PART ONE: Testing for One-Way ANOVA

Answer

PART ONE: Testing for One-Way ANOVA

Selected Data set: HS Longitudinal Study

One may want to determine whether perceptions of collective responsibility if affected by the level of an individual’s education.

Research question: Do Math teacher's perceptions of collective responsibility depend on highest degree earned?

Null hypothesis: The null hypothesis to be tested is: Math teacher’s perceptions of collective responsibility does change as highest degree earned changes

Dependent variable: Math teacher’s perceptions of collective responsibility which is measured as a continuous variable.

Independent variable: Math teacher’s highest degree earned. This is a categorical variable measured on an ordinal scale.

In order to decide which post-hoc test to use, we have to test whether equality of variances in the data can be assumed or not (Laureate Education, 2016; Wagner, 2016).

From the table above, equality of variances cannot be assumed, p=0.006. We shall therefore choose a post-hoc test that does not assume equality of variances.

Table showing descriptive statistics of scale of math teacher's perceptions of collective responsibility across the levels of highest degree earned.

The results indicated in the ANOVA table concludes that on the overall, the mean scale of math teacher's perceptions of collective responsibility varied across the different levels of highest degree earned F (3, 15031) = 22.520, and at =0.000 (95%). The null hypotheses that Math teacher’s perceptions of collective responsibility does change as highest degree earned changes is thus rejected. To decide on the specific levels of highest degree earned which had different mean score of Math teacher’s perceptions of collective responsibility does change as highest degree earned changes, a Games-Howell Post-Hoc test is run since equality of variances cannot be assumed (Norris, et. al., 2013; Frankfort-Nachmias & Leon-Guerrero 2015).

Results from the post hoc test show that math teachers with Bachelor’s degree had a significantly lower mean score than those with Master’s degree, Mean difference of 0.12067, p<0.05. The same group also had a 0.20930 lower score than Educational Specialist diploma, p=0.007. Those with a Master’s degree had a 0.32490 score higher than the Ph.D./M.D./law degree/other prof degree group, p=0.01. The Educational Specialist diploma had a 0.41352 higher than Ph.D./M.D./law degree/other prof degree, p=0.004. The remaining groups did not now statistically significant differences.

Implication for social change

Perceptions about collective responsibility varied differently across the different levels of highest degree earned. This suggests that a more targeted approach towards enhancing collective social responsibility.

PART TWO: One-Way ANOVA in Practice by critiquing the use of one-way ANOVA in a research article.

Article title: Self-Management Training for Increasing Job Attendance; A Follow-Up and a Replication. The article was published in the Journal of Applied Psychology in 1989, volume 74, and issue number 3 from page 411 to 416. The subject discussed is self-efficacy and how it relates to job attendance. 

The author’s purpose, approach or methods, hypothesis, and major conclusions: This study had two main purposes. The first purpose was to measure the extent to which relapse occurred after the initial training on self-management by taking measurement of self-efficacy at four different levels namely pre-training, three months, six months, nine months and one year after training. The second purpose was to examine how self-management training resulted in trainees’ self-efficacy in responding to obstacles in job attendance. Comparisons were made with a control group who received the same training from a different person. Performance as relates job attendance was compared between the group that received the initial training and the control group. The main hypothesis was that one’s perceived self-efficacy would be increased by training in self-management in responding to challenges in job attendance. Study researchers hypothesized that training in self-management would increase job attendance through increasing self-efficacy.  The variables that were measured include: learning measures to determine whether the employees retained the training; perceived self-efficacy to determine its relationship with job attendance. Job attendance was also measured, which was the dependent variable of primary interest. It was concluded that self-efficacy predicted job attendance.

Critique of Analysis of data using ANOVA

To examine whether the trainees retained learned knowledge significantly across months 3, 6 and 9 after the initial training on self-management, a one-way ANOVA test was used. Findings were that the knowledge acquired did not decrease over time. The authors used a one-way ANOVA test in order to examine differences in mean score of retained knowledge across the three different times: 3, 6 and 9 months. This was an appropriate choice of test, because it is used to compare groups. The authors however, did not display the results from the ANOVA analysis although the results explained are well understood.

To examine mean scores of retained knowledge at three months between the experimental and control groups. A one-way ANOVA was used. However a better test to use would have been an independent sample t-test because it involves comparison of only two groups (Howitt, et. al., 2014). The results were only explained sufficiently but not displayed.

To examine how job attendance and sick leave varied between the experimental and control groups the authors used one-way ANOVA, although they could have used a t-test as a better choice. However results were not displayed.

To examine differences in job attendance over 4, 6 and 9 months, a one-way ANOVA test was appropriately used. However the authors did not display the data, but rather explained the results sufficiently.