Lecture 4 Task
Connor Barkley
26/03/2024
Task 1
1.1 Provide a brief description of the study in Task 1
- What is the study design?
A cross-sectional investigation of 396 collegiate professors in the US from 2008 to 2009 looking at gender pay gap
###What is the null hypothesis? #### That there is no difference in salaries between male and female professors ### - What is the alternative hypothesis? #### There is a difference in salaries between male and female professors
1.2 Import the data set “Professorial Salaries.csv” into R
salary = read.csv("C:\\Users\\12884742\\Downloads\\Professorial Salaries.csv")1.3 Describe characteristics of the study sample by sex.
library(table1)##
## Attaching package: 'table1'## The following objects are masked from 'package:base':
##
## units, units<-table1(~ Rank + Discipline + Yrs.since.phd + Yrs.service + NPubs + Ncits + Salary | Sex, data=salary)| Female (N=39) |
Male (N=358) |
Overall (N=397) |
|
|---|---|---|---|
| Rank | |||
| AssocProf | 10 (25.6%) | 54 (15.1%) | 64 (16.1%) |
| AsstProf | 11 (28.2%) | 56 (15.6%) | 67 (16.9%) |
| Prof | 18 (46.2%) | 248 (69.3%) | 266 (67.0%) |
| Discipline | |||
| A | 18 (46.2%) | 163 (45.5%) | 181 (45.6%) |
| B | 21 (53.8%) | 195 (54.5%) | 216 (54.4%) |
| Yrs.since.phd | |||
| Mean (SD) | 16.5 (9.78) | 22.9 (13.0) | 22.3 (12.9) |
| Median [Min, Max] | 17.0 [2.00, 39.0] | 22.0 [1.00, 56.0] | 21.0 [1.00, 56.0] |
| Yrs.service | |||
| Mean (SD) | 11.6 (8.81) | 18.3 (13.2) | 17.6 (13.0) |
| Median [Min, Max] | 10.0 [0, 36.0] | 18.0 [0, 60.0] | 16.0 [0, 60.0] |
| NPubs | |||
| Mean (SD) | 20.2 (14.4) | 17.9 (13.9) | 18.2 (14.0) |
| Median [Min, Max] | 18.0 [1.00, 50.0] | 13.0 [1.00, 69.0] | 13.0 [1.00, 69.0] |
| Ncits | |||
| Mean (SD) | 40.7 (16.2) | 40.2 (17.0) | 40.2 (16.9) |
| Median [Min, Max] | 36.0 [14.0, 70.0] | 35.0 [1.00, 90.0] | 35.0 [1.00, 90.0] |
| Salary | |||
| Mean (SD) | 101000 (26000) | 115000 (30400) | 114000 (30300) |
| Median [Min, Max] | 104000 [62900, 161000] | 108000 [57800, 232000] | 107000 [57800, 232000] |
1.4 Develop a graph to check the distribution of professors’ salaries.
The data is positively skewed, and thereby not normal
library(ggplot2)
p = ggplot(data=salary, aes(x=Salary)) + geom_histogram()
p## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.5 Determine whether salaries significantly differed between male and female professors:
p = ggplot(data = salary, aes(x = Salary, y = Sex)) + geom_boxplot()
p
z = ggplot(data=salary, aes(x=Salary, colour=Sex)) + geom_histogram(fill="white", alpha=0.5, position="identity")
z## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
t.test(Salary ~ Sex, data = salary)##
## Welch Two Sample t-test
##
## data: Salary by Sex
## t = -3.1615, df = 50.122, p-value = 0.002664
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
## -23037.916 -5138.102
## sample estimates:
## mean in group Female mean in group Male
## 101002.4 115090.4- Is there evidence that salaries significantly differed between male and female professors?
Salaries for female professors is clearly lower across the board, and as we can see in the t-test, this is all but certain
- How did male professors’ salaries differ from female professors’ salaries? What was the range of the differences?
As we can see from this box plot, the average salary is somewhat similar, but the top end of the range is massively skewed towards men
Task 2:
2.1 Provide a brief description of the study in Task 2
- What is the study design?
26 associate professors in the Theoretical discipline to see if there is a gender gap in publication numbers
- What is the null hypothesis?
There is no disparity in publication numbers across gender
- What is the alternative hypothesis?
There is a disparity in publication numbers across gender
2.2 Select a subgroup of associate professors in the Theoretical discipline
Assoc.A = subset(salary, Rank == "AssocProf" & Discipline == "A")
dim(Assoc.A)## [1] 26 92.3 Describe characteristics of the study sample by sex
table1(~ Rank + Discipline + Yrs.since.phd + Yrs.service + NPubs + Ncits + Salary | Sex, data=Assoc.A)| Female (N=4) |
Male (N=22) |
Overall (N=26) |
|
|---|---|---|---|
| Rank | |||
| AssocProf | 4 (100%) | 22 (100%) | 26 (100%) |
| Discipline | |||
| A | 4 (100%) | 22 (100%) | 26 (100%) |
| Yrs.since.phd | |||
| Mean (SD) | 18.5 (8.19) | 17.7 (12.2) | 17.8 (11.5) |
| Median [Min, Max] | 19.0 [10.0, 26.0] | 12.5 [8.00, 49.0] | 13.0 [8.00, 49.0] |
| Yrs.service | |||
| Mean (SD) | 15.5 (8.70) | 13.1 (12.3) | 13.5 (11.7) |
| Median [Min, Max] | 15.0 [8.00, 24.0] | 8.00 [1.00, 49.0] | 8.00 [1.00, 49.0] |
| NPubs | |||
| Mean (SD) | 10.0 (4.97) | 21.6 (14.2) | 19.8 (13.8) |
| Median [Min, Max] | 10.0 [4.00, 16.0] | 16.0 [3.00, 48.0] | 16.0 [3.00, 48.0] |
| Ncits | |||
| Mean (SD) | 38.5 (18.5) | 44.3 (15.2) | 43.4 (15.5) |
| Median [Min, Max] | 37.5 [19.0, 60.0] | 47.0 [24.0, 69.0] | 47.0 [19.0, 69.0] |
| Salary | |||
| Mean (SD) | 72100 (6400) | 85000 (10600) | 83100 (11100) |
| Median [Min, Max] | 74100 [62900, 77500] | 82400 [70000, 108000] | 81900 [62900, 108000] |
2.4 Develop a graph to check the distribution of the number of publications.
The data is not normally distributed, and is both Positive and Platykurtic
p = ggplot(data=Assoc.A, aes(x=NPubs)) + geom_histogram()
p## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
2.5 Conduct a non-parametric test to determine whether the number of publications differed between male and female professors:
kruskal.test(NPubs ~ Sex, data = Assoc.A)##
## Kruskal-Wallis rank sum test
##
## data: NPubs by Sex
## Kruskal-Wallis chi-squared = 2.5726, df = 1, p-value = 0.1087- Is there evidence that the number of publications significantly differed between male and female professors?
Based on the P-Value returned by this test, the suggestion is that there isn’t a significant difference
- What is the limitation of this non-parametric test?
Well, looking at the table, there clearly is a difference, but the limited power of the sample sizes means we cannot state this conclusively. If I had to provide a limitation, overly conservative.
2.6 Carry out a bootstrap to determine whether the mean number of publications differed between male and female professors:
library(lmboot)
boot = ANOVA.boot(NPubs ~ Sex, B = 1000, seed = 1000, data = Assoc.A)
boot$'p-values'## [1] 0.117