Lecture 5 Task
Connor Barkley
27/03/2024
Task 1
Study design
Cross-sectional investigation
What is the null hypothesis?
That there is no significant difference in professors salaries across rank
What is the alternative hypothesis
There is a significant difference in professors salaries across rank
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 professors’ ranks
library(table1)##
## Attaching package: 'table1'## The following objects are masked from 'package:base':
##
## units, units<-table1(~ Salary + Discipline + Yrs.since.phd + Yrs.service + NPubs + Ncits + Sex | Rank, data=salary)| AssocProf (N=64) |
AsstProf (N=67) |
Prof (N=266) |
Overall (N=397) |
|
|---|---|---|---|---|
| Salary | ||||
| Mean (SD) | 93900 (13800) | 80800 (8170) | 127000 (27700) | 114000 (30300) |
| Median [Min, Max] | 95600 [62900, 126000] | 79800 [63100, 97000] | 123000 [57800, 232000] | 107000 [57800, 232000] |
| Discipline | ||||
| A | 26 (40.6%) | 24 (35.8%) | 131 (49.2%) | 181 (45.6%) |
| B | 38 (59.4%) | 43 (64.2%) | 135 (50.8%) | 216 (54.4%) |
| Yrs.since.phd | ||||
| Mean (SD) | 15.5 (9.65) | 5.10 (2.54) | 28.3 (10.1) | 22.3 (12.9) |
| Median [Min, Max] | 12.0 [6.00, 49.0] | 4.00 [1.00, 11.0] | 28.0 [11.0, 56.0] | 21.0 [1.00, 56.0] |
| Yrs.service | ||||
| Mean (SD) | 12.0 (10.1) | 2.37 (1.50) | 22.8 (11.6) | 17.6 (13.0) |
| Median [Min, Max] | 8.00 [1.00, 53.0] | 3.00 [0, 6.00] | 21.0 [0, 60.0] | 16.0 [0, 60.0] |
| NPubs | ||||
| Mean (SD) | 18.7 (13.5) | 15.9 (11.2) | 18.6 (14.7) | 18.2 (14.0) |
| Median [Min, Max] | 16.0 [1.00, 50.0] | 12.0 [2.00, 50.0] | 13.0 [1.00, 69.0] | 13.0 [1.00, 69.0] |
| Ncits | ||||
| Mean (SD) | 42.0 (15.6) | 36.3 (16.7) | 40.8 (17.2) | 40.2 (16.9) |
| Median [Min, Max] | 36.5 [14.0, 83.0] | 34.0 [1.00, 83.0] | 35.0 [1.00, 90.0] | 35.0 [1.00, 90.0] |
| Sex | ||||
| Female | 10 (15.6%) | 11 (16.4%) | 18 (6.8%) | 39 (9.8%) |
| Male | 54 (84.4%) | 56 (83.6%) | 248 (93.2%) | 358 (90.2%) |
1.4 Develop a graph to check the distribution of professors’ salaries.
positively skewed salary distribution
library(ggplot2)
p = ggplot(data = salary, aes(x = Salary))
p = p + geom_histogram(aes(y = ..density..), color = "white", fill = "blue")
p = p + geom_density(col="red")
p + ggtitle("Distribution of professors' salaries") + theme_bw()## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
p## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.5 Develop a box plot to describe the differences in salaries among professors’ ranks.
clear differences in average wage and IQR across rank
p = ggplot(data = salary, aes(y=Salary, x=Rank, fill=Rank)) + geom_boxplot()
p
1.6 Determine whether salaries significantly differed among professors’ ranks. Interpret the finding:
sal.rank = aov(Salary ~ Rank, data=salary)
summary(sal.rank)## Df Sum Sq Mean Sq F value Pr(>F)
## Rank 2 1.432e+11 7.162e+10 128.2 <2e-16 ***
## Residuals 394 2.201e+11 5.586e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Is there evidence that salaries significantly differed among professors’ ranks?
Yes
- What is the next step?
