Descriptive Statistics
All statistical analyses were conducted using Stata Statistical Software: Release 12
(2011). Data included survey responses from 40 fourth and fifth grade teachers, nested within six schools. The survey consisted of two questions, which indicated the IC implementation time and involvement type/group for each teacher (the two independent variables). The data for the dependent variable, academic change (AC) score, was acquired from a database containing each teacher’s corresponding classroom average AC reading score for students on the EOG reading test. For analysis, the relationships between
classroom average AC reading score, IC implementation time, and IC involvement type were examined.
Due the clustered nature of the data (i.e., classrooms nested within schools), the intraclass correlation coefficient (ICC) was calculated. The ICC was calculated to determine whether hierarchical multiple linear regression was appropriate for statistical analysis, or whether a multilevel model was needed. The ICC for this study indicated that there was no significant between cluster variance (ICC= -.001). Given this finding, hierarchical regression analyses were employed in a non-clustered format.
Prior to conducting the regression analysis to test the hypotheses, descriptive statistics were derived for the variables in the study (see Table 2). For teachers in classrooms with an average AC score of zero, students performed equally as well as they did in previous years. For teachers in classrooms with a positive average AC reading score, students had a gain in
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academic achievement. For teachers in classrooms with a negative average AC score, students had an average loss in student academic achievement. The average AC reading scores and teacher implementation time were normally distributed.
Table 2 Descriptive Statistics N = 40 Teacher IC Implementation Time (years) Classroom AC Score Mean 0.81 0.00 SD 1.15 0.18 Range 0.5-5.0 -0.44-0.26 Skewness 0.76 0.03 Kurtosis 0.00 0.65
The second independent variable, type of involvement, was based on teachers’ survey response: Group A, never worked with the IC-Team; Group B, participated on the IC-Team as an active team member, attending meetings and managing IC cases; Group C, requested assistance of the IC-Team; and Group D, requested assistance of IC-Team and participated on the IC-Team as an active team member, attending meetings and managing IC cases. Teachers that responded Group A or Group B had a corresponding IC implementation time of “0.” Only three teachers responded Group B, as such, that group was too small for analysis (see Table 3). Since all Group A and Group B teachers had a corresponding time of “0” for IC implementation, Groups A and B were combined to form Group A/B. Subsequently, analyses of the categorical variable “IC group” included three groups: Group A/B, C, and D.
51 Table 3
IC GroupDescriptive Statistics
N Teacher Involvement Group Classroom Mean AC Score SD 14 A -.11 .18 3 B .09 .09 15 C .07 .13 8 D .01 .18
Groups A/B (N = 17), C (N = 15), and D (N = 8) were dummy coded within Stata to enable multiple regression analysis. The teachers who did not request ICT assistance to implement IC in the classroom (Group A/B) served as the reference variable in the subsequent analysis. Statistical Analysis
To test the first research hypothesis, bivariate regression analysis was used to determine whether there was a relationship between classroom average AC scores and the amount of time teachers were involved with IC. A p-value less than or equal to the alpha (of .05), indicated a significant effect. The bivariate regression yielded an equation that
indicated whether teacher IC implementation time was predictive of classroom reading growth scores. Specifically, the bivariate regression analysis indicated that 8% of the variance in the classroom reading AC score was associated with teacher IC implementation time, r(38) = .29, p = .07. Thus, no statistically significant linear relationship between teacher IC time and classroom AC score was found.
To address the second research question, teacher IC group (a categorical variable), was entered as dummy code in the linear regression model. Beta coefficients were examined to determine if at least one teacher group mean was significantly different from the reference group, i.e., if the mean scores for Group C and Group D were significantly different from
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mean score of Group A/B. The analysis indicated that one of the means was statistically significantly different from the reference group, F(2, 37) = 3.17, p = .05. Group D was not statistically significant from Group A/B, β = .19, t(37) = 1.18, p = .25 whereas, Group C was statistically significant from Group A/B, β = .41, t(37) = 2.51, p = .01.
Hierarchical multiple linear regression analysis was used to test the third hypothesis regarding possible interactions. In this analysis, the predictor variables of IC time and IC group, representing main effects, were entered in the first step of the model. The regression analysis indicated that IC time and IC group did not account for significant variability in AC scores, R2 = .18, F(3, 36) = 2.61, p = .07. Only 18% of the variability of AC scores was accounted for by its linear relation with IC time and IC group.
In the second step, the interaction term was added to the model. In this step, one interaction term was automatically omitted from the analysis due to collinearity. As all cases in Group A/B had a corresponding implementation time of “0,” there was no variance for this variable. The new model with main effects and the remaining interaction term (Group C and time) accounted for 19% of the variability in AC scores, R2=.19, ∆R2 = .01, F(4, 35) = 2.09, p
= .10. There was thus only a 1% increase in the amount of variance explained by adding the remaining interaction term in the model (see Table 4 for summary table). These results did not support the third hypothesis that the relationship between teacher IC implementation time and classroom reading growth was significantly moderated by teacher IC involvement group.
53 Table 4
Summary Table for Research Question Three
SS df MS F p Step 1 Model .218 3 .078 2.61 .07 Residual 1.003 36 .028 Step 2 Model .235 4 .059 2.09 .10 Residual .986 35 .028
A post hoc power analysis was conducted to determine if the sample size (N = 40) was large enough to detect an interaction effect in the hierarchical multiple linear regression. The post hoc power analysis indicated that the statistical power was .39 for detecting a moderate effect (ƒ2
= .15) in the second step of the model. Thus, there may not have been enough statistical power to detect a moderate effect as the result of the addition of the interaction term.
CHAPTER FOUR