

Note that this hypothesis is NOT stated as equality of means. If we had observed, say, 50 people with CA = 20, 50 with CA=25, and 50 with CA=30, and 50 with CA=35, then it could have been stated as a hypothesis that the means of the faking scores at the 4 levels of CA were equal. But since we have multiple CA values with just a few scores at each, perhaps only 1, it is more efficient to examine the relationship of faking to CA, rather than to examine the differences in means.

The Interaction of Persdim and gscore

H0: The correlation of gscore with individual dimension faking scores will be the same for each individual dimension.

or

Differences between dimension faking score means will be the same for each level of gscore.

Average Diff scores

-.11 = Av Diff Score 20 = Av Diff Score 3

-.10 = Av Diff Score 1

1.14 = Av Diff Score 4



-0.04 = Av Diff Score 7


And so on . .

gscore

Faking Ability

Repeated Measures Lecture - 45 5/7/2023General Linear Model

The failure to meet the sphericity criterion means that we cannot use the “Sphericity Assumed” F printed below.

The multivariate tests below indicate that there is NOT a main effect of Persdim (Personality dimension). This means that there are not overall significant differences in the amount of faking between the 5 dimensions.

The significant interaction suggests, however, that there are gscore-specific differences in the amount of faking between the 5 dimensions, i.e., differences that vary with gscore..

Equivalently, the interaction means that the correlation of gscore with faking of each dimensions varies from one dimension to the next.


Measure: MEASURE_1

DSURG

DAGREE

DCONS

DES

DOPEN

PERSDIM1

2

3

4

5

DependentVariable


.4797 1.01526 203

.3556 1.00172 203

.5854 .97258 203

.7474 1.06989 203

.3921 .98581 203

DSURG

DAGREE

DCONS

DES

DOPEN

Mean Std. Dev iation N

Mu ltiv a ria te T e s ts c

.0 4 0 2 .0 4 1 b 4 .0 0 0 1 9 8 .0 0 0 .0 9 0 .0 4 0 8 .1 6 3 .6 0 3

.9 6 0 2 .0 4 1 b 4 .0 0 0 1 9 8 .0 0 0 .0 9 0 .0 4 0 8 .1 6 3 .6 0 3

.0 4 1 2 .0 4 1 b 4 .0 0 0 1 9 8 .0 0 0 .0 9 0 .0 4 0 8 .1 6 3 .6 0 3

.0 4 1 2 .0 4 1b

4 .0 0 0 1 9 8 .0 0 0 .0 9 0 .0 4 0 8 .1 6 3 .6 0 3

.0 5 1 2 .6 3 5 b 4 .0 0 0 1 9 8 .0 0 0 .0 3 5 .0 5 1 1 0 .5 3 8 .7 3 0

.9 4 9 2 .6 3 5 b 4 .0 0 0 1 9 8 .0 0 0 .0 3 5 .0 5 1 1 0 .5 3 8 .7 3 0

.0 5 3 2 .6 3 5 b 4 .0 0 0 1 9 8 .0 0 0 .0 3 5 .0 5 1 1 0 .5 3 8 .7 3 0

.0 5 3 2 .6 3 5b

4 .0 0 0 1 9 8 .0 0 0 .0 3 5 .0 5 1 1 0 .5 3 8 .7 3 0

P illa i's T ra c e

Wilk s ' L a mb d a

Ho te llin g 's T ra c e

Ro y 's L a rg e s tRo o t

P illa i's T ra c e

Wilk s ' L a mb d a

Ho te llin g 's T ra c e

Ro y 's L a rg e s tRo o t

E ffe c tP E RS D IM

P E RS D IM *GS COR E

V a lu e F Hy p o th e s is d f E rro r d f S ig .P a rtia l E ta

S q u a re dNo n c e n t.P a ra me te r Ob s e rv e d P o w e r

a

Co mp u te d u s in g a lp h a = .0 5a .

E x a c t s ta tis ticb .

