mixed between-within groups anova
TRANSCRIPT
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Mixed between-within groups ANOVA
By Mahsa FarahanyniaPhD studentAllameh Tabataba‘i University, Iran 2015
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Null Hypothesis
Null hypothesis: Different methods of instruction (lecture type
instruction, present the topics using slides, given instruction
combined with student presentation, and pair work discussion of
issues) do not have a significant effect on the learners’ linguistics
achievement.
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Method
Thirty two students in an introductory linguistics class were assigned to
four groups randomly. A linguistics test was administered (as pretest).
The interventions started and the first group received lecture type
instruction. Group two was required to present the topics using slides.
Group 3 was given instruction combined with student presentation. The
last group was involved in pair work discussion of issues. After 5
sessions, the groups sat for another linguistics test (as posttest).
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Data Analysis
Variables 1. One categorical independent between-subjects variable with two
or more levels (group1/group2/group3/group4)
2. One categorical independent within-subjects variable with two or more levels (time1/time2)
3. One continuous dependent variable (scores on linguistic test measured at each time period)
Mixed between-within groups ANOVA
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Step 1: Normality of the dataAnalyze explore
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Step 1: Normality of the data (output)Table 1. one-sample K-S tests and Shapiro-Wilk tests for normality of the data
As seen in Table 1, the data in all sets of scores in both pretest and posttest was normally distributed since the significance levels were all greater than 0.05.
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Mixed between-within groups ANOVA in SPSS Analyze General Linear Model Repeated measures
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Mixed between-within groups ANOVA in SPSS
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Mixed between-within groups ANOVA in SPSS
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Step 2: Descriptive Statistics
As seen in Table 2, the number of participants in each group was eight. In the pretest, group 3 had the best performance (M= 4, SD = 2.07), and group 2 (M=3.75, SD = 1.488) and group 4 (M= 3.50, SD = 2.07) had lower ranks, and the last group was group 1 (M= 3, SD 1.195). Regarding posttest, group 4 (M=8.75, SD=1.035) had the best performance. Group 1 (M= 8.25, SD =1.389) and Group 2 (M= 5.62, SD = 1.923) had moderate performance, and group 3 (M=3.75, SD=1.909) had the worst performance. The means of all groups increased from the pretest to posttest, but group 3.
Table 2. Descriptive statistics of the performance of the four groups in the pretest and posttest
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Step 3: Checking Assumptions1. The assumption of homogeneity of variances
Table 3. Levene’s Test of Equality of Error Variances
As seen in Table 3, the levels of significance in both pretest and posttest are greater than 0.05 (.069 and .191). Therefore, the assumption of homogeneity of variances was not violated.
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Step 3: Checking Assumptions (Cont.)2. The Equality of Covariance Matrices
Table 4. Box’s Test of Equality of Covariance Matrices.
As seen in Table 4, the Sig. value was bigger than .001 (.558); therefore, this
assumption was not violated as well.
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Step 4: Interaction effect and Main effectTable 5. The interaction effect of time and groups
As seen in Table 5, the interaction between time of measurement and groups was significant with a large effect size since Wilks’ Lambda = .432, F (3, 28) = 12.288, p = 0.00, partial eta squared = .568. As seen in Table 5, there was a substantial main effect for time with a large effect size, Wilks’ Lambda = .312, F (1, 28) = 61.727, p ≤ 0.05, partial eta squared = .688. This suggests that there was a change in Linguistics Test scores across the two different time periods. The main effect for time was significant.
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Step 5: Between-subjects effect Table 6. The results of the main effect of groups
As observed in table 6, the main effect comparing the four types of intervention was significant with large effect size, F(3, 28) = 4.905, p= .007, partial eta squared = .344, suggesting a considerable difference in the effectiveness of the four methods.
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Step 6: Post hocTable 6: Multiple comparisons among groups
As seen in Table 6, the difference in the means of group 1 and group 3 as well as that in the means of group 3 and group 4 was statistically significant; while the difference in the means of group 1-2, group1-4, group2-3, group 2-4, and group 4-3 was not significant.
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Step 7: Graphical display
Figure 1. The performance of four groups in the pretest and posttest