October 16, 2014

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 theclassroom: instructors' pulchritude and putative pedagogical productivity" (Hamermesh and Parker, 2005) found that instructors who are viewed to be better looking receive higher instructional ratings. Today we'll use data from this study.

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. http://www.sciencedirect.com/science/article/pii/S0272775704001165.

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.

load(url("http://www.openintro.org/stat/data/evals.RData"))

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).

variable | description |
---|---|

`score` |
average professor evaluation score: (1) very unsatisfactory - (5) excellent. |

`rank` |
rank of professor: teaching, tenure track, tenured. |

`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. |

variable | description |
---|---|

`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 second 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 second upper level male: (1) lowest - (10) highest. |

`bty_avg` |
average beauty rating of professor. |

`pic_outfit` |
outfit of professor in picture: not formal, formal. |

`pic_color` |
color of professor's picture: color, black & white. |

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?qplot(score, data = evals)

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:

qplot(bty_avg, score, data = evals, geom = "jitter")

Fit a linear model called

`m_bty`

to predict average professor score from average beauty rating. Is beauty score a statistically or practically significant predictor?m_bty = lm(score ~ bty_avg, data = evals) summary(m_bty)

## ## Call: ## lm(formula = score ~ bty_avg, data = evals) ## ## Residuals: ## Min 1Q Median 3Q Max ## -1.925 -0.369 0.142 0.398 0.931 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.8803 0.0761 50.96 < 2e-16 *** ## bty_avg 0.0666 0.0163 4.09 5.1e-05 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.535 on 461 degrees of freedom ## Multiple R-squared: 0.035, Adjusted R-squared: 0.0329 ## F-statistic: 16.7 on 1 and 461 DF, p-value: 5.08e-05

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.

Would we expect these variables to be dependent or independent?

ggpairs(evals[,13:19], alpha=0.7)

These 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.

Create a visualization that displays the relationship of score and beauty, while controlling for gender.

qplot(bty_avg, score, data = evals, geom = "jitter", color = gender)