unit 4 slides

Single-Factor Repeated Measures Design

Psychology 3800, Lab 002

Lab Overview

▪ comments assignment #3 (one-way ANOVA)

▪ overview of the repeated measures ANOVA

▪ example analysis

▪ assignment #4 info

MORE ANOVA???

Assignment #3: Feedback

▪ complete list of common errors on the Monte Carlo assignments is available on the lab blog: http://uwo3800g.tumblr.com/post/76436563501/assignment-2-

commonly-made-errors

OH, I SEE…

▪ solutions are also posted: http://uwo3800g.tumblr.com/post/76435783755/assignment-2-solutions

▪ variation of the one-way ANOVA▪ one factor (IV), with 3 or more levels ▪ one measured DV▪ assessing overall differences between means via F-test▪ assessing specific differences via post hoc tests

▪ main difference: ▪ nature of the factor levels assessed▪ one-way ANOVA: random assignment to factor levels▪ repeated measures ANOVA: all participants tested under every

level of the factor (tested repeatedly, cells not independent)

Repeated Measures ANOVA: Features

Repeated Measures ANOVA: Example

Does the type of ’80s movie viewed by participants affect their immediate academic performance?

Research Question

independent variable (IV) type of ‘80s movie 3 types of movies (3 levels)

dependent variable (DV) academic performance test out of 10 marks

Variables of Interest

One-Way ANOVA

Repeated Measures ANOVA: Features

Movie from the 1980s

Ferris Bueller’s Day Off Raiders of the Lost Ark The Terminator

Repeated Measures ANOVA

Repeated Measures ANOVA: Features

Movie from the 1980s

Ferris Bueller’s Day Off Raiders of the Lost Ark The Terminator

Repeated Measures ANOVA: Features

Movie from the 1980s

Ferris Bueller’s Day Off Raiders of the Lost Ark The Terminator

Repeated Measures ANOVA

Repeated Measures ANOVA: Features

Movie from the 1980s

Ferris Bueller’s Day Off Raiders of the Lost Ark The Terminator

Repeated Measures ANOVA

Participant Ferris Raiders Terminator

12345...

34376...

27795...

35485...

Each row is a participant, and each column is the participant’s dependent variable score at one of the 3 levels of the independent variable.€

x = 4.34

€

x = 2.21

€

x = 6.92

Repeated Measures ANOVA: Features

Repeated Measures ANOVA

o carry-over effects getting cumulative effects of all conditions (all movies having

combined effect on academic performance) can buffer against them with long intervals between conditions

o order effects order in which conditions delivered influencing results

o memory/fatigue effects could just be getting used to the nature of the academic test

Some Issues to Consider… (textbook: pp. 116-117)

Benefits of Repeated Measures

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F =MSTreatment

MSError

▪ obtained value is (in general terms) the variance due to treatment over the variance due tor error

▪ if we can decrease error, then we can increase F-obtained values (and thereby increase power)

▪ one way to decrease error is increase the amount of variance in the data that we can account for

Benefits of Repeated Measures

TreatmentErrorIndividual differences

60% 60%40%25%

15%

Non-Repeated Design Repeated Design

Hypotheses and Conclusions

Hypotheses assessed via omnibus ANOVA test:

H0: μ1 = μ2 = μ3 = … = μk HA: at least two means differ significantly

• to determine where significant differences can be found, post hoc tests will have to be run using the POSTHOC program (L: drive)

• recall: each post hoc comparison assesses whether each pair of means is equal (H0) or whether the two means differ significantly (HA)

PRETTY MUCH TWINS

Assumptions

1. independent random sampling▪ “independent” does not mean that observations in one treatment condition are unrelated to those in another

2. normality sample drawn from normally distributed population

3. circularity of the covariance matrix

oslightly different way of considering homogeneity of variance variance of the difference scores between each pair of populations is

the same if there is circularity of covraince matrix

oif variances are not equal, Type I error rate is inflated

o tested using Mauchly’s W

oeven if this assumption is not violated, use Greenhouse-Geisser values from the SPSS output in your report

Circularity of the Covariance Matrix

The Data

Does the type of ’80s movie viewed by participants affect their immediate academic performance?

