One-sample T-Test Homework
Like the Alabama State School Superintendent, you become interested in the teacher qualifications of all of the districts in the state. From the Alabama State Department of Education website, you accessed a dataset with the level of education of teachers in each school district in Alabama. You are curious as to how the percent of education specialists (6 Year Column) teaching in Alabama’s public schools compare to the national average for public schools. You determine that U. S. public school teachers with a specialist's degree were equal to 7.60% based on the 2017-2018 NCES data. Answer the following questions.
Descriptive Statistics
1. What is the mean percent of teachers holding a specialist’s degree employed in the school districts in Alabama? 5.60
2. What is the median percent of teachers holding a specialist’s degree employed in the school districts in Alabama? 5.39
3. What is the value of the standard deviation? 3.19
4. What is the value of the skewness statistic? Is this value computed by SPSS supported by a comparison of the mean and median? Explain. Skewness was calculated as .747. Yes, this value is supported. The deviation from zero is relatively small just as the difference is between the mean and the median.
One-Sample t-test Assumptions
5. Does the sample meet the assumptions for conducting a one-sample t-test? Why or why not? Explain the reasoning for each assumption. The assumptions for calculating a one-sample t-test are:
• Interval or ratio data
• Normally distributed population
• Availability of the population mean
Yes, because the population of Ed.S. degreed teachers is a ratio.
Yes, the population data near the mean are more frequent in occurrence than data far from the mean. It is not a perfect normal distribution, but the majority of the data is near the mean.
Yes, the population mean is readily available as all teachers are recorded in the national database.
6. a. Write an acceptable null hypothesis using written statement form.
There is no difference between the percentage of Alabama teachers with an Education Specialist Degree as compared to other US public school teachers.
b. Write an acceptable research or alternative non-directional hypothesis.
There is a difference between the percentage of Alabama teachers with an Education Specialist Degree as compared to other US public school teachers.
c. Write acceptable research or alternative directional hypothesis.
The number of Alabama teachers with an Education Specialist Degree is greater than other US public school teachers.
7. What is the observed or computed value of t?(do not round) -5.648
8. What is the value of the degrees of freedom that are reported in the output)? 80
9. What is the reported level of significance? (do not round) .001
10. Based on the reported level of significance, would you reject the null hypothesis? Explain. Yes, we have to reject the null hypothesis because p is less than .05.
11. Use the critical t value chart C. 4, the known sample size, degrees of freedom, and the level of significance to determine the critical t-value. What is this value? What is the interpretation of this value? Support your answer.1.66
12. What is the reported confidence interval?CI [4.91, 6.30]
13. What is the value of Cohen’s d? Interpret this effect size. -.63, There is a medium effect as it is just above the absolute value .6 and below the large effect size of .8.
14. Present a table with the results, a paragraph reporting the results, and a discussion of the meaning of the results as they might appear in an article.
Results
The Alabama State Superintendent is interested in comparing Alabama teachers with an Education Specialist qualification to the national average of US public school teachers with the same degree. A One-Sample t-Test was computed to compare the groups using the “equal variances not assumed” results. The independent t-test results were significant, t = -5.648, p = .001, d = -.63. Cohen’s d was calculated and gave an effect size of .63, which is moderate. With a mean difference of -2.00, we can see that Alabama teachers have fewer education specialist degrees than the national average. Therefore, we reject the null hypothesis as differences have been evidenced. We are 95% confident that the difference of the means falls between 4.91 and 6.30.
Table 1
Category | n | M | SD | t | df | p d | |
AL Teachers | 81 | 5.60 | 3.19 | -5.648 | 80 | .001 .63 | |
Discussion
Teacher qualification has been a much-debated issue. The standards vary from state to state within our nation, making it hard to compare teacher certifications and credentials across state boundaries. Even teachers with multiple degrees cannot teach in every state, only states with reciprocity. Teachers who can go beyond the bachelor’s degree may not have the desired student growth effect in the classroom. The variables that lead to higher student achievement are not solely tied to teachers obtaining a higher degree. “Equally common, however, is the finding that formal education is irrelevant, leading others to argue for the elimination of colleges of education.” (Harris & Sass, 2008, p 2) With a teacher field dominated by women, it is also much more challenging for teachers to pursue a higher degree even if they desired one. Carving out time to commit to a higher degree comes with both risk and rewards for teachers who are also parents.
Teachers have several issues internally and externally related to obtaining a higher degree. One of the most prevalent is the cost return on obtaining a higher degree. Teacher salary does not grow exponentially with a higher degree. Many would argue that the cost of the degree in cost and time may not add up to being worth the effort. “The degrees with the largest losses over the period were, in order, education, computer science, and English.” (Zimmerman &Altonji, 2007, p. 20) Another consideration is the lack of a ladder of success in teaching. Most teachers have no pathway to promotion unless they are willing to leave the classroom. Obtaining a higher degree becomes moot for a teacher who is not interested in becoming an administrator or leaving the classroom. “Since teachers traditionally are either probationary or not, the only route to advancement is to leave teaching and become an administrator.” (Whitt, 2020)
Several issues prevent teachers from obtaining higher degrees. Alabama teachers face many, if not all, of the issues that hinder obtaining a higher degree. Nevertheless, there is hope that change is on the horizon. With the advent of the current pandemic, maybe a teacher’s worth will be reevaluated and compensated like other professions. Teachers can only hope that this might be a silver lining to the onslaught happening in schools now.
Reference
Altonji, J., & Zimmerman, S. (2017). The Costs of and Net Returns to College Major. National Bureau of Economic Research, 1-45. doi:10.3386/w23029
Harris, D. N., & Sass, T. R. (2007). Teacher training, teacher quality and student achievement. PsycEXTRA Dataset, 1-61. doi:10.1037/e722772011-001
Witte J. F. (2010). Accountability metrics and paying for performance in education and health care. Preventing chronic disease, 7(5), A100.