De s ig n : In te rc e p t+ GS COR E With in S u b je c ts D e s ig n : P E R S D IM

c .

Ma uchly 's Tes t of Sphericity b

Me as ure : MEASURE_1

.88 8 23 .663 9 .00 5 .946 .97 1 .250

With in Sub jec tsEffe c tPERSDIM

Ma uc h ly 's WAp prox .

Ch i-Squa re df Sig .Gre enhous e-

Ge is s er Huy nh-Feld t Lower-bound

Eps ilona

Tes ts the nu ll hy po thes is that th e e rror c ov a rianc e ma trix o f the o rthono rma liz e d trans fo rmed dep endent v a riab les is p roportion alto an iden tity matrix .

Ma y be us e d to ad jus t the deg ree s o f freedom for the av e raged tes ts of s ign ific anc e . Co rrec ted tes ts a re d is p lay ed inthe Tes ts of With in -Sub jec ts Effec ts ta b le .

a.

De s ign : In terc ep t+GSCORE With in Sub jec ts Des ign: PERSDIM

b.


The Tests of Within-subjects Contrasts are automatically printed, but make no sense since the personality dimensions are not on a quantitative dimension.

The significant main effect of gscore means that there is a correlation of overall faking with cognitive ability. That is, there are differences in amount of faking at different levels of cognitive ability.

Inspection of the graph below shows that it’s positive – smarter people faked more.

T e s ts o f With in -S u b je c ts E ffe c ts

Me a s u re : ME A S UR E _ 1

5 .4 3 7 4 1 .3 5 9 2 .2 1 7 .0 6 6 .0 11 8 .8 6 6 .6 5 3

5 .4 3 7 3 .7 8 5 1 .4 3 7 2 .2 1 7 .0 6 9 .0 11 8 .3 8 9 .6 3 5

5 .4 3 7 3 .8 8 5 1 .3 9 9 2 .2 1 7 .0 6 8 .0 11 8 .6 1 3 .6 4 4

5 .4 3 7 1 .0 0 0 5 .4 3 7 2 .2 1 7 .1 3 8 .0 11 2 .2 1 7 .3 1 7

6 .0 6 7 4 1 .5 1 7 2 .4 7 4 .0 4 3 .0 1 2 9 .8 9 4 .7 0 8

6 .0 6 7 3 .7 8 5 1 .6 0 3 2 .4 7 4 .0 4 6 .0 1 2 9 .3 6 1 .6 9 0

6 .0 6 7 3 .8 8 5 1 .5 6 1 2 .4 7 4 .0 4 5 .0 1 2 9 .6 11 .6 9 8

6 .0 6 7 1 .0 0 0 6 .0 6 7 2 .4 7 4 .11 7 .0 1 2 2 .4 7 4 .3 4 7

4 9 2 .9 8 1 8 0 4 .6 1 3

4 9 2 .9 8 1 7 6 0 .7 0 0 .6 4 8

4 9 2 .9 8 1 7 8 0 .9 7 4 .6 3 1

4 9 2 .9 8 1 2 0 1 .0 0 0 2 .4 5 3

S p h e ric ity A s s u me d

Gre e n h o u s e -Ge is s er

Hu y n h -F e ld t

L o w e r-b o u n d



Hu y n h -F e ld t

L o w e r-b o u n d



Hu y n h -F e ld t

L o w e r-b o u n d

S o u rc eP E R S D IM

P E R S D IM *GS C OR E

E rro r(P E R S D IM)

T y p e III S u mo f S q u a re s d f Me a n S q u a re F S ig .

