Grading the professor

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

In this lab we will analyze the data from this study in order to learn what goes into a positive professor evaluation.

The data

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 aslightly 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.

load("more/evals.RData")
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.
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.

Exploring the data

  1. 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.

Answer This is an observational study. No experiment were set-up. The observations were gathered by end of class evaluations and questionair answered by 6 students pertaining on the beauty assessment of the professors.

Because this is not an experiment, we cannot conclude casual relationship. We would need to rephrase the question as follows

Question: Does beauty impact a professor evaluation or is the difference due to sampling variation?

  1. 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?

Answer

hist(evals$score)

From the histogram, we can see that the distribution of ‘score’ is skewed to the left, with the majority of the observation with score of between 4 and 5. This is as expected, most students will provide feeback with positive evaluation (4 or 5).

  1. Excluding score, select two other variables and describe their relationship using an appropriate visualization (scatterplot, side-by-side boxplots, or mosaic plot).

Answer We will consider the following variables: cls_perc_eval and cls_level. We will plot percentage of sutdent that complete evaluation dependent on the class level.

plot(evals$cls_perc_eval ~ evals$cls_level)

The percentage of student completing the evaluation has less variability for upper level class (since the box plot is smaller) than for lower. There is no clear apparent difference for the median. There is a marked difference for the lower whiskers. For upper level class, the lower whisker ends higher with outliers. There are no outiers for lower class level.

Simple linear regression

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:

plot(evals$score ~ evals$bty_avg)

Before 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?

nrow(evals)
## [1] 463
summary(evals)
##      score                 rank            ethnicity      gender   
##  Min.   :2.300   teaching    :102   minority    : 64   female:195  
##  1st Qu.:3.800   tenure track:108   not minority:399   male  :268  
##  Median :4.300   tenured     :253                                  
##  Mean   :4.175                                                     
##  3rd Qu.:4.600                                                     
##  Max.   :5.000                                                     
##         language        age        cls_perc_eval     cls_did_eval   
##  english    :435   Min.   :29.00   Min.   : 10.42   Min.   :  5.00  
##  non-english: 28   1st Qu.:42.00   1st Qu.: 62.70   1st Qu.: 15.00  
##                    Median :48.00   Median : 76.92   Median : 23.00  
##                    Mean   :48.37   Mean   : 74.43   Mean   : 36.62  
##                    3rd Qu.:57.00   3rd Qu.: 87.25   3rd Qu.: 40.00  
##                    Max.   :73.00   Max.   :100.00   Max.   :380.00  
##   cls_students    cls_level      cls_profs         cls_credits 
##  Min.   :  8.00   lower:157   multiple:306   multi credit:436  
##  1st Qu.: 19.00   upper:306   single  :157   one credit  : 27  
##  Median : 29.00                                                
##  Mean   : 55.18                                                
##  3rd Qu.: 60.00                                                
##  Max.   :581.00                                                
##   bty_f1lower     bty_f1upper     bty_f2upper      bty_m1lower   
##  Min.   :1.000   Min.   :1.000   Min.   : 1.000   Min.   :1.000  
##  1st Qu.:2.000   1st Qu.:4.000   1st Qu.: 4.000   1st Qu.:2.000  
##  Median :4.000   Median :5.000   Median : 5.000   Median :3.000  
##  Mean   :3.963   Mean   :5.019   Mean   : 5.214   Mean   :3.413  
##  3rd Qu.:5.000   3rd Qu.:7.000   3rd Qu.: 6.000   3rd Qu.:5.000  
##  Max.   :8.000   Max.   :9.000   Max.   :10.000   Max.   :7.000  
##   bty_m1upper     bty_m2upper       bty_avg           pic_outfit 
##  Min.   :1.000   Min.   :1.000   Min.   :1.667   formal    : 77  
##  1st Qu.:3.000   1st Qu.:4.000   1st Qu.:3.167   not formal:386  
##  Median :4.000   Median :5.000   Median :4.333                   
##  Mean   :4.147   Mean   :4.752   Mean   :4.418                   
##  3rd Qu.:5.000   3rd Qu.:6.000   3rd Qu.:5.500                   
##  Max.   :9.000   Max.   :9.000   Max.   :8.167                   
##        pic_color  
##  black&white: 78  
##  color      :385  
##                   
##                   
##                   
##

The dataframe evals has total 463 observations and summary says that there is no missing observation which would represent ‘NA’. So the scatter plot should have 463 points. But the scatter plot has only 250 points. Thatst he awry.

  1. Replot the scatterplot, but this time use the function jitter() on the \(y\)- or the \(x\)-coordinate. (Use ?jitter to learn more.) What was misleading about the initial scatterplot?

