Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
Prepared by:
Prof. Dr Bahaman Abu SamahDepartment of Professional Development and Continuing Education
Faculty of Educational StudiesUniversiti Putra Malaysia
Serdang
Use in experiment, quasi-experiment and field studies in
which the same subject is measured under all levels of
one or more trials
The dependent variable is interval or ratio
Trials is referred to as repeated-measure factor or within-
subjects factor
Test the effect of within-subjects factor (trial), between-
subjects factor (treatment) and interaction on the
dependent variable
1. Treatment main effect: Is there any significant difference
in sentence construction scores among the three
treatment groups?
2. Trial main effect: Is there any significant difference in
sentence construction scores among the three trials?
3. Interaction between treatment and trial: Do the
differences in means for the sentence construction scores
among the treatment groups vary depending on the
trials?
1 DV is normally distributed in the population for each level of the within-subjects factor (trial)
2 The population variances of the difference scores computed between any two levels of a within-subjects factor are the same value regardless of which two levels are chosen.This assumption is also known as the sphericity assumption or homogeneity of variance of differences assumption
3 The cases represent a random samples from the populations, and the scores are independent of each other
Set Alpha
State
HO and HA
(3 Hypotheses)
Report
F & sig-F
Decision
Conclusion
Next ►
- Post-Hoc Comparison
- Effect size (Partial Eta2)
Criteria Decision
sig-F> α Reject HO
sig-F ≥ α Fail to reject HO
Steps in:
State HO and HA
Set confidence level (α)
Run analysis & report F and sig-F
Decision
Conclusion
1
2
3
4
5
Next ►
1. Trial Main Effect (Within-Subjects)
HO: μt1 = μt2 = μt3
HA: Not all means are equal
2. Treatment Main Effect (Between-Subjects)
HO: μ1 = μ2 = μ2
HA: Not all means are equal
3. Interaction (I*J)
HO: μij = μˈijHA: μij ≠ μˈij
Next ►
α = .05
F and sig-F
Reject HO: sig-F ≤ α
Fail to reject HO: sig-F > α
– Only two (2) possible decisions.
– Reject or Fail to Reject HO
Criteria Decision
sig-F ≤ α Reject HO
sig-F > α Fail to reject HO
Treatment (Group) Main effect
Reject HO There is a significant treatment (group)
main effect on the DV
Fail to reject HO There is no significant treatment (group)
main effect on the DV
Decision criteria
Criteria Decision
sig-F ≤ α Reject HO
sig-F > α Fail to reject HO
Trial Main effect
Reject HO There is a significant trial main effect on the DV
Fail to reject HO There is no significant trial main effect on the
DV
Interaction: Treatment x Trial
Reject HO There is a significant treatment-by-trial
interaction effect on the DV
Fail to reject HO There is no significant treatment-by-trial
interaction effect on the DV
– Use partial eta squared (η2) as a measure of effect size
– Formula to calculate partial η2
– Partial η2 indicated relationship between repeated-measures factor
and the dependent variable; ranges between 0 to 1
– 0 indicates no relationship; 1 constitutes highest possible relationship
between repeated measures factor and the dependent variable
SSESSB
SSBPartial
ninteractioorMain
ninteractioorMain
ninteractioorMain
2
Effect size Conventions:< .10 Trivial.10 Small.25 Medium.40 Large
Cohen, 1992
In a study, a researcher is interested to
access the effectiveness of a training
program to improve students’ thinking skill.
Students were randomly assigned into
three groups based on their academic
achievement (low, moderate, and high).
Data were collected at pre, post1, and
post2.
16 17 25
9 17 22
10 18 26
6 18 25
8 17 24
17 19 28
16 18 27
10 17 26
9 15 24
10 14 23
9 13 22
8 12 22
9 13 21
8 13 21
9 13 21
8 12 22
7 8 9
2 3 4
1 7 9
4 10 20
8 10 12
9 11 13
5 10 14
4 11 14
1
2
3
4
5
6
7
8
1
1
2
3
4
5
6
7
8
2
1
2
3
4
5
6
7
8
3
ACHIEVE
PRE POST1 POST2
Data set: D8 Twowar Repeated Measure ANOVA THINKING SKILL
1. Treatment main effect: Is there any significant difference in
thinking skill scores among the three treatment groups?
2. Trial main effect: Is there any significant difference in thinking
skill scores among the three trials?
3. Interaction between treatment and trial: Do the differences in
means for the thinking skill scores among the treatment groups
vary depending on the trials?
HO: μ1 = μ2 = μ3
HA: Not all means are equal
1. Treatment main effect (Between group)
HO: μ1 = μ2 = μ3
HA: Not all means are equal
2. Trial main effect (Within-Subjects factor)
HO: μij = μ’ij
HA: μij ≠ μ’ij
3. Interaction treatment x trial
α = .05
Multivariate Testsc
.940 157.836a 2.000 20.000 .000
.060 157.836a 2.000 20.000 .000
15.784 157.836a 2.000 20.000 .000
15.784 157.836a 2.000 20.000 .000
.749 6.288 4.000 42.000 .000
.313 7.879a 4.000 40.000 .000
1.999 9.494 4.000 38.000 .000
1.894 19.890b 2.000 21.000 .000
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
Effect
TRIAL
TRIAL * ACHIEVE
Value F Hypothesis df Error df Sig.