P a rtia l E taS q u a re d

No n c e n t.P a ra me te r Ob s e rv e d P o w e r

a


T e s ts o f With in -Su b je c ts Co n tra s ts

Me a s u re : ME AS URE _ 1

3 .7 1 5 1 3 .7 1 5 5 .4 5 2 .0 2 1 .0 2 6 5 .4 5 2 .6 4 2

.0 5 2 1 .0 5 2 .0 8 8 .7 6 8 .0 0 0 .0 8 8 .0 6 0

.0 5 8 1 .0 5 8 .0 7 9 .7 7 9 .0 0 0 .0 7 9 .0 5 9

1 .6 1 2 1 1 .6 1 2 3 .5 9 7 .0 5 9 .0 1 8 3 .5 9 7 .4 7 1

2 .9 9 6 1 2 .9 9 6 4 .3 9 7 .0 3 7 .0 2 1 4 .3 9 7 .5 5 1

.6 2 2 1 .6 2 2 1 .0 4 8 .3 0 7 .0 0 5 1 .0 4 8 .1 7 5

.6 8 1 1 .6 8 1 .9 3 4 .3 3 5 .0 0 5 .9 3 4 .1 6 1

1 .7 6 7 1 1 .7 6 7 3 .9 4 3 .0 4 8 .0 1 9 3 .9 4 3 .5 0 7

1 3 6 .9 6 9 2 0 1 .6 8 1

11 9 .3 1 2 2 0 1 .5 9 4

1 4 6 .6 2 1 2 0 1 .7 2 9

9 0 .0 7 9 2 0 1 .4 4 8

PE RS DIML in e a r

Qu a d ra tic

Cu b ic

Ord e r 4

L in e a r

Qu a d ra tic

Cu b ic

Ord e r 4

L in e a r

Qu a d ra tic

Cu b ic

Ord e r 4

So u rc ePE RS DIM

PE RS DIM *GS CORE

Erro r(P E RS DIM)

T y p e III S u mo f S q u a re s d f Me a n S q u a re F S ig .

Pa rtia l E taSq u a re d

No n c e n t.Pa ra me te r Ob s e rv e d P o we r

a


Te s ts of Be twee n-Subje c ts Effe c ts

Me a s u re : MEASURE_1

Tra n s fo rme d Va ria b le : Av e ra ge

6 .2 9 2 1 6 .2 9 2 2 .6 3 2 .10 6 .01 3 2 .6 3 2 .36 5

49 .9 2 4 1 49 .9 2 4 20 .8 8 2 .00 0 .09 4 20 .8 8 2 .99 5

48 0 .5 40 20 1 2 .3 9 1

So u rc eIn te rc e p t

GSCORE

Erro r

Ty p e III Su mo f Sq u a re s d f Me a n Sq u a re F Sig .

Pa rtia l EtaSq u a red

No n c en t.Pa ra me te r Ob s e rv e d Powe ra

Co mp u te d u s in g a lpha = .0 5a .

Repeated Measures Lecture - 47 5/7/2023Estimated Marginal Means

Profile Plots

Graphing the Main Effect of gscore.I computed an average faking score (those values illustrated on the right on p. 22 above.)graph /scatterplot = gscore with fakescor.

Graph

This is a display of the main effect of cognitive ability. The average difference scores are called FAKESCOR in this plot. On the right, persons with similar gscore values have been grouped together. This shows the positive relationship of faking to Gscore more strikingly.

Ext Agr Con Sta Opn

These are identical to the observed means since there is only one group of respondents.Dimensions are listed as E A C S O.So the largest amount of faking was in the Emotional Stability dimension (4th in the list). The least was in Agreeableness and Openness. But remember that the differences in means were not officially significant.

Note – Persdim main effect was not significant, so this graph shouldn’t be overinterpreted.

PERSDIM

Me a s u re : MEASURE_ 1

.4 8 0 a .0 6 9 .3 4 4 .6 1 5

.3 5 6 a .0 6 8 .2 2 2 .4 8 9

.5 8 5 a .0 6 7 .4 5 3 .7 1 8

.7 4 7 a .0 7 3 .6 0 4 .8 9 1

.3 9 2 a .0 6 9 .2 5 6 .5 2 8

PERSDIM1

2

3

4

5

Me a n Std . Erro r L o we r Bo u n dUp p e r Bo u n d

9 5 % Co n f i d e n c e In te rv a l

Co v a ri a te s a p p e a ri n g i n th e mo d e l a re e v a l u a te d a t th efo l l o wi n g v a l u e s : GSCORE wo n d e rl i c te s t s c o re = 2 4 .6 1 .

a .