Answer

Add a small amount of noise to the score by using jitter function

plot(jitter(evals$score) ~ evals$bty_avg)

May points have the same values for (x,y). So they could not be differenciated on the scatter plot. As a small amount of noise is added on the score variable(y),the points can be differenciated. So instead of 250 points, all 463 points are visible.

  1. 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 score by average beauty rating and add the line to your plot using abline(m_bty). 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?

Answer

m_bty<- lm(score ~ bty_avg, data = evals)
plot(jitter(evals$score) ~ evals$bty_avg)
abline(m_bty)

summary(m_bty)
## 
## Call:
## lm(formula = score ~ bty_avg, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9246 -0.3690  0.1420  0.3977  0.9309 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.88034    0.07614   50.96  < 2e-16 ***
## bty_avg      0.06664    0.01629    4.09 5.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5348 on 461 degrees of freedom
## Multiple R-squared:  0.03502,    Adjusted R-squared:  0.03293 
## F-statistic: 16.73 on 1 and 461 DF,  p-value: 5.083e-05

\(\hat { y } ={ b }_{ 0 }+{ b }_{ 1 }x\)

\(\hat { y } =3.88034+0.06664\times bty\_ avg\)

slope of the line is 0.06664. That means when average beauty of the professor goes up by 1, the score goes up by 0.6664.

p-value is 5.083e-05 which is close to zero. It may not be a practically significant predictor of evaluation score though since for every 1 point increase in bty_ave, the model only predicts an increase of 0.06664 which barely changes the evaluation score.

  1. Use residual plots to evaluate whether the conditions of least squares regression are reasonable. Provide plots and comments for each one (see the Simple Regression Lab for a reminder of how to make these).

Answer

plot(m_bty$residuals ~ evals$bty_avg)
abline(h = 0, lty = 4)  # adds a horizontal dashed line at y = 0

#Historgream
hist(m_bty$residuals)

# normal probability plot of the residuals
qqnorm(m_bty$residuals)
qqline(m_bty$residuals)

Conditions for the least squares line

Linearity: The data show a slightly linear and it is positive linearity.

Nearly Normal residuals: From the Histogram, the residuals show a slightly left skewed distribution. The normal probability plot of the residuals shows that the points do not follow the line for upper quadriles.

Constant Variability: From the residual plot, we can observe that there seems to have constant variability.

Independent observations: We do not have much information on how the sample was taken. We can assume indenpendence of the observations.

Multiple linear regression

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.

plot(evals$bty_avg ~ evals$bty_f1lower)
cor(evals$bty_avg, evals$bty_f1lower)

As expected the relationship is quite strong - after all, the average score is calculated using the individual scores. We can actually take a look at the relationships between all beauty variables (columns 13 through 19) using the following command:

plot(evals[,13:19])

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.

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.

m_bty_gen <- lm(score ~ bty_avg + gender, data = evals)

summary(m_bty_gen)
## 
## Call:
## lm(formula = score ~ bty_avg + gender, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8305 -0.3625  0.1055  0.4213  0.9314 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.74734    0.08466  44.266  < 2e-16 ***
## bty_avg      0.07416    0.01625   4.563 6.48e-06 ***
## gendermale   0.17239    0.05022   3.433 0.000652 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5287 on 460 degrees of freedom
## Multiple R-squared:  0.05912,    Adjusted R-squared:  0.05503 
## F-statistic: 14.45 on 2 and 460 DF,  p-value: 8.177e-07
  1. 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.

Answer

# Normal Probability Plot
qqnorm(m_bty_gen$residuals)
qqline(m_bty_gen$residuals)

# residual plot against each predictor variable
plot(m_bty_gen$residuals ~ evals$bty_avg)
abline(h = 0, lty = 4)  # adds a horizontal dashed line at y = 0

plot(m_bty_gen$residuals ~ evals$gender)
abline(h = 0, lty = 4)  # adds a horizontal dashed line at y = 0

#Resiual vs Fitted, Normal Probability Plot, Scale-Location, Residual vs Leverage
plot(m_bty_gen)

#Historgream
hist(m_bty_gen$residuals)

# Checking linearlidity
plot(jitter(evals$score) ~ evals$bty_avg)

plot(evals$score ~ evals$gender)

The histogram of residuals suggests that the residuals distribution is slightly skewed to the left.

The residuals do not follow the lines for upper quadriles in the Normal Probability Plot for residuals, .

Residuals vs Fitted, show that it appears to be constant variability for residuals. But as was established in the previous exercises, there is a linear relationship between beauty average and teaching evaluation score.

  1. Is bty_avg still a significant predictor of score? Has the addition of gender to the model changed the parameter estimate for bty_avg?

