Title of Resource Activity: Conducting a Repeated Measures ANOVA Author(s) Natalie Ciarocco & Jaclyn Racaniello

Institution Monmouth University

Brief Description:

This activity has students conduct a repeated measures ANOVA using data from a research scenario. Students determine the statistical analysis to use, identify the independent and dependent variables, set up a data file, enter the provided data, run the appropriate analysis, and summarize the results.

Keywords: Repeated Measures ANOVA; PASW (SPSS) Calculation; Identifying IVs & DVs; Interpretation of Output

Author Contact Information: nciarocc@monmouth.edu

Additional Information: TeachPsychScience.org is made possible with grant support from the American Psychological Society (APS) Fund for Teaching and Public Understanding of Psychological Science to the site creators Gary Lewandowski, Natalie Ciarocco, and David Strohmetz. All materials on this site have been subjected to a peer review process. We welcome additional resources (www.teachpsychscience.org/submissions). © 2010 Natalie Ciarocco and Jaclyn Racaniello. All Rights Reserved. This material may be used for noncommercial educational purposes. All other uses require the written consent of the authors.

Instructors: In this activity, students will take data from a fictitious design to practice conducting a repeated measures ANOVA. First, provide students with the research scenario and the accompanying questions to have them determine the research design, statistical analysis to use, and independent and dependent variables. Next, have students set up a data file using the included data from the study and run the appropriate analysis. Students should summarize their results. An answer key and output are included. Although PASW (SPSS) output is provided, this activity could be run using any statistics program or students could perform calculations by hand.

Research Scenario A researcher is interested in testing which brand of coffee tastes better. Ten people were selected to participate in tasting four different types of coffee: Maxwell House, Folgers, Starbucks, and Dunkin Donuts. All coffee brands were made by the researcher from fresh grinds and the order in which each participant tasted the coffees was counterbalanced. After tasting each brand of coffee, participants rated the quality of taste on a 7-point scale (1 = terrible to 7 = delicious). It is hypothesized that the brands will differ in quality of taste.

1. What type of methodological design is being utilized?

2. What statistical analysis should be utilized to test the prediction?

3. Identify the independent variable(s):

4. Identify the dependent variable(s):

5. Set up an appropriate data file and enter the provided data.

6. Run the appropriate analysis and summarize your findings below:

_____ ______

Participant #: 1

Age: ,;{S

Gender: ~e mCl Ie..

Dunkin Donuts score out of7: L\

Folgers score out of7: 1Starbucks score out of 7: \

Maxwell score out of7: S

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --

Participant #: 2

Age: ~ 1

Gender: rn C/k:

Dunkin Donuts score out of 7: L1

Folgers score out of7: lo

Starbucks score out of7:.J

Maxwell score out of 7: \.p

- - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - -- - --- - -- - - - - - - --

Participant #: 3

Age: 36

Gender: ~malt'

Dunkin Donuts score out of 7:Lj

Folgers score out of7: (p

Starbucks score out of 7: I

Maxwell score out of7: (Q

- - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --

Participant #: 4

Age: ;<0,

Gender: +cmo k:

Dunkin Donuts score out of 7: S

Folgers score out of7: lP

Starbucks score out of7: 3

Maxwell score out of 7: 5

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - - - - --

Participant #: 5

Age: \~

Gender: ~mo. \.e

Dunkin Donuts score out of 7: (p

Folgers score out of7: ':)

Starbucks score out of7: L-I

Maxwell score out of7: 1-)

- - - - - -- - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - --

Participant #: 6

Age: 31

Gender: pi u\e

Dunkin Donuts score out of7: S

Folgers score out of7: ~

Starbucks score out of7: \

Maxwell score outof 7: 4

- - - - - - - - - - - - - - - -- - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --

Participant #: 7

Age: L\0

Gender: ~e /YO Ie

/

Dunkin Donuts score out of 7: ;)

Folgers score out of7: -,

Starbucks score out of7: J-

Maxwell score out of 7: Lv

- - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - --

Participant #: 8

Age: S \

Gender: )'YIQ\e.

Dunkin Donuts score out of7: 3

Folgers score out of7: I

Starbucks score out of7: :;l.

Maxwell score out of 7: c:)

- - - - - - - - - - - - - - - -- - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - --

Participant #: 9

Age: L\d

Gender: +'cYnCt l-e

Dunkin Donuts score out of 7: ~

Folgers score out of 7: {p

Starbucks score out of7: J

Maxwell score out of 7: S

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -- - --

Participant #: 10

Age: (06

Gender: n1C\ 1<:

Dunkin Donuts score out of7: 5

Folgers score out of 7: 1.0

Starbucks score out of7: L\

Maxwell score out of7: Y

ANSWER KEY Conducting a One-way ANOVA

Research Scenario A researcher is interested in testing which brand of coffee tastes better. Ten people were selected to participate in tasting four different types of coffee: Maxwell House, Folgers, Starbucks, and Dunkin Donuts. All coffee brands were made by the researcher from fresh grinds and the order in which each participant tasted the coffees was counterbalanced. After tasting each brand of coffee, participants rated the quality of taste on a 7-point scale (1 = terrible to 7 = delicious). It is hypothesized that the brands will differ in quality of taste.