Estimated Marginal Means of MEASURE_1

PERSDIM

54321

Es

tim

ate

d M

arg

ina

l M

ea

ns

. 8

. 7

. 6

. 5

. 4

. 3

wo n d e rl i c te s t s c o re

50403020100

FA

KE

SC

OR

4

3

2

1

0

-1

-2 Rsq = 0. 0941

Repeated Measures Lecture - 48 5/7/2023The interactions.

Recall what the interaction is: The relationship of average faking to gscore differed across dimensions.

Below are displays of the relationship of faking for each dimension to cognitive ability. These displays are analogous to the “interaction” plots when the between-subjects factor is a categorical factor.

I’m not sure of the explanation of the interaction. Why is the relationship of faking to cognitive ability stronger for Extraversion than it is for Openness, for example? That is, smart people faked Extraversion a lot more than less smart people did. But smart people didn’t fake Openness much more than less smart people. ??

graph /scatterplot = gscore with dsurg.

Graph r = +.27

graph /scatterplot = gscore with dagree.

Graph r = +.28

graph /scatterplot = gscore with dcons.

Graph r = +.19

graph /scatterplot = gscore with des.

Graph r = +.26

graph /scatterplot = gscore with dopen.

Graph r = +.09

It may be that for some items, there may be disagreement on what constitutes a “good” response. That is, some people might have thought that agreeing was the appropriate way to fake while others thought that disagreeing was the appropriate way to fake. The result was that the relationships of faking to cognitive ability was suppressed for those items.


50403020100

DS

UR

G

5

4

3

2

1

0

-1

-2 Rsq = 0. 0744


50403020100

DA

GR

EE

4

3

2

1

0

-1

-2

-3

-4 Rsq = 0. 0802


50403020100

DC

ON

S

6

4

2

0

-2

-4 Rsq = 0. 0362


50403020100D

ES

5

4

3

2

1

0

-1

-2 Rsq = 0. 0685


50403020100

DO

PE

N

4

3

2

1

0

-1

-2

-3 Rsq = 0. 0076


Using a correlation matrix to examine the individual dimension correlations.

correlation gscore dsurg to dopen fakescore.

Correlations


W ar ni ngs

Text : FAKESCO REA var iable nam e is m or e t han 8 char act er s long. O nly t he f ir st 8 char act er s will be used.

Co rre la tio n s

1 .2 7 3 .2 8 3 .1 9 0 .2 6 2 .0 8 7 .3 0 7

. .0 0 0 .0 0 0 .0 0 7 .0 0 0 .2 1 5 .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.2 7 3 1 .4 1 6 .3 2 9 .4 5 2 .3 7 5 .7 1 9

.0 0 0 . .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.2 8 3 .4 1 6 1 .3 9 7 .2 6 0 .3 3 1 .6 6 6

.0 0 0 .0 0 0 . .0 0 0 .0 0 0 .0 0 0 .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.1 9 0 .3 2 9 .3 9 7 1 .4 9 8 .4 3 5 .7 3 6

.0 0 7 .0 0 0 .0 0 0 . .0 0 0 .0 0 0 .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.2 6 2 .4 5 2 .2 6 0 .4 9 8 1 .4 5 1 .7 5 0

.0 0 0 .0 0 0 .0 0 0 .0 0 0 . .0 0 0 .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.0 8 7 .3 7 5 .3 3 1 .4 3 5 .4 5 1 1 .7 1 8

.2 1 5 .0 0 0 .0 0 0 .0 0 0 .0 0 0 . .0 0 0

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

.3 0 7 .7 1 9 .6 6 6 .7 3 6 .7 5 0 .7 1 8 1

.0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .0 0 0 .