Yes it is. In fact, gender made beauty average even more significant as the p-value computed is even smaller (6.48e-06 < 5.08e-05) now compared to a model where beauty average was the only variable.

Note that the estimate for gender is now called gendermale. You’ll see this name change whenever you introduce a categorical variable. The reason is that R recodes gender from having the values of female and male to being an indicator variable called gendermale 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.

\[ \begin{aligned} \widehat{score} &= \hat{\beta}_0 + \hat{\beta}_1 \times bty\_avg + \hat{\beta}_2 \times (0) \\ &= \hat{\beta}_0 + \hat{\beta}_1 \times bty\_avg\end{aligned} \]

We can plot this line and the line corresponding to males with the following custom function.

multiLines(m_bty_gen)
  1. What is the equation of the line corresponding to males? (Hint: For males, the parameter estimate is multiplied by 1.) For two professors who received the same beauty rating, which gender tends to have the higher course evaluation score?

\(\hat { score } =\quad 3.74734\quad +\quad 0.07416\quad ×\quad beauty\_ avg\quad +\quad 0.17239\quad ×\quad gender\_ male\)

For gender = Male, we will evaluate the equation with gender_male = 1. In case, of female gender, we will substitute a 0.

\(\hat { score } =\quad 3.74734\quad +\quad 0.07416\quad ×\quad beauty\_ avg\quad +\quad 0.17239\)

Male professor will have a evaluation score higher by 0.17239 all other things being equal.

The decision to call the indicator variable gendermale instead ofgenderfemale has no deeper meaning. R 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 therelevel function. Use ?relevel to learn more.)

  1. Create a new model called m_bty_rank with gender removed and rank added in. How does R appear to handle categorical variables that have more than two levels? Note that the rank variable has three levels: teaching, tenure track, tenured.

Answer

m_bty_rank <- lm(score ~ bty_avg + rank, data = evals)
summary(m_bty_rank)
## 
## Call:
## lm(formula = score ~ bty_avg + rank, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8713 -0.3642  0.1489  0.4103  0.9525 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3.98155    0.09078  43.860  < 2e-16 ***
## bty_avg           0.06783    0.01655   4.098 4.92e-05 ***
## ranktenure track -0.16070    0.07395  -2.173   0.0303 *  
## ranktenured      -0.12623    0.06266  -2.014   0.0445 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5328 on 459 degrees of freedom
## Multiple R-squared:  0.04652,    Adjusted R-squared:  0.04029 
## F-statistic: 7.465 on 3 and 459 DF,  p-value: 6.88e-05

For variable with more than 2 levels, it appears to handle it considerering them 2 different variables.

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.

The search for the best model

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, number of credits, average beauty rating, outfit, and picture color.

  1. Which variable would you expect to have the highest p-value in this model? Why? Hint: Think about which variable would you expect to not have any association with the professor score.

Answer :

The “number of professors” (cls_profs) as the variable to have the least assoication with the professor’s evaluation score.

Let’s run the model…

m_full <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval 
             + cls_students + cls_level + cls_profs + cls_credits + bty_avg 
             + pic_outfit + pic_color, data = evals)
summary(m_full)
  1. Check your suspicions from the previous exercise. Include the model output in your response.

Answer

The “number of professors” (cls_profs) as the variable to have the least assoication with the professor’s evaluation score. That has the maximum p-value(0.77806)

  1. Interpret the coefficient associated with the ethnicity variable.

Answer All other things being equal, Evaluation for professor that not minority tends to be 0.1234929 higher.

  1. 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?

Answer

m_full_1 <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval 
             + cls_students + cls_level + cls_credits + bty_avg 
             + pic_outfit + pic_color, data = evals)
summary(m_full_1)
## 
## Call:
## lm(formula = score ~ rank + ethnicity + gender + language + age + 
##     cls_perc_eval + cls_students + cls_level + cls_credits + 
##     bty_avg + pic_outfit + pic_color, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7836 -0.3257  0.0859  0.3513  0.9551 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            4.0872523  0.2888562  14.150  < 2e-16 ***
## ranktenure track      -0.1476746  0.0819824  -1.801 0.072327 .  
## ranktenured           -0.0973829  0.0662614  -1.470 0.142349    
## ethnicitynot minority  0.1274458  0.0772887   1.649 0.099856 .  
## gendermale             0.2101231  0.0516873   4.065 5.66e-05 ***
## languagenon-english   -0.2282894  0.1111305  -2.054 0.040530 *  
## age                   -0.0089992  0.0031326  -2.873 0.004262 ** 
## cls_perc_eval          0.0052888  0.0015317   3.453 0.000607 ***
## cls_students           0.0004687  0.0003737   1.254 0.210384    
## cls_levelupper         0.0606374  0.0575010   1.055 0.292200    
## cls_creditsone credit  0.5061196  0.1149163   4.404 1.33e-05 ***
## bty_avg                0.0398629  0.0174780   2.281 0.023032 *  
## pic_outfitnot formal  -0.1083227  0.0721711  -1.501 0.134080    
## pic_colorcolor        -0.2190527  0.0711469  -3.079 0.002205 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4974 on 449 degrees of freedom
## Multiple R-squared:  0.187,  Adjusted R-squared:  0.1634 
## F-statistic: 7.943 on 13 and 449 DF,  p-value: 2.336e-14

