# The Efficacy of MOOC to Support Students in Pedagogical Research
## 4 Analyses and Results
### The Analysis of Covariance with the Pretest Control  
Table 3 contains descriptive statistics such as the mean, the standard deviation, the standard error and 95% confidence interval of the mean. From the means we can see slight differences in the pretest score between the groups, the standard deviations indicate that the variability of the test score is approximately the same in both groups. Figure 3: Example from the project assignment for the experimental group (posttest). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Level of Factor** & **N** & **Pretest Mean** & **Pretest Std. Dev.** & **Pretest Std. Err.** & **Pretest \(-\)95.00\%** & **Pretest +95.00\%** \\ \hline Total & & 109 & 2.01 & 0.89 & 0.09 & 1.84 & 2.18 \\ Group 2 & con & 68 & 2.11 & 0.90 & 0.11 & 1.89 & 2.33 \\ Group 2 & exp & 41 & 1.84 & 0.87 & 0.14 & 1.57 & 2.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics for the pretest. From Table 4 of the descriptive statistics we see the differences in the posttest score between the groups in favor of the experimental group, the standard deviations are approximately the same which means also the variability in both groups and the error obtain values close to zero. To find whether the posttest values were not affected by any other variable, we apply the analysis of covariance for the pretest and the posttest data. Using this analysis, we find out whether the variable of the posttest is not dependent on the variable of the pretest (covariate), which means whether the existing knowledge of the participants before the experiment did not affect the results in the posttest. We have identified only small deviations from the normality. For this reason, in addition to parametric tests (_Hartley F-max_ = 1.168, _Cochran C_ = 0.538, _Bartlett Chi-Sqr_ = 0.296, \(p\) = 0.5865) we also used a nonparametric Levene's test (_F_ = 1.457, \(p\) = 0.2301) to verify the assumptions of the equality of variances. Assumptions for using the analysis of covariance:  
* the assumptions of the analysis of variance are valid,
* the regression coefficient Beta is the same in all groups. We have fulfilled the assumptions of the analysis of variance. To verify the assumption of the equality of variances, we also use the parametric multivariate Box M test designed for the analysis of covariance (_Box M_ = 5.677, _Chi-Sqr_ = 5.552, _df_ = 3, \(p\) = 0.1356). The test is statistically insignificant, so the hypothesis of the equality of variances (homogeneity of variance-covariance matrices) is not rejected. We can state that there was no violation of the assumption. The easiest way to verify the condition of the equality of the regression coefficient in the groups is to check the categorized correlation graph for each factor level (Figure 4a,b). There is a quantitative factor on the horizontal axis, the dependent variable depends on the vertical axis. If the particular lines have approximately the same slope, the condition is met. The curves have the same slope, which means the regression coefficient is approximately the same in both groups. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Level of Factor** & **N** & **Posttest Mean** & **Posttest Std. Dev.** & **Posttest Std. Err.** & **Posttest \(-\)95.00\%** & **Posttest +95.00\%** \\ \hline Total & 109 & 0.69 & 0.21 & 0.02 & 0.65 & 0.73 \\ Group 2 & con & 68 & 0.60 & 0.18 & 0.02 & 0.56 & 0.65 \\ Group 2 & exp & 41 & 0.83 & 0.17 & 0.03 & 0.78 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics for the posttest. Figure 4: Scatter plot for the: (**a**) control group; (**b**) experimental group. From Table 5 we can see that the relationship between the posttest and the pretest is statistically significant (\(p<0.05\)), which means the pretest results affected the posttest results.