2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3 2 0 3

Pe a rs o nCo rre la tio n

S ig . (2 -ta ile d )

N



N



N



N



N



N



N

GS CORE wo n d e rlic te s ts c o re

DS URG

DA GRE E

DCONS

DE S

DOP E N

F A K E S COR

GS CORE wo n d e rlic te s t

s c o re DS URG DA GRE E DCONS DE S DOP E N F A K E S COR


Repeated Measures ANOVA – Skipped in 20151 Between Groups Factor

2 Repeated Measures Factors in factorial arrangementThe 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 . .

C1B1 C1B2 C1B3 C2B1 C2B2 C2B3 A

80 48 45 76 45 41 1 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 2

Specify the factor that varies slowest across columns first

Then specif the factor whose levels vary fastest next, in this case the B factor . . .


Interestingmaterial

Uninterestingmaterial

Much distraction

Littledistraction

Mike – show the pull down menus in more detail.


Click on the “Define” button, then . . .



Click on the name of each variable in the left-hand field and click on the right-pointing arrow to move the name into the “Withing-Subjects Variables” field.

GLM c1b1 c1b2 c1b3 c2b1 c2b2 c2b3 BY a /WSFACTOR = c 2 Polynomial b 3 Polynomial /METHOD = SSTYPE(3) /PLOT = PROFILE( b*a*c ) /PRINT = DESCRIPTIVE ETASQ OPOWER HOMOGENEITY /CRITERIA = ALPHA(.05) /WSDESIGN = c b c*b /DESIGN = a .

I believe it’s given because the number of persons in each cell is not larger than the number of measures on each person.


Warnings

Box's Test of Equality of CovarianceMatrices is not computed becausethere are fewer than twononsingular cell covariancematrices.

Much distraction

Littledistraction

Much distraction

Littledistraction

Much distraction

Littledistraction

µB1 µB2 µB3


Hypotheses tested

The C (Interest) - Repeated Measures Main Effect


80 48 45 76 45 41 1 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 2

The B (Time) - Repeated Measures Main Effect


80 48 45 76 45 41 1 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 2

The A – Distraction - Between-Subjects Main Effect


80 48 45 76 45 41 46 37 34 42 34 33 51 49 36 45 38 30 72 57 50 66 51 42 68 40 33 58 38 30 65 44 36 56 37 28

70 55 52 68 57 56 88 69 66 91 74 70 58 60 54 50 41 38 63 57 52 61 58 56 78 81 75 79 78 74 84 82 80 80 73 76


µC1 µC2

µA1

µA2

Sample is treated as one giant group for the repeated measures comparisons

Sample is treated as one giant group for the repeated measures comparisons





Measure: MEASURE_1

C1B1

C1B2

C1B3

C2B1

C2B2

C2B3

B1

2

3

1

2

3

C1

2

DependentVariable

Between-Subjects Factors

6

6

1

2

AValue Label N


63.67 12.88 6

73.50 11.86 6

68.58 12.87 12

45.83 7.14 6

67.33 11.98 6

56.58 14.64 12

39.00 6.87 6

63.17 12.37 6

51.08 15.82 12

57.17 12.75 6

71.50 14.79 6

64.33 15.14 12

40.50 6.28 6

63.50 14.07 6

52.00 15.88 12

34.00 6.03 6

61.67 14.50 6

47.83 17.91 12

A1

2

Total

1

2

Total

1

2

Total

1

2

Total

1

2

Total

1

2

Total

C1B1

C1B2

C1B3

C2B1

C2B2

C2B3

Mean Std. Dev iation N


The multivariate tests. The less powerful but more robust multivariate tests are always printed first. These tests indicate that there is a significant effect associated with Factor C (Interest), with Factor B (Time), and with the B * A (Time by Distraction) interaction.

The significant C Main effect indicates that the mean amount recalled depends on the Interest.