The coefficients and significance changed slightly. Since the values changed, the drop variable was slightly collinear with the other explanatory variables.

  1. 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.
m_full_best <- lm(score ~ ethnicity + gender + language + age + cls_perc_eval 
             +   cls_credits + bty_avg + pic_color, data = evals)
summary(m_full_best)
## 
## Call:
## lm(formula = score ~ ethnicity + gender + language + age + cls_perc_eval + 
##     cls_credits + bty_avg + pic_color, data = evals)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.85320 -0.32394  0.09984  0.37930  0.93610 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            3.771922   0.232053  16.255  < 2e-16 ***
## ethnicitynot minority  0.167872   0.075275   2.230  0.02623 *  
## gendermale             0.207112   0.050135   4.131 4.30e-05 ***
## languagenon-english   -0.206178   0.103639  -1.989  0.04726 *  
## age                   -0.006046   0.002612  -2.315  0.02108 *  
## cls_perc_eval          0.004656   0.001435   3.244  0.00127 ** 
## cls_creditsone credit  0.505306   0.104119   4.853 1.67e-06 ***
## bty_avg                0.051069   0.016934   3.016  0.00271 ** 
## pic_colorcolor        -0.190579   0.067351  -2.830  0.00487 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4992 on 454 degrees of freedom
## Multiple R-squared:  0.1722, Adjusted R-squared:  0.1576 
## F-statistic:  11.8 on 8 and 454 DF,  p-value: 2.58e-15

\(\hat { score } =\quad \hat { { \beta }_{ 0 } } \quad +\quad \hat { { \beta }_{ 1 } } \quad ×\quad ethnicitynot\_ minority\quad +\quad \hat { { \beta }_{ 2 } } ×gendermale\quad +\quad \hat { { \beta }_{ 3\quad } } ×\quad languagenon-english+\quad \hat { { \beta }_{ 4 } } ×\quad age\quad +\quad \hat { { \beta }_{ 5 } } ×\quad cls\_ perc\_ eval\quad +\quad \hat { { \beta }_{ 6 } } ×\quad cls\_ reditsone\_ credit\quad +\quad \hat { { \beta }_{ 7 } } ×\quad bty\_ avg\quad +\quad \hat { { \beta }_{ 8 } } ×\quad pic\_ colorcolor\)

  1. Verify that the conditions for this model are reasonable using diagnostic plots.
# Normal Probability Plot
qqnorm(m_full_best$residuals)
qqline(m_full_best$residuals)

# 4 plots: Resiual vs Fitted, Normal Probability Plot, Scale-Location, Residual vs Leverage
plot(m_full_best)

#Historgream
hist(m_full_best$residuals) 

# Checking linearlidity
plot(jitter(evals$score) ~ evals$bty_avg)

plot(jitter(evals$score) ~ evals$gender)

plot(jitter(evals$score) ~ evals$ethnicity)

plot(jitter(evals$score) ~ evals$language
     )

plot(jitter(evals$score) ~ evals$age)

plot(jitter(evals$score) ~ evals$cls_perc_eval)

plot(jitter(evals$score) ~ evals$cls_credits)

plot(jitter(evals$score) ~ evals$pic_color)

  1. 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?

Answer

No. Even if the course is being taught by the same professor, Class courses are independent of each other so evaluation scores from one course is indpendent of the other

  1. 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.

Answer

Based on the coefficients Professor would be younger male teaching one credit class, he would not belong to a minority group, he would have received this degree from a universtity where english is the language. The professor would have a black and white picture and who have been rated beautifull.

  1. Would you be comfortable generalizing your conclusions to apply to professors generally (at any university)? Why or why not?

Answer

No, this was not conducted as an experiment but based on a sample in a given university. As cultural value changes, these results may be different in other university or in a different time frame.

This is a product of OpenIntro that is released under a Creative Commons Attribution-ShareAlike 3.0 Unported. This lab was written by Mine Çetinkaya-Rundel and Andrew Bray.