Teacher self-efficacy is a critical factor in ensuring commitment and confidence of teachers, in the interest of service delivery. In this study, the author used the High School Longitudinal Study dataset to investigate two potential factors that could affect self-efficacy of mathematics teachers, namely: Mathematics teachers perception on principals support and teachers perception of collective responsibility.
RQ1: What is the relationship between mathematics teachers self-efficacy and perception on principals support and perception of collective responsibility?
Ha1: There is a statistically significant association between mathematics teachers self-efficacy and mathematics teachers perception on principals support and teachers perception of collective responsibility.
Ho1: There is a statistically significant relationship between mathematics teachers self-efficacy and mathematics teachers perception on principals support and teachers perception of collective responsibility.
The study applied multiple regressions to test the hypothesis formulated
Results and Analysis
The output in Table 1 illustrated the output of multiple regression conducted.
Table 1: Model Summary
Table 2: ANOVA
Table 3: Coefficients
The model summary (table1) indicates the adjusted r-square value is 0.004, suggesting that about only 0.4% of the variation in mathematics teachers self-efficacy is explained by variation in the both math teacher's perceptions of collective responsibility and teachers perception of principals support. This is a marginal contribution to the change. The ANOVA results as indicated in Table 2 indicated that there is a significant association (p=0.000). The Standardized Beta coefficient is 0.004 for math teacher's perceptions of principal support, suggesting that a unit change in math teacher's perceptions of principal support contributes towards 0.4% change in the teacher's self-efficacy while perceptions of collective responsibility would contribute towards 6% (as the beta coefficient is 0.06. The results affirm that perceptions of collective responsibility are a greater determinant of math-teacher self-efficacy than the perception of principal's support. Perception of principal's support is an insignificant factor, as p=.737for that specific factor.
Conclusion and Implications
Math teachers self-efficacy is significantly associated with perceptions of collective responsibility while the perception of the principal's support has an association with the teachers self-efficacy. There is a need to build a sense of collective responsibility among math teachers as a means of promoting teacher's self-efficacy.
Article Critique: Reviewing Baron et al.s Application of Multiple Regression
In their study, Baron et al. (2015) apply multiple linear regression to examined the association between various gene biomarkers and gene functional regulation impacts on the tolerance of renal allograft. This section reviews the application of multiple linear regression in this study. The review essentially focuses on the statistical analysis of the paper, rather than the substantive validity of the study.
The authors of this study opted to use multiple regression because there were several gene biomarkers and functional gene regulation, which in this case are the independent variable. However, there was only one dependent variable, namely tolerance of renal allograft. All the independent variables were measurable as continuous variables, just as the case with the dependent variable. Using multiple regression allowed the researchers to examine how several gene biomarkers and functional gene regulation would impact on tolerance to the renal allograft. Further, it allowed the researcher to compare the relative strength of various gene biomarkers and functional gene regulation in influencing tolerance to the renal allograft. The choice of multiple regression was therefore suitable. Alternative methods for measuring the statistical association of scale variables such as binary regression or correlation analysis would not have been suitable as these options only apply if there was one factor to be investigated against the dependent variables.
Also, in presenting their results, the authors presents the most important statistical values that the readers need to interpret the results from regression. In reporting on whether or not gene biomarkers and functional gene regulation have a significant statistical impact on the tolerance of renal allograft, the authors reports the p-value for relevant regression output. They report whether p is > or < 0.05 as a measure of the significance of the association. In addition to this, they report the coefficients for the genes. By reporting coefficients, they enable the readers interested in their study to evaluate the direction and strength of the relationships and thereby examine which among the gene biomarkers and gene functional regulation have the most significant effect on tolerance of allograft. Essentially, these are the most crucial statistical values needed. Even then, the reporting would have been more rigorous if they reported the r-square value in the regression output. By adding this component, the readers may examine the proportion of gene tolerance attributed to the gene biomarkers and gene functional regulation. Even then, the results still make sense without this component.
The results cannot stand alone, and therefore needs to be examined in light of other studies. While regression can help predict the impact of one variable on the other, the existence of statistical association does not necessitate causal link. That is, even though gene tolerance may change as some gene biomarkers and gene functional regulation change, there is no guarantee that adjustments in tolerance are caused by the gene biomarkers and gene functional regulation. The study, therefore, needs to examine other studies to highlight on the functioning of gene biomarkers and gene functional regulation, so as to give evaluate the biochemical possibility of such cause. The authors have therefore made efforts to refer to the past studies to account for their results and to support their inferences.
Overall, the methodological choice in this study, namely using multiple regression, was suitable in light of multiple scalable independent variables it had and further considering that the dependent variable too was expressible as a scale.
Baron, D., Ramstein, G., Chesneau, M., Echasseriau, Y., Pallier, A., Paul, C., ... & Giral, M. (2015). A common gene signature across multiple studies relate biomarkers and functional regulation in tolerance to renal allograft. Kidney international, 87(5), 984-995.
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