University of North Texas Dr. J. Kyle Roberts © 2004

Unit 6: Analysis of Variance (ANOVA)

Lesson 2: Computing Post Hoc Tests and Effect Sizes

EDER 6010: Statistics for Educational Research

Dr. J. Kyle Roberts

University of North Texas

I know they’re different, but

where??

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University of North Texas Dr. J. Kyle Roberts © 2004

Post Hoc Tests

ANOVA only tells if there is a difference

Post Hoc tests tell specifically where these differences lay

43210 : XXXXH

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University of North Texas Dr. J. Kyle Roberts © 2004

Running Post Hocs in SPSS

Asian Black Hispanic White

9 7 6 8

7 9 5 8

8 3 2 7

7 5 1 7

7 8 3 5

2 Variables:Grouping VariableScore Variable

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University of North Texas Dr. J. Kyle Roberts © 2004

Running an ANOVA in SPSSAnalyzeCompare MeansOne-Way ANOVA

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University of North Texas Dr. J. Kyle Roberts © 2004

SPSS Output for Post Hoc TestsMultiple Comparisons

Dependent Variable: SCORE

Tukey HSD

1.2000 1.11355 .708 -1.9859 4.3859

4.2000* 1.11355 .008 1.0141 7.3859

.6000 1.11355 .948 -2.5859 3.7859

-1.2000 1.11355 .708 -4.3859 1.9859

3.0000 1.11355 .069 -.1859 6.1859

-.6000 1.11355 .948 -3.7859 2.5859

-4.2000* 1.11355 .008 -7.3859 -1.0141

-3.0000 1.11355 .069 -6.1859 .1859

-3.6000* 1.11355 .024 -6.7859 -.4141

-.6000 1.11355 .948 -3.7859 2.5859

.6000 1.11355 .948 -2.5859 3.7859

3.6000* 1.11355 .024 .4141 6.7859

(J) ETHNICBlack

Hispanic

White

Asian

Hispanic

White

Asian

Black

White

Asian

Black

Hispanic

(I) ETHNICAsian

Black

Hispanic

White

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound

95% Confidence Interval

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

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University of North Texas Dr. J. Kyle Roberts © 2004

SPSS Output for Post Hoc Tests

SCORE

Tukey HSDa

5 3.4000

5 6.4000 6.4000

5 7.0000

5 7.6000

.069 .708

ETHNICHispanic

Black

White

Asian

Sig.

N 1 2

Subset for alpha = .05

Means for groups in homogeneous subsets are displayed.

Uses Harmonic Mean Sample Size = 5.000.a.

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University of North Texas Dr. J. Kyle Roberts © 2004

Effect Size Measures

Total

Between

SS

SS2

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Eta-squared – the percent variance accounted for by the factor (way) of the dependent variable

How good is our way at describing the variation in the dependent variable?

University of North Texas Dr. J. Kyle Roberts © 2004

Effect Size

2 = .513

Score variableSS = 101.80

EthnicitySS = 52.20

Percent variance explained

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University of North Texas Dr. J. Kyle Roberts © 2004

Unit 6: Analysis of Variance (ANOVA)

Lesson 2: Computing Post Hoc Tests and Effect Sizes

EDER 6010: Statistics for Educational Research

Dr. J. Kyle Roberts

University of North Texas

I know they’re different, but

where??