1. What type of methodological design is being utilized? multi-group design (repeated measures)

2. What statistical analysis should be utilized to test the prediction? Repeated Measures ANOVA

3. Identify the independent variable(s): brand of coffee

4. Identify the levels of each independent variable: Maxwell House, Folgers, Starbucks, and Dunkin Donuts

5. Identify the dependent variables: quality of taste (range 1-7)

6. Set up an appropriate data file and enter the provided data.

7. Run the appropriate analysis and summarize your findings below:

The hypothesis was supported. The quality of taste was rated as significantly different between brands.

Pairwise comparisons revealed that the ratings of Folgers (M = 6.20) coffee were significantly higher

than the ratings of Maxwell House (M = 5.00) , Starbucks (M = 2.30), and Dunkin Donuts (M = 4.20).

Similarly, Starbucks was rated significantly lower than each of the other brands.

PASW (SPSS) Output Conducting a Repeated Measures ANOVA

General Linear Model Within-Subjects Factors

Measure:MEASURE_1

coffee_1 Dependent Variable

1 Dunkin_Donuts

2 Folgers

3 Starbucks

4 Maxwell

Multivariate Testsb

Effect Value F Hypothesis df Error df Sig.

coffee_1 Pillai's Trace .904 21.953a 3.000 7.000 .001

Wilks' Lambda .096 21.953a 3.000 7.000 .001

Hotelling's Trace 9.409 21.953a 3.000 7.000 .001

Roy's Largest Root 9.409 21.953a 3.000 7.000 .001

a. Exact statistic

b. Design: Intercept Within Subjects Design: coffee_1

Mauchly's Test of Sphericityb

Measure:MEASURE_1

Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig.

Epsilona

Greenhouse-Geisser Huynh-Feldt Lower-bound

coffee_1 .348 8.151 5 .151 .609 .756 .333

Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.

a. 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.

b. Design: Intercept Within Subjects Design: coffee_1

Descriptive Statistics

Mean Std. Deviation N

Dunkin_Donuts 4.2000 1.13529 10

Folgers 6.2000 .63246 10

Starbucks 2.3000 1.15950 10

Maxwell 5.0000 .81650 10

Tests of Within-Subjects Contrasts

Measure:MEASURE_1

Source coffee_1 Type III Sum of

Squares df Mean Square F Sig.

coffee_1 Linear 1.125 1 1.125 1.074 .327

Quadratic 1.225 1 1.225 2.436 .153

Cubic 78.125 1 78.125 41.790 .000

Error(coffee_1) Linear 9.425 9 1.047

Quadratic 4.525 9 .503

Cubic 16.825 9 1.869

Tests of Between-Subjects Effects

Measure:MEASURE_1 Transformed Variable:Average

Source Type III Sum of

Squares df Mean Square F Sig.

Intercept 783.225 1 783.225 2791.693 .000 Error 2.525 9 .281 Estimated Marginal Means

1. Grand Mean

Measure:MEASURE_1

Mean Std. Error

95% Confidence Interval

Lower Bound Upper Bound

4.425 .084 4.236 4.614

Tests of Within-Subjects Effects

Measure:MEASURE_1

Source Type III Sum of

Squares df Mean Square F Sig.

coffee_1 Sphericity Assumed 80.475 3 26.825 23.535 .000

Greenhouse-Geisser 80.475 1.827 44.048 23.535 .000

Huynh-Feldt 80.475 2.268 35.480 23.535 .000

Lower-bound 80.475 1.000 80.475 23.535 .001

Error(coffee_1) Sphericity Assumed 30.775 27 1.140

Greenhouse-Geisser 30.775 16.443 1.872

Huynh-Feldt 30.775 20.414 1.508

Lower-bound 30.775 9.000 3.419

2. coffee_1

Estimates

Measure:MEASURE_1

coffee_1 Mean Std. Error

95% Confidence Interval

Lower Bound Upper Bound

1 4.200 .359 3.388 5.012

2 6.200 .200 5.748 6.652

3 2.300 .367 1.471 3.129

4 5.000 .258 4.416 5.584

Pairwise Comparisons

Measure:MEASURE_1

(I) coffee_1

(J) coffee_1

Mean Difference (I-J) Std. Error Sig.a

95% Confidence Interval for Differencea

Lower Bound Upper Bound

1 2 -2.000* .537 .005 -3.216 -.784

3 1.900* .379 .001 1.044 2.756

4 -.800 .573 .196 -2.097 .497

2 1 2.000* .537 .005 .784 3.216

3 3.900* .504 .000 2.759 5.041

4 1.200* .249 .001 .636 1.764

3 1 -1.900* .379 .001 -2.756 -1.044

2 -3.900* .504 .000 -5.041 -2.759

4 -2.700* .539 .001 -3.918 -1.482

4 1 .800 .573 .196 -.497 2.097

2 -1.200* .249 .001 -1.764 -.636

3 2.700* .539 .001 1.482 3.918

Based on estimated marginal means

*. The mean difference is significant at the .05 level.

a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

Multivariate Tests

Value F Hypothesis df Error df Sig.

Pillai's trace .904 21.953a 3.000 7.000 .001

Wilks' lambda .096 21.953a 3.000 7.000 .001

Hotelling's trace 9.409 21.953a 3.000 7.000 .001

Roy's largest root 9.409 21.953a 3.000 7.000 .001

Each F tests the multivariate effect of coffee_1. These tests are based on the linearly independent pairwise comparisons among the estimated marginal means.

a. Exact statistic