participant identifier academic test

score after viewingeach movie(out of 10)

Analyze General Linear Model Repeated Measures

• type in factor name (Movie) and number of levels (3)• click “Add” (should pop up in lower box)• select “Define”

Repeated Measures ANOVA in SPSS

• highlight first option [_?_(1)] in “Within-Subjects Variables” box• select the first DV level (Ferris) from the DV column• click the arrow to define the first variable• repeat for second and third variables

• select “Options”

Repeated Measures ANOVA in SPSS

Options Menu

Repeated Measures ANOVA in SPSS

Repeated Measures ANOVA in SPSS

click “OK” to run theanalyses (output willpop up in separate

output window)

Mauchly’s Test of Sphericity(assessing assumption of circularity of covariance matrix)

Mauchly’s W = 0.800, X2(2) = 4.907, ns

o little reason to assume that assumption of circularity has been violated

Repeated Measures ANOVA: Output

Overall ANOVA Test(assessing whether at least two means differ significantly)

F(2, 39) = 15.679, p < .001, η2 = .405, power = .997

o Greenhouse-Geisser corrected values to ensure sound resultso round up for all degrees of freedomo at least two of the condition means differ significantly

Repeated Measures ANOVA: Output

Estimated Marginal Means: Descriptives and Post Hoc Tests(assessing which pairs of means differ significantly)

enter these means intothe POST HOC program

to get clearer senseof overall effect

Repeated Measures ANOVA: Output

Repeated Measures ANOVA: Post Hoc

Reporting Obtained Values: q(k,dferror)

Raiders vs. Terminator q(3, 46) = 5.959 Raiders vs. Ferris q(3, 46) = 7.497 Terminator vs. Ferris q(3, 46) = 1.539

o make sure to provide the unadjusted means square error value and degrees of freedom to POSTHOC (not the Greenhouse-Geisser adjusted values)

o k = number of levels defining IVo dferror = uncorrected df for error (Test of Within-Subjects Effects)

Repeated Measures ANOVA: Post Hoc

o use the following website to determine your critical value: http://vassarstats.net/tabs.html#q

o D.R. reject Ho at α = .05 if qOBT > 3.43o D.R. reject Ho at α = .01 if qOBT > 4.34

Repeated Measures ANOVA: Post Hoc

Reporting Obtained Values

Raiders vs. Terminator q(3, 46) = 5.959, p < .01 Raiders vs. Ferris q(3, 46) = 7.497, p < .01 Terminator vs. Ferris q(3, 46) = 1.539, ns

Assignment

Assignment Overview

APA-style results section (2 pages maximum)▪one-inch margins▪name in header▪double spacing▪12-point serif-type font

•labeled output attached (SPSS and POSTHOC)

ONWARD

NOBLE STEED!

What to Include…

1. introduction (design, IV, DV, levels)2. type of test being conducted3. test(s) of assumptions (statistics, interpretation)4. results of the omnibus test (hypotheses, F-statistic, conclusion)5. results of all post hoc tests (Tukey, hypotheses, q-statistics,

conclusion)6. overall conclusion and practical recommendations (concise but

thorough)7. response to final question regarding Greenhouse-Geisser

Note: Make sure to include descriptive statistics, power values, and effect sizes where appropriate.

From your output, you can delete (or ignore):▪ Multivariate Tests tables▪ Tests of Within-Subjects Contrasts table▪ Tests of Between-Subjects Effects table

A reminder about degrees of freedom:▪ always round your outputted Greenhouse-Geisser df value up

to a whole number when reporting results▪ for post hoc tests, use “sphericity assumed” df value rather

than any adjusted df value (i.e., Greenhouse-Geisser)

For the final question:▪ helpful information can be found in your textbook and in the

lecture slides (be brief but thorough)

Helpful Hints…

• Reading Week next week: no lecture, labs, office hours

• assignments due in two weeks: Thursday, February 27

• lab and lecture on completely randomized factorial design (a.k.a., two-way ANOVA)

review the textbook chapter, paying particular attention to the information on interactions

In Two Weeks…