The Massachusetts Comprehensive Assessment System (MCAS) is a standardized exam administered to students in the state of Massachusetts since 1993. Under law, students educated with public funds are required to participate in statewide testing. Students take exams according to their grade level in subjects such as Mathematics and English Language Arts; passing grades on the Grade 10 MCAS are required for high school graduation. Exam results are used to check student progress as well as measure school and district performance. However, research has shown that variation in standardized test scores is often explained by factors such as race and socioeconomic class; students of color and students from economically disadvantaged backgrounds tend to score lower on standardized tests as a result of having less access to educational resources than their peers. For example, a New York Times article from October 2020 reported the results of a study demonstrating that in the United States, students performed worse on standardized tests for every additional day that was 80 degrees Fahrenheit or higherthe association was observed for Black and Hispanic students, in addition to students with lower family income, but not for white students. In this problem, you will use data from the 2018 Grade 10 Mathematics MCAS to investigate evidence of achievement gaps in standardized test score at the school level. The mcas data contains information on 355 schools in Massachusetts. Scores on the MCAS are classified into levels: warning/failing, needs improvement, proficient, and advanced. Students who score in the "proficient" category are said to "demonstrate a solid understanding of challenging subject matter", while those in the "advanced" category are said to "demonstrate a comprehensive and in-depth understanding of rigorous subject matter"; the variable PA_perc represents the percentage of students at a school who score at the proficient or advanced level. The descriptions of the variables are as follows. Variable Description PA_perc percentage of students scoring proficient or advanced class_size average class size math_class_size average math class size student_teacher_ratio student to teacher ratio attendance_rate average percentage of days attended across students number_of_students total number of students who took the exam largest_minority largest minority group among the student body white_less50 coded TRUE if less than 50% of students are white exp_per_pupil average expenditures per pupil in USD econ_dis percentage of economically disadvantaged students Some additional background on certain variables: - Whether a student is economically disadvantaged is a proxy measure for student family income; a student is considered economically disadvantaged if they are participating in one or more of the following programs: the Supplemental Nutrition Assistance Program (SNAP), the Transitional Assistance for Families with Dependent Children (TAFDC), the Department of Children and Families' (DCF) foster care program, MassHealth (Medicaid). - Expenditures per pupil is a proxy measure for the amount of funding available to a school district. This variable is measured by district (i.e., constant for schools in the same district). 6

Use these data to answer the following questions. a)

Explore the data. i. Briefly summarize features of the sampled schools, focusing on the percentage of students scoring at the proficient/advanced levels, the average expenditures per student, and the percentage of economically disadvantaged students. Reference appropriate numerical and graphical summaries as needed. ii. How many schools have a student body that is greater than (or equal to) 50% white? Of the schools where less than 50% of students are white, describe the distribution of largest_minority. iii. Create a single graphical summary showing the relationship between percentage of students scoring at the proficient/advanced levels, percentage of economically disadvantaged students, and whether a school has a student body that is less than 50% white. Provide an informative description of what you see. b) Examine the association between racial demographics and the percentage of economically disadvantaged students. i. Conduct a formal analysis comparing the percentage of economically disadvantaged students between schools where less than 50% of the students are white and schools where 50% or more of the students are white. Summarize the results, including reporting and interpreting an appropriate confidence interval. Check any necessary assumptions. ii. Among schools where less than 50% of the students are white, conduct a formal analysis comparing the percentage of economically disadvantaged students between schools where the largest minority group is African American versus those where the largest minority group is Hispanic. Summarize the results and check any necessary assumptions. c) Use a modeling approach to estimate the association between the percentage of students scoring at the proficient/advanced levels and whether a school's student body is less than 50% white, adjusting for the following potential confounders. i. Why it would not be advisable to include both class_size and math_class_size in a model predicting PA_perc? Explain your answer. ii. Would you recommend including number_of_students in a model predicting PA_perc? Explain your answer. iii. Fit a model predicting PA_perc from white_less50, math_class_size, attendance_rate, and student_teacher_ratio. Interpret the slope coefficient for white_less50. iv. Add econ_dis to the model from part iii. and interpret the slope coefficient for white_less50. Explain the difference in the interpretation of the slope coefficient for white_less50 in this model versus the model from part iii., using terms accessible to someone who has not taken a statistics course. v. Is the model from part iii. or the model from part iv. preferable for understanding the relationship between the percentage of students scoring at the proficient/advanced levels and whether a school's student body is less than 50% white? Explain your answer. 7 vi. Check the modeling assumptions for the model chosen in part v. Summarize the results. d) Formally assess whether the association between the percentage of students scoring at the proficient/advanced levels and the percentage of students who are economically disadvantaged differs by whether less than 50% of the students are white, after adjusting for math class size, attendance rate, and student-teacher ratio. Summarize the results. e) Consider a school with the following features: an average math class size of 20 students, attendance rate of 93%, and student to teacher ratio of 11, where 60% of students are African American and 45% of students are economically disadvantaged. Suppose that in 2018, 90% of students at this school scored at the proficient/advanced level on the Mathematics Grade 10 MCAS. Based on the model from part c) iv., is this percentage of high scorers considered unusual for schools with the same features? Explain your answer. f) The results from these analyses will be discussed at a future meeting of the Racial Imbalance Advisory Council, which advises the Massachusetts Commissioner of Education and the Board of Education on matters related to providing access to effective educational programs for all students in the state regardless of race or socioeconomic class. Prepare a short statement, no more than ten sentences long, summarizing the main findings of the analyses with respect to understanding whether these data show indication of poverty and/or race-based achievement gaps in Grade 10 Mathematics MCAS scores. Be sure to use language that is accessible to a general audience. Reference previous numerical results as needed