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” by Hamermesh and Parker found that instructors who are viewed to be better looking receive higher instructional ratings.
In this lab we 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. The result is a data frame where each row contains a different course and columns represent variables about the courses and professors.
Let’s load the data:
use "evals.dta"We have observations on 21 different variables, some categorical and some numerical.
Is this an observational study or an experiment? The original research question posed in the paper is whether beauty leads directly to the differences in course evaluations. Given the study design, is it possible to answer this question as it is phrased? If not, rephrase the question.
Describe 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?
Excluding score, select two other variables and describe their relationship with each other using an appropriate visualization.
The fundamental phenomenon suggested by the study is that better looking teachers are evaluated more favorably. Let’s create a scatterplot to see if this appears to be the case. We need the variables score and average beauty rating of the professor, bty_avg.
twoway scatter score bty_avgBefore we draw conclusions about the trend, compare the number of observations in the data frame with the approximate number of points on the scatterplot. Is anything awry?
jitter(5). What was misleading about the initial scatterplot?twoway scatter score bty_avg, jitter(5)score) by average beauty rating. Write out the equation for the linear model and interpret the slope. Is average beauty score a statistically significant predictor? Does it appear to be a practically significant predictor?Add the line of the best fit model to your plot using the following:
twoway scatter score bty_avg || lfit score bty_avgThe red line is the model, indicated in the legend as “Fitted values”.
The data set contains several variables on the beauty score of the professor: individual ratings from each of the six students who were asked to score the physical appearance of the professors and the average of these six scores. Let’s take a look at the relationship between one of these scores and the average beauty score.
twoway scatter bty_avg bty_f1lower
cor bty_avg bty_f1lowerAs expected the relationship is quite strong—after all, the average score is calculated using the individual scores. We can actually look at the relationships between all beauty variables (columns 13 through 19) using the following command:
graph matrix bty_f1lower bty_f1upper bty_f2upper bty_m1lower bty_m1upper bty_m2upper bty_avgThese variables are collinear (correlated), and adding more than one of these variables to the model would not add much value to the model. In this application and with these highly-correlated predictors, it is reasonable to use the average beauty score as the single representative of these variables.
In order to see if beauty is still a significant predictor of professor score after we’ve accounted for the gender of the professor, we can add the gender term into the model.
regress score bty_avg i.genderNote that we use i.gender because gender is a categorical variable.
P-values and parameter estimates should only be trusted if the conditions for the regression are reasonable. Verify that the conditions for this model are reasonable using diagnostic plots.
Is bty_avg still a significant predictor of score? Has the addition of gender to the model changed the parameter estimate for bty_avg?
Note that the row in the regression output for gender is now called gender male. You’ll see this name change whenever you introduce a categorical variable. The reason is that Stata recodes gender from having the values of female and male to being an indicator variable called gender male that takes a value of \(0\) for females and a value of \(1\) for males (Such variables are often referred to as “dummy” variables.).
As a result, for females, the parameter estimate is multiplied by zero, leaving the intercept and slope form familiar from simple regression.
\[ \begin{aligned} \widehat{score} &= \hat{\beta}_0 + \hat{\beta}_1 \times bty\_avg + \hat{\beta}_2 \times (0) \\ &= \hat{\beta}_0 + \hat{\beta}_1 \times bty\_avg\end{aligned} \]
The decision to call the indicator variable gender male instead ofgender female has no deeper meaning. Stata simply codes the category that comes first alphabetically as a \(0\). (You can change the reference level of a categorical variable, which is the level that is coded as a 0, using ibX.gender in place of i.gender in the model, where X is the desired reference level. In the case of gender, there are two categories: (1) male and (2) female. Therefore, to change the reference group to females,
regress score bty_avg ib2.gendergender removed and rank added in. How does Stata appear to handle categorical variables that have more than two levels? Note that the rank variable has three levels: teaching, tenure track, tenured.The interpretation of the coefficients in multiple regression is slightly different from that of simple regression. The estimate for bty_avg reflects how much higher a group of professors is expected to score if they have a beauty rating that is one point higher while holding all other variables constant. In this case, that translates into considering only professors of the same rank with bty_avg scores that are one point apart.
We will start with a full model that predicts professor score based on rank, ethnicity, gender, language of the university where they got their degree, age, proportion of students that filled out evaluations, class size, course level, number of professors teaching the course, number of credits, average beauty rating, outfit, and picture color.
Let’s run the model:
regress score rank ethnicity gender language age cls_perc_eval cls_students cls_level cls_profs cls_credits bty_avg pic_outfit pic_colorCheck your suspicions from the previous exercise. Include the model output in your response.
Interpret the coefficient associated with the ethnicity variable.
Drop the variable with the highest p-value and re-fit the model. Did the coefficients and significance of the other explanatory variables change? (One of the things that makes multiple regression interesting is that coefficient estimates depend on the other variables that are included in the model.) If not, what does this say about whether or not the dropped variable was collinear with the other explanatory variables?
Using backward-selection and p-value as the selection criterion, determine the best model. You do not need to show all steps in your answer, just the output for the final model. Also, write out the linear model for predicting score based on the final model you settle on.
Verify that the conditions for this model are reasonable using diagnostic plots.
The original paper describes how these data were gathered by taking a sample of professors from the University of Texas at Austin and including all courses that they have taught. Considering that each row represents a course, could this new information have an impact on any of the conditions of linear regression?
Based on your final model, describe the characteristics of a professor and course at University of Texas at Austin that would be associated with a high evaluation score.
Would you be comfortable generalizing your conclusions to apply to professors generally (at any university)? Why or why not?
This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was adapted for Stata by Jenna R Krall from a lab written by Mine Çetinkaya-Rundel and Andrew Bray.