Mixed between-within groups ANOVA

By Mahsa FarahanyniaPhD studentAllameh Tabataba‘i University, Iran 2015

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.

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).

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

Step 1: Normality of the dataAnalyze explore

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.

Mixed between-within groups ANOVA in SPSS Analyze General Linear Model Repeated measures

Mixed between-within groups ANOVA in SPSS

Mixed between-within groups ANOVA in SPSS

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

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.

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.

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.

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.

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.

Step 7: Graphical display

Figure 1. The performance of four groups in the pretest and posttest