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Statistics and Statistical Programming (Winter 2021)/Problem set 16
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=== PC2: Analyze and interpret a simulated study of education and income === The second part of this problem set poses an open-ended set of questions about a simulated dataset from an observational study of high school graduates' academic achievement and subsequent income. You can '''[https://communitydata.science/~mako/2021-COM520/grads.rds download the data here]'''. The file is an RDS file which is the other data format in R (RData is the other one). To load an RDS file you do: <pre syntaxhighlight="R">grads <- readRDS("FILENAME.rds")</pre> <code>load()</code> is for RData files and it will contain the names of the variables when when you run <code>load(whatever.rdata)</code> a bunch of variables pop into being in your environment. RDS files contain just one object (like an R dataframe) so you need to load them with <code>readRSD()</code> and then assign (i.e., with <code><-</code>) the output and store in a variable like you with with <code>read.csv()</code>. I have provided some information about the "study design" below ('''reminder/note: this is not data from an actual study'''): :: You have been hired as a statistical consultant on a project studying the role of income in shaping academic achievement. Data from twelve cohorts of public high school students was collected from across the Chicago suburbs. Each cohort incorporates a random sample of 142 students from a single suburban school district. For each student, researchers gathered a standardized measure of the students' aggregate GPA as a proxy for their academic achievement. The researchers then matched the students' names against IRS records five years later and collected each student's reported pre-tax earnings for that year. I have provided you with a version of the dataset from this hypothetical study in which each row corresponds to one student. For each student, the dataset contains the following variables: * <code>id</code>: A unique numeric identifier for each student in the study (randomly generated to preserve student anonymity). * <code>cohort</code>: An anonymized label of the cohort (school district) the student was drawn from. * <code>gpa</code>: Approximate GPA percentile of the student within the entire district. Note that this means all student GPAs within each district were aggregated and converted to an identical scale before percentiles were calculated. * <code>income</code>: Pre-tax income (in thousands of US dollars) reported to the U.S. federal government (IRS) by the student five years after graduation. For the rest of this programming challenge, you should use this dataset to answer the following research questions: # How does high school academic achievement relate to earnings? # (How) does this relationship vary by school district? You may use any analytical procedures you deem appropriate given the study design and your current statistical knowledge. Some things you may want to keep in mind: * Different tests like ANOVAs, T-tests, or linear regression might help you test different kinds of hypotheses.
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