Lab 04 - Data Modelling course evaluations, Pt 1

Published

October 27, 2023

Introduction

Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. The article titled, “Beauty in the classroom: instructors’ pulchritude and putative pedagogical productivity” (Hamermesh and Parker, 2005) found that instructors who are viewed to be better looking receive higher instructional ratings.

Daniel S. Hamermesh, Amy Parker, Beauty in the classroom: instructors pulchritude and putative pedagogical productivity, Economics of Education Review, Volume 24, Issue 4, August 2005, Pages 369-376, ISSN 0272-7757, 10.1016/j.econedurev.2004.07.013. link.

For this assignment you will analyze the data from this study in order to learn what goes into a positive professor evaluation.

The data were gathered from end of semester student evaluations for a large sample of professors from the University of Texas at Austin. In addition, six students rated the professors’ physical appearance. (This is a slightly modified version of the original data set that was released as part of the replication data for Data Analysis Using Regression and Multilevel/Hierarchical Models (Gelman and Hill, 2007).) The result is a data frame where each row contains a different course and columns represent variables about the courses and professors.

Important

This lab is maybe longer than what you’ll be able to complete in an hour. We will be looking to see that you minimally ran and interpreted at least a single model (completed Part 3). If you’re able to finish the whole thing, awesome! If not, that’s OK.

Getting started

To get started, accept the lab04 assignment (link on Canvas), clone the repo (using SSH) into RStudio on datahub. Update the author name at the top of the .Rmd file in the YAML to be your name. And, then you’re ready to go!

Packages

When you install the tidyverse package, a long list of packages get installed with it. However when you load it (with the library function) only a few of them get loaded, e.g. dplyr, ggplot2, and forcats. The broom package is installed with the tidyverse, but we need to load it separately in order to make use of it.

In this lab we will work with the tidyverse, tidymodels, and broom packages. Be sure to load them in before continuing with the lab.

The data

In this lab you will first read in the data (‘evals-mod.csv’) from the data/ folder (provided in the template).

Codebook

Variable name	Description
`score`	Average professor evaluation score: (1) very unsatisfactory - (5) excellent
`rank`	Rank of professor: teaching, tenure track, tenure
`ethnicity`	Ethnicity of professor: not minority, minority
`gender`	Gender of professor: female, male
`language`	Language of school where professor received education: english or non-english
`age`	Age of professor
`cls_perc_eval`	Percent of students in class who completed evaluation
`cls_did_eval`	Number of students in class who completed evaluation
`cls_students`	Total number of students in class
`cls_level`	Class level: lower, upper
`cls_profs`	Number of professors teaching sections in course in sample: single, multiple
`cls_credits`	Number of credits of class: one credit (lab, PE, etc.), multi credit
`bty_f1lower`	Beauty rating of professor from lower level female: (1) lowest - (10) highest
`bty_f1upper`	Beauty rating of professor from upper level female: (1) lowest - (10) highest
`bty_f2upper`	Beauty rating of professor from upper level female: (1) lowest - (10) highest
`bty_m1lower`	Beauty rating of professor from lower level male: (1) lowest - (10) highest
`bty_m1upper`	Beauty rating of professor from upper level male: (1) lowest - (10) highest
`bty_m2upper`	Beauty rating of professor from upper level male: (1) lowest - (10) highest

Exercises

Part 1: Data Manipulation

The rowwise function is useful for applying mathematical operations to each row.

Exercise 1

Create a new variable called bty_avg that is the average attractiveness score of the six students for each professor (bty_f1lower through bty_m2upper). Add this new variable to the evals data frame. Do this in one pipe, using the rowwise function. Since rowwise is new to you, incomplete code is given below to guide you in the right direction, however you will need to fill in the blanks.

___ <- evals |>
  rowwise() |>
  ___(bty_avg = mean( c( ___ ) )) |>
  ungroup()

Note that we end the pipeline with ungroup() to remove the effect of the rowwise function from earlier in the pipeline. The rowwise function works a lot like group_by, except it groups the data frame one row at a time so that any operations applied to the data frame is done once per each row. This is helpful for finding the mean beauty score for each row. However in the remainder of the analysis we don’t want to, say, calculate summary statistics for each row, or fit a model for each row. Hence we need to undo the effect of rowwise, which we can do with ungroup.

Part 2: Exploratory Data Analysis

Exercise 2

Visualize the distribution of score. Is the distribution skewed? What does that tell you about how students rate courses? Is this what you expected to see? Why, or why not? Include any summary statistics and visualizations you use in your response.

Exercise 3

Visualize and describe the relationship between score and the new variable you created, bty_avg.

Hint: See the help page for the function at http://ggplot2.tidyverse.org/reference/index.html.

Exercise 4

Replot the scatterplot from Exercise 3, but this time use
geom_jitter()? What does “jitter” mean? What was misleading about the initial scatterplot?

Part 3: Linear regression with a numerical predictor

Linear model is in the form \(\hat{y} = b_0 + b_1 x\).

Exercise 5

Let’s see if the apparent trend in the plot is something more than natural variation. Fit a linear model called m_bty to predict average professor evaluation score by average beauty rating (bty_avg). Based on the regression output, write the linear model.

Exercise 6

Replot your visualization from Exercise 3, and add the regression line to this plot in orange color. Turn off the shading for the uncertainty of the line.

Exercise 7

Interpret the slope of the linear model in context of the data.

Exercise 8

Interpret the intercept of the linear model in context of the data. Comment on whether or not the intercept makes sense in this context.

Exercise 9

Determine the \(R^2\) of the model and interpret it in context of the data.

Part 4: Linear regression with a categorical predictor

Exercise 10

Fit a new linear model called m_gen to predict average professor evaluation score based on gender of the professor. Based on the regression output, write the linear model and interpret the slope and intercept in context of the data.

Exercise 11

What is the equation of the line corresponding to male professors? What is it for female professors?

Exercise 12

Fit a new linear model called m_rank to predict average professor evaluation score based on rank of the professor. Based on the regression output, write the linear model and interpret the slopes and intercept in context of the data.

See the course slides on using the forcats package for changing the order of levels.

Exercise 3

Create a new variable called rank_relevel where "tenure track" is the baseline level.

Exercise 14

Fit a new linear model called m_rank_relevel to predict average professor evaluation score based on rank_relevel of the professor. This is the new (releveled) variable you created in Exercise 13. Based on the regression output, write the linear model and interpret the slopes and intercept in context of the data. Also determine and interpret the \(R^2\) of the model.

Exercise 15

Create another new variable called tenure_eligible that labels "teaching" faculty as "no" and labels "tenure track" and "tenured" faculty as "yes".

Exercise 16

Fit a new linear model called m_tenure_eligible to predict average professor evaluation score based on tenure_eligibleness of the professor. This is the new (regrouped) variable you created in Exercise 15. Based on the regression output, write the linear model and interpret the slopes and intercept in context of the data. Also determine and interpret the \(R^2\) of the model.

Submit

Important

You’ll always want to knit your RMarkdown document to HTML and review that HTML document to ensure it includes all the information you want and looks as you intended, as we grade from the knit HTML.

Yay, you’re done! To finish up and submit, first knit your file to HTML. Be sure to select both your .Rmd and .html documents when choosing what to commit! Then, commit all remaining changes and push. Before you wrap up the assignment, make sure all documents are updated on your GitHub repo.