1 DV is normally distributed in the population for each level of the within-subjects factor 2 The population variances of the difference scores

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1 One-way Prepared by: Prof. Dr Bahaman Abu Samah Department of Professional Development and Continuing Education Faculty of Educational Studies Universiti Putra Malaysia Serdang

2 The purpose is to test the effect of within-subject factor on the dependent variable Use in experiment in which the same subject is measured under all levels trials Trial is referred to as repeated-measure factor or withinsubjects factor Next

3 1 DV is normally distributed in the population for each level of the within-subjects factor 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

4 Use partial eta squared (η ) as a measure of effect size Formula to calculate partial η Partial factor SS SS factor factor SS error Partial η indicated relationship between repeatedmeasures factor and the dependent variable Partial η ranges between 0 to 1 0 indicates no relationship; 1 constitutes highest possible relationship between factor and the dependent variable

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6 Manual Calculate F-ratio Criteria F cal F critical F cal < F critical Decision Reject H O Fail to reject H O State H O and H A Decision Conclusion Critical value Effect size (Partial Eta ) Next

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8 1 State H O and H A 4 3 Calculate Test Statistics Determine Critical Value Decision 5 Conclusion Next

9 H O : μ 1 = μ = μ 3 H A : Not all means are equal Next

10 1. Calculate Sum of Squares Total Sum of Squares S S Between Subjects S S Between Factor Sum of Squares Error ( Y ) SST Y N Ts ( Y ) SSBs n N SSB SSE f T n f f s ( Y ) N SST SSB s SSB f

11 . Determine Degrees of Freedom Total df T N 1 Subject Factor Error df s n df df f error s n f 1 1 ( n 1) ( n 1) s f Where: n s Number of subjects n f Number/levels of factors

12 Source SS df MS F Subject SSB s n s -1 MSB s F s Factor SSB f n f -1 MSB f F f Error SSE (n s -1) (n f -1) MSE TOTAL SST N-1

13 3. Critical value F n n f 1 ( ) ( 1)( n 1) s f

14 4. Decision and Conclusion Reject H O There is a significant difference in DV among different levels of withinsubjects factors Fail to reject H O There is no significant difference in DV among different level of within-subjects factor Decision criteria Criteria Decision F cal F critical F cal < F critical Reject H O Fail to reject H O

15 In a study to determine the effectiveness of relaxation techniques in controlling migraine headaches, nine migraine sufferers were selected. They were asked to record the frequency and duration of their migraine headaches for a five week period. Data for the first two weeks were based on no training and act as baseline while the third to fifth weeks were given relaxation training.

16 Baseline Training week week week week week Subject Subject total Total Mean

17 H O : μ 1 = μ = μ 3 = μ 4 = μ 5 H A : Not all means are equal

18 Sum of Squares SST Y ( Y ) N , ,060 1, ,

19 ) ( N Y n T SS f s S , , , ,380.4

20 ) ( N Y n T SSB s f f , ,086, , , SSB s SSB f SST SSE, , , , f s SSB SSB SST

21 Total Subjects Factor Error df T N df S n s df df f error n f ( n 1) ( n 1) s 4 ( 9 1) (5 1) (8) (4) 3 f Where: n s Number of subjects n f Number/levels of factors

22 Source SS df MS F Subject Factor, Error TOTAL 3,

23 F 4 3 (.05).69

24 F cal (85.08) is bigger than F critical (.69) Reject H O There is a significant factor (relaxation training) effect on duration of migraine at.05 level of significance Decision criteria Criteria F cal F critical F cal < F critical Decision Reject H O Fail to reject H O

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26 1. Click Analyze General Linear Model Repeated Measures

27 . At the dialog box below, type training as within-subject factor name. and type 5 for the number of levels. Click Add button. Then click Define button.

28 3. Block all the within-subjects factor, Click Arrow button

29 4. Finally, click the OK button

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31 Use of this Multivariate tests does not require the assumption of sphericity

32 Sig-value (.537) > α indicates meeting the sphericity assumption

33 Tests of Within-Subjects Effects Use this value if the test meets the sphericity assumption Measure: MEASURE_1 Source TRAINING Error(TRAINING) Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Type III Sum of Squares df Mean Square F Sig Use any of the other three values if the sphericity assumption is violated

34 If the ANOVA reveals a significant result, proceed with the pairwise comparisons to assess which means differ from each other

35 Click the first factor, displays as Variable 1 Click the second factor, displays as Variable Click Arrow button

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37 Pair 1 Pair Pair 3 Pair 4 Pair 5 Pair 6 Pair 7 Pair 8 Pair 9 Pair 10 W1 - W W1 - W3 W1 - W4 W1 - W5 W - W3 W - W4 W - W5 W3 - W4 W3 - W5 W4 - W5 Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Error Difference Mean Std. Deviation Mean Lower Upper t df Sig. (-tailed) Use the Holm s sequential Bonferroni procedure to control for familywise error rate across the 10 pairs /10 = /5 = /9 = /4 = /8 = /3 = /7 = / = /6 = /1 =.05