The significant B main effect indicates that the mean amount recalled depends on the time at which recall occurred.

The significant B*A interaction indicates that the change in mean amount over time is different for persons under much distraction than it is for persons under little distraction.


M ul t i var i at e Test sc

. 442 7. 935b 1. 000 10. 000 . 018 . 442 7. 935 . 719

. 558 7. 935b 1. 000 10. 000 . 018 . 442 7. 935 . 719

. 793 7. 935b 1. 000 10. 000 . 018 . 442 7. 935 . 719

. 793 7. 935b 1. 000 10. 000 . 018 . 442 7. 935 . 719

. 109 1. 226b 1. 000 10. 000 . 294 . 109 1. 226 . 171

. 891 1. 226b 1. 000 10. 000 . 294 . 109 1. 226 . 171

. 123 1. 226b 1. 000 10. 000 . 294 . 109 1. 226 . 171

. 123 1. 226b 1. 000 10. 000 . 294 . 109 1. 226 . 171

. 893 37. 678 b 2. 000 9. 000 . 000 . 893 75. 356 1. 000

. 107 37. 678 b 2. 000 9. 000 . 000 . 893 75. 356 1. 000

8. 373 37. 678 b 2. 000 9. 000 . 000 . 893 75. 356 1. 000

8. 373 37. 678 b 2. 000 9. 000 . 000 . 893 75. 356 1. 000

. 567 5. 883b 2. 000 9. 000 . 023 . 567 11. 766 . 734

. 433 5. 883b 2. 000 9. 000 . 023 . 567 11. 766 . 734

1. 307 5. 883b 2. 000 9. 000 . 023 . 567 11. 766 . 734

1. 307 5. 883b 2. 000 9. 000 . 023 . 567 11. 766 . 734

. 323 2. 150b 2. 000 9. 000 . 173 . 323 4. 299 . 329

. 677 2. 150b 2. 000 9. 000 . 173 . 323 4. 299 . 329

. 478 2. 150b 2. 000 9. 000 . 173 . 323 4. 299 . 329

. 478 2. 150b 2. 000 9. 000 . 173 . 323 4. 299 . 329

. 186 1. 028b 2. 000 9. 000 . 396 . 186 2. 055 . 177

. 814 1. 028b 2. 000 9. 000 . 396 . 186 2. 055 . 177

. 228 1. 028b 2. 000 9. 000 . 396 . 186 2. 055 . 177

. 228 1. 028b 2. 000 9. 000 . 396 . 186 2. 055 . 177

Pilla i's Tr ac e

W ilk s ' Lam bda

Hot e lling 's Tr ac e

Roy 's Lar ges t Root

Pilla i's Tr ac e

W ilk s ' Lam bda



Pilla i's Tr ac e

W ilk s ' Lam bda



Pilla i's Tr ac e

W ilk s ' Lam bda



Pilla i's Tr ac e

W ilk s ' Lam bda



Pilla i's Tr ac e

W ilk s ' Lam bda



Ef f ec tC

C * A

B

B * A

C * B

C * B * A

Value F Hy pot hes is dfEr r or df Sig. Et a Squar edNonc ent .

Par am et erO bs er v ed

Powera

Com put ed us ing alpha = . 05a.

Ex ac t s t at is t icb.

Des ign: I nt er c ept +A W it h in Subjec t s Des ign: C+B+C* B

c .


The sphericity test . Mauchly's test indicates that the sphericity condition is NOT met. So we must either go with the multivariate tests or use one of the tests which adjusts for lack of sphericity. Fortunately, they all give the same result with respect to significance and they all agree with the multivariate tests with respect to significance, so the point is moot.


M auchl y's Test of Spher i ci t yb

M easur e: M EASURE_1

1. 000 . 000 0 . 1. 000 1. 000 1. 000

. 263 12. 031 2 . 002 . 576 . 668 . 500

. 491 6. 402 2 . 041 . 663 . 801 . 500

W it hin Subject s Ef f ectC

B

C * B

M auchly's WAppr ox.