Find which pair has the significant difference
1.7
par(mfrow=c(2,2))
plot(sal.rank)
1.8 Conduct post-hoc analyses to determine which particular groups significantly differ from each other.
All three pairs are significantly different, AssocProf has (on average) 13100.45 higher salary tahn AsstProf, with a low of 3382.195, and a high of 22818.71
tukey.sal.rank = TukeyHSD(sal.rank)
tukey.sal.rank## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Salary ~ Rank, data = salary)
##
## $Rank
## diff lwr upr p adj
## AsstProf-AssocProf -13100.45 -22818.71 -3382.195 0.0046514
## Prof-AssocProf 32895.67 25154.51 40636.836 0.0000000
## Prof-AsstProf 45996.12 38395.94 53596.307 0.0000000Task 2
Task 2.1
Study design
Exploratory analysis
Null Hypothesis
The average number of publications does not differ between professor ranks
Alternative Hypothesis
The average number of publications does differ between professor ranks
2.2 Select a subgroup of women from the applied division
B.Female = subset(salary, Sex=="Female" & Discipline=="B")
dim(B.Female)## [1] 21 92.3 Describe characteristics of the study sample by professors’ ranks
table1(~ Salary + Discipline + Yrs.since.phd + Yrs.service + NPubs + Ncits + Sex | Rank, data=B.Female)| AssocProf (N=6) |
AsstProf (N=5) |
Prof (N=10) |
Overall (N=21) |
|
|---|---|---|---|---|
| Salary | ||||
| Mean (SD) | 99400 (14100) | 84200 (9790) | 132000 (17500) | 111000 (25400) |
| Median [Min, Max] | 104000 [71100, 110000] | 80200 [74700, 97000] | 128000 [105000, 161000] | 105000 [71100, 161000] |
| Discipline | ||||
| B | 6 (100%) | 5 (100%) | 10 (100%) | 21 (100%) |
| Yrs.since.phd | ||||
| Mean (SD) | 13.5 (2.88) | 6.60 (3.65) | 21.5 (5.95) | 15.7 (7.72) |
| Median [Min, Max] | 12.5 [11.0, 19.0] | 5.00 [3.00, 11.0] | 19.0 [17.0, 36.0] | 17.0 [3.00, 36.0] |
| Yrs.service | ||||
| Mean (SD) | 8.83 (1.94) | 2.60 (1.82) | 17.9 (4.77) | 11.7 (7.36) |
| Median [Min, Max] | 9.50 [6.00, 11.0] | 3.00 [0, 5.00] | 17.5 [10.0, 26.0] | 10.0 [0, 26.0] |
| NPubs | ||||
| Mean (SD) | 16.3 (14.3) | 18.8 (18.3) | 21.3 (14.2) | 19.3 (14.6) |
| Median [Min, Max] | 14.5 [1.00, 38.0] | 11.0 [3.00, 50.0] | 20.0 [6.00, 50.0] | 18.0 [1.00, 50.0] |
| Ncits | ||||
| Mean (SD) | 45.8 (12.9) | 46.4 (24.1) | 38.0 (15.7) | 42.2 (16.9) |
| Median [Min, Max] | 49.0 [26.0, 60.0] | 49.0 [14.0, 69.0] | 36.5 [18.0, 60.0] | 48.0 [14.0, 69.0] |
| Sex | ||||
| Female | 6 (100%) | 5 (100%) | 10 (100%) | 21 (100%) |
2.4 Develop a graph to check the distribution of the number of publications.
heavily positived skewed and leptokurtic
p = ggplot(data = salary, aes(x = NPubs))
p = p + geom_histogram(aes(y = ..density..), color = "white", fill = "blue")
p = p + geom_density(col="red")
p + ggtitle("Distribution of female applied professors publications") + theme_bw()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
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 among professors’ ranks.
no difference
kruskal.test(NPubs ~ Rank, data=B.Female)##
## Kruskal-Wallis rank sum test
##
## data: NPubs by Rank
## Kruskal-Wallis chi-squared = 0.81015, df = 2, p-value = 0.66692.6 Carry out a bootstrap to determine whether the mean number of publications differed among professors’ ranks.
somehow even LESS of a difference! There is NO evidence (p=0.82)
library(lmboot)
boot = ANOVA.boot(NPubs ~ Rank, B = 1000, seed = 1234, data = B.Female)
boot$'p-values'## [1] 0.821