1. Quantitative Analysis

Scenario: You are an education policy analyst for the Governor of California. The Governor is facing pressure from many different groups to bring about reforms that will increase graduation rates. Among the stakeholders are teacher organizations. Their primary argument is that the size of schools should be reduced on the basis that smaller schools allow for a more community-oriented atmosphere, which, in turn, leads to higher performance and graduation rates. Another group of stakeholders consists of community-organizations and parental groups, who argue that schools should be districted so that there is a more even mix of students with high and low family incomes. Both teacher groups and parental groups argue for an increase in spending on instruction. In order to determine the best course of action, the Governor has asked you to conduct a study to examine the effect of all of these variables on graduation rates among California public schools. You randomly select 101 schools across the state. You have prepared a table of descriptive statistics as well as a table of results for OLS multiple regression, so that you can explain your findings.

Table 1. Descriptive Statistics.

GradRate = percentage graduation rate of school.

LowIncRate = percentage of low income students enrolled in school.

ParContactRate = measure of parental involvement in school as a percentage of students whose parents were in contact with the school.

InstrExpd = Expenditures on instruction per pupil (in $1,000s).

LowStuEnroll = indicates a low (0-500 student) number of students enrolled in school (this is a dummy variable – its effect is compared to high student enrollment (1,000+ pupils)).

MidStuEnroll = indicates a mid (501-1,000) number of students enrolled in school (this is a dummy variable – its effect is compared to high student enrollment (1,000+ pupils)).

(1A.) Table 1 includes the means of each of the variables. For the purposes of interpretation, do you think there is an argument for including any other measures of central tendency for any of the other variables? If so, which ones and why? (2)

(Observe that the computation of the mean and median makes sense for all variables in the set except for LowStuEnroll and MidStuEnroll, which are nominal variables, so the mode should be reported instead)

(1B.) Taking a look at Table 1, how would you explain the meaning of standard deviations to the Governor in a way that he/she could easily understand their significance? (2)

(4A.) Using the values in Table 4, write out the regression model in the form of an equation. (2)

(1C.) If you wanted to conduct a more in depth examination of the distributions of the variables, what measures and/or graphical displays might you use? Why would such measures or visuals aid one’s understanding of the distributions of the variables? (3)

In order to examine the effects of your independent variables on graduation rates, you ran an OLS multiple regression model. You received the following outputs (Tables 2-3). You need to be able to interpret and present the results of your findings in plain English to the Governor.

Table 2. Model Summary.

(2A.) Taking a look at Table 2, would you report the results of the R Square or the Adjusted R Square? Why? (2)

(2B.) How would you interpret the results of the R-Square or Adjusted R Square in plain English to the Governor? (2)

Table 3. ANOVA.

(3A.) What is the purpose of the ANOVA table in regression analysis? How would you report the results of Table 3 in a written report to the Governor, including an interpretation of the F statistic? (3)

Table 4. Coefficients.

(4B.) Explain, in plain English, the factors that are associated with higher graduation rates. What evidence do you use to support your conclusion? (4)

(4C.) If you wanted to compare the relative strengths of the effects of the individual coefficients on graduation rates, could you use the unstandardized coefficients? Why or why not? (2)

(4D.) Returning to the original purpose of the study, interpret the findings in plain English. What kinds of reforms might the Governor consider on the basis of your findings? (3)

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