Exact statistica.
The statistic is an upper bound on F that yields a lower bound on the significance level.b.
Design: Intercept+ACHIEVE
Within Subjects Design: TRIAL
c.
Use of Multivariate tests does not require the assumption of sphericity
Report F-ratio. Decision is based on sig-F
Sig-F (.000) < .05; Significant trial main effect
Multivariate Tests
Mauchly's Test of Sphericityb
Measure: MEASURE_1
.628 9.316 2 .009 .729 .844 .500
Within Subjects Effect
TRIAL
Mauchly's W
Approx.
Chi-Square df Sig.
Greenhous
e-Geisser Huynh-Feldt Lower-bound
Epsilona
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is
proportional to an identity matrix.
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.
a.
Design: Intercept+ACHIEVE
Within Subjects Design: TRIAL
b.
Sig-value < α indicates violation of sphericityassumption
Tests of Sphericity
Tests of Within-Subjects Effects
Measure: MEASURE_1
1554.778 2 777.389 200.411 .000
1554.778 1.457 1066.857 200.411 .000
1554.778 1.687 921.405 200.411 .000
1554.778 1.000 1554.778 200.411 .000
137.639 4 34.410 8.871 .000
137.639 2.915 47.223 8.871 .000
137.639 3.375 40.784 8.871 .000
137.639 2.000 68.819 8.871 .002
162.917 42 3.879
162.917 30.604 5.323
162.917 35.435 4.598
162.917 21.000 7.758
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Source
TRIAL
TRIAL * ACHIEVE
Error(TRIAL)
Type III Sum
of Squares df Mean Square F Sig.
Tests of Within-Subjects Effects Use this value if the test meets the sphericity assumption
Use any of the other three values if the sphericity assumption is violated
Tests of Between-Subjects Effects
Measure: MEASURE_1
Transformed Variable: Average
13667.556 1 13667.556 1064.675 .000 .981
1137.528 2 568.764 44.306 .000 .808
269.583 21 12.837
Source
Intercept
ACHIEVE
Error
Type III Sum
of Squares df Mean Square F Sig.
Partial Eta
Squared
Report the F-value. However, decision is based on sig-F
Sig-F (.000) < .05; reject the null hypothesis. Significant treatment effect
Effect size
Tests of Between-Subjects Effects
Decision criteria
Treatment (Group) Main effect
F = 44.306, sig –F = .000
sig-F (.000) is smaller than α (.05)
Reject HO
There is a significant treatment (group) main effect on
sentence construction scores at .05 level of significance
Criteria Decision
sig-F> α Reject HO
sig-F ≥ α Fail to reject HO
Trial Main effect
F = 200.411, sig-F = .000
sig-F (.000) is smaller than α (.05)
Reject HO
There is a significant trial main effect on sentence
construction scores at .05 level of significance
Interaction: Treatment x Trial
F = 8.871, sig-F = .000
sig-F (.000) is smaller than α (.05)
Reject HO
There is a significant treatment-by-trial interaction effect on
sentence construction scores at .05 level of significance
If the ANOVA reveals a significant result, proceed with the pairwise
comparisons to assess which means differ from each other
Pairwise Comparisons
Measure: MEASURE_1
3.542* 1.034 .003 1.391 5.693
9.625* 1.034 .000 7.474 11.776
-3.542* 1.034 .003 -5.693 -1.391
6.083* 1.034 .000 3.932 8.234
-9.625* 1.034 .000 -11.776 -7.474
-6.083* 1.034 .000 -8.234 -3.932
(J) Academic
achievement
2
3
1
3
1
2
(I) Academic achievement
1
2
3
Mean
Difference
(I-J) Std. Error Sig.a
Lower Bound Upper Bound
95% Confidence Interval for
Differencea
Based on estimated marginal means
The mean difference is significant at the .05 level.*.
Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).a.
Pairwise comparison: Treatment
There are significant differences for the following pairs of groups:
1. 1 and 2
2. 1 and 3
3. 2 and 3
Pairwise Comparisons
Measure: MEASURE_1
-4.750* .560 .000 -5.915 -3.585
-11.333* .706 .000 -12.802 -9.865
4.750* .560 .000 3.585 5.915
-6.583* .397 .000 -7.408 -5.759
11.333* .706 .000 9.865 12.802
6.583* .397 .000 5.759 7.408
(J) TRIAL
2
3
1
3
1
2
(I) TRIAL
1
2
3
Mean
Difference
(I-J) Std. Error Sig.a
Lower Bound Upper Bound
95% Confidence Interval for
Differencea
Based on estimated marginal means
The mean difference is significant at the .05 level.*.
Adjustment for multiple comparisons: Least Significant Difference (equivalent to no
adjustments).
a.
Pairwise comparison: Trial
There are significant differences for the following pairs of trials:
1. 1 and 2
2. 1 and 3
3. 2 and 3
1. Click Analyze | General Linear Model | Repeated Measures
2. At the dialog box below, type ‘trial’ as within-subject factor name.
and type 3 for the number of levels.
- Click Add button.
- Then click Define button.
3. Block all the within-subjects factors (Pre, Post1 and Post2),
click the right arrow button.
4. Click the Academic achievement and enter into Between-
Subject Factor(s) box. Then click the Option button
5. In the following Option dialog box, tick and select the following
options. Click the Continue button
6. In the following Option dialog box, click OK