Chi- Squar e df Sig.G r eenhouse- G eisser Huynh- Feldt Lower - bound

Epsilona

Test s t he null hypot hesis t hat t he er r or covar iance m at r ix of t he or t honor m alized t r ansf or m ed dependentvar iables is pr opor t ional t o an ident it y m at r ix.

M ay be used t o adjust t he degr ees of f r eedom f or t he aver aged t est s of signif icance. Cor r ect edt est s ar e displayed in t he Test s of W it hin- Subject s Ef f ect s t able.

a.

Design: I nt er cept +A W it hin Subject s Design: C+B+C* B

b.



Te sts of Within-Subje cts Effec ts

Me as ure : MEASURE_1

29 2 .0 14 1 29 2 .0 14 7.9 35 .01 8 .44 2 7.9 35 .71 9

29 2 .0 14 1.0 00 29 2 .0 14 7.9 35 .01 8 .44 2 7.9 35 .71 9

29 2 .0 14 1.0 00 29 2 .0 14 7.9 35 .01 8 .44 2 7.9 35 .71 9

29 2 .0 14 1.0 00 29 2 .0 14 7.9 35 .01 8 .44 2 7.9 35 .71 9

45 .12 5 1 45 .12 5 1.2 26 .29 4 .10 9 1.2 26 .17 1

45 .12 5 1.0 00 45 .12 5 1.2 26 .29 4 .10 9 1.2 26 .17 1

45 .12 5 1.0 00 45 .12 5 1.2 26 .29 4 .10 9 1.2 26 .17 1

45 .12 5 1.0 00 45 .12 5 1.2 26 .29 4 .10 9 1.2 26 .17 1

36 8 .0 28 10 36 .80 3

36 8 .0 28 10 .00 0 36 .80 3

36 8 .0 28 10 .00 0 36 .80 3

36 8 .0 28 10 .00 0 36 .80 3

36 83 .111 2 18 41 .55 6 36 .41 0 .00 0 .78 5 72 .82 1 1.0 00

36 83 .111 1.1 51 31 99 .37 8 36 .41 0 .00 0 .78 5 41 .91 5 1.0 00

36 83 .111 1.3 35 27 58 .60 5 36 .41 0 .00 0 .78 5 48 .61 3 1.0 00

36 83 .111 1.0 00 36 83 .111 36 .41 0 .00 0 .78 5 36 .41 0 1.0 00

61 6 .3 33 2 30 8 .1 67 6.0 93 .00 9 .37 9 12 .18 6 .83 3

61 6 .3 33 1.1 51 53 5 .3 85 6.0 93 .02 7 .37 9 7.0 14 .65 2

61 6 .3 33 1.3 35 46 1 .6 26 6.0 93 .02 1 .37 9 8.1 35 .70 1

61 6 .3 33 1.0 00 61 6 .3 33 6.0 93 .03 3 .37 9 6.0 93 .60 6

10 11 .5 56 20 50 .57 8

10 11 .5 56 11.5 12 87 .87 0

10 11 .5 56 13 .35 1 75 .76 4

10 11 .5 56 10 .00 0 10 1 .1 56

5.7 78 2 2.8 89 .69 1 .51 2 .06 5 1.3 83 .15 0

5.7 78 1.3 25 4.3 59 .69 1 .46 0 .06 5 .91 6 .12 9

5.7 78 1.6 03 3.6 05 .69 1 .48 4 .06 5 1.1 08 .13 8

5.7 78 1.0 00 5.7 78 .69 1 .42 5 .06 5 .69 1 .117

7.0 00 2 3.5 00 .83 8 .44 7 .07 7 1.6 76 .17 3

7.0 00 1.3 25 5.2 82 .83 8 .40 9 .07 7 1.11 0 .14 6

7.0 00 1.6 03 4.3 67 .83 8 .42 7 .07 7 1.3 43 .15 8

7.0 00 1.0 00 7.0 00 .83 8 .38 2 .07 7 .83 8 .13 2

83 .55 6 20 4.1 78

83 .55 6 13 .25 3 6.3 04

83 .55 6 16 .02 9 5.2 13

83 .55 6 10 .00 0 8.3 56

Sp he ric ity As s u me d

Gre en ho us e-Ge is s er

Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d



Hu y n h-Fe ld t

Lo we r-bo un d

So urc eC

C * A

Erro r(C)

B

B * A

Erro r(B)

C * B

C * B * A

Erro r(C*B)

Ty pe III Su mof Squ are s df Me an Sq ua re F Sig . Eta Sq ua red

No nc en t.Pa ramete r

Ob s e rv e dPo we r

a

Co mp ute d u s in g a lpha = .0 5a.


Test of equality of variances across groups . Levene's test is for the between-subjects effects. It indicates generally that the variances are not significantly different.

Test of between-subjects main effect . The comparison between the two distracter conditions indicates that there is a significant difference in mean recall between the two.


Levene's Test of E quality of E r r or Var iances a

.007 1 10 .936

3.186 1 10 .105

4.778 1 10 .054

.311 1 10 .589

5.205 1 10 .046

5.000 1 10 .049

C1B 1

C1B 2

C1B 3

C2B 1

C2B 2

C2B 3

F df1 df2 S ig.

Tests the null hypothesis that the error variance ofthe dependent variable is equal across groups.

Design: Intercept+A W ithin S ubjects Design: C+B +C* B

a.

Test s of Bet w een- Subj ect s Ef f ect s

M easur e: M EASURE_1

Tr ansf or m ed Var iable: Aver age

231767. 014 1 231767. 014 363. 878 . 000 . 973 363. 878 1. 000

7260. 125 1 7260. 125 11. 399 . 007 . 533 11. 399 . 860

6369. 361 10 636. 936

Sour ceI nt er cept

A

Er r or

Type I I I Sumof Squar es df M ean Squar e F Sig. Et a Squar ed

Noncent .Par am et er

O bser vedPower

a

Com put ed using alpha = . 05a.


Profile Plots


Distraction.

Main Effect of A: Mean recall was better in the low distraction condition.

Time.

Main Effect of B: Mean recall decreased over time periods.


A

Low dist r act ion condHigh dist r act ion con

Es

tim

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70

60

50

40


B

321

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70

60

50

40



Distraction by Time.

Interaction of A and B: The effect of distraction was greater at longer recall times. (This was the only significant interaction.)

Main Effect of Factor C: Mean recall was greater for more interesting material.

MoreInteresting

LessInteresting


C

21

Es

tim

ate

d M

arg

ina

l M

ea

ns

59

58

57

56

55

54


B

321

Es

tim

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d M

arg

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l M

ea

ns

80

70

60

50

40

30

A

High dist ract ion con

dit ion

Low dist ract ion cond

it ion


B * A * C


Even though the three way interaction, B*A*C was not significant, it is of value to see how it would be visualized. A significant three way interaction means that a two-way interaction was not the same across levels of a third variable.

In this case, if the B*A*C interaction were significant, that would mean that the B*A interaction varied across levels of C. The way to visualize that is to plot the B*A interaction for each level of C. Those plots are on the left. The fact that they're nearly identical supports the fact that there was NO B*A*C interaction. If there had been, the two plots (one for C=1 and the other for C=2) would have been different.

So . . .

A two-way interaction is a difference of effect of one variable across levels of a second variable.

A three-way interaction is a difference of INTERACTION of two variables across levels of a third variable.


At C = 1

B

321

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tim

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80

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A


dit ion


it ion


At C = 2

B

321

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A


dit ion


it ion

Documents

Repeated Measures ANOVA - - The University of … · Web viewThat is, power to detect a difference is a positive function of r - the larger the correlation between paired scores,