library(chisq.posthoc.test)
library(table1)
## 
## Attaching package: 'table1'
## The following objects are masked from 'package:base':
## 
##     units, units<-

Task 1:

Task 1.1:

  • Study Design: cross-sectional investigation of 396 collegiate professors in the US from 2008 to 2009 was conducted to determine whether ranks significantly differed between male and female professors.
  • Null Hypothesis: There are no difference in rank between male and female professors.
  • Alternative Hypothesis: There are difference in rank between male and female professors.

Task 1.2: Import the dataset

salary = read.csv("D:\\OneDrive\\ANDREAS\\ACADEMICS_UNIVERSITY\\Year_4_2024\\Autumn\\32931\\Classes\\R_Basic\\Professorial_Salaries.csv")
dim(salary)
## [1] 397   9
head(salary)
##   ID      Rank Discipline Yrs.since.phd Yrs.service  Sex NPubs Ncits Salary
## 1  1      Prof          B            19          18 Male    18    50 139750
## 2  2      Prof          B            20          16 Male     3    26 173200
## 3  3  AsstProf          B             4           3 Male     2    50  79750
## 4  4      Prof          B            45          39 Male    17    34 115000
## 5  5      Prof          B            40          41 Male    11    41 141500
## 6  6 AssocProf          B             6           6 Male     6    37  97000

Task 1.3: Describe characteristics of the study sample by professors’ ranks

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]

Task 1.4:Determine whether ranks significantly differed between male and female professors. Interpret the findings

table(salary$Rank, salary$Sex)
##            
##             Female Male
##   AssocProf     10   54
##   AsstProf      11   56
##   Prof          18  248
chisq.test(salary$Rank, salary$Sex)
## 
##  Pearson's Chi-squared test
## 
## data:  salary$Rank and salary$Sex
## X-squared = 8.5259, df = 2, p-value = 0.01408
  • There is evidence (P = ~0.014) that professors’ ranks differed significantly between male and female professors.

Task 1.5: Determine which particular groups of professors’ ranks differed between male and female professors. Interpret the findings

chisq.tab = as.table(rbind(c(10, 11, 18), c(54, 56, 248)))
dimnames(chisq.tab) = list(sex = c("Female", "Male"),
                           rank = c("AssocProf", "AsstProf", "Prof"))
chisq.tab
##         rank
## sex      AssocProf AsstProf Prof
##   Female        10       11   18
##   Male          54       56  248
chisq.posthoc.test(chisq.tab)
##   Dimension     Value AssocProf  AsstProf      Prof
## 1    Female Residuals  1.702577  1.989100 -2.915939
## 2    Female  p values  0.531883  0.280141  0.021277
## 3      Male Residuals -1.702577 -1.989100  2.915939
## 4      Male  p values  0.531883  0.280141  0.021277
  • There is evidence (P = ~0.02) that professors differed between males and females; whereas there is no evidence that assistant and associate professors differed between males and females (P = ~0.28 and ~0.53, respectively)

Task 2:

Task 2.1:

  • Study Design: An exploratory analysis was conducted in a subgroup of 64 associate professors to determine whether the disciplines differed between male and female professors.
  • Null Hypothesis: There is no difference between male and female professors’ disciplines.
  • Alternative Hypothesis: There is difference between male and female professors’ disciplines.

Task 2.2: Select a subgroup of associate professors

assoc.P = subset(salary, Rank == "AssocProf")
dim(assoc.P)
## [1] 64  9
head(assoc.P)
##    ID      Rank Discipline Yrs.since.phd Yrs.service    Sex NPubs Ncits Salary
## 6   6 AssocProf          B             6           6   Male     6    37  97000
## 11 11 AssocProf          B            12           8   Male    30    28 119800
## 25 25 AssocProf          A            13           8 Female    11    60  74830
## 40 40 AssocProf          B             9           9   Male    32    33 100938
## 42 42 AssocProf          B            23          23   Male    12    54  93418
## 55 55 AssocProf          B            12          11   Male    19    83 103760

Task 2.3: Describe characteristics of the study sample by sex

table1(~ Rank + Discipline + Yrs.since.phd + Yrs.service + NPubs + Ncits + Salary | Sex, data = assoc.P)
Female
(N=10)		 Male
(N=54)		 Overall
(N=64)
Rank
AssocProf 10 (100%) 54 (100%) 64 (100%)
Discipline
A 4 (40.0%) 22 (40.7%) 26 (40.6%)
B 6 (60.0%) 32 (59.3%) 38 (59.4%)
Yrs.since.phd
Mean (SD) 15.5 (5.80) 15.4 (10.2) 15.5 (9.65)
Median [Min, Max] 13.0 [10.0, 26.0] 11.5 [6.00, 49.0] 12.0 [6.00, 49.0]
Yrs.service
Mean (SD) 11.5 (6.26) 12.0 (10.7) 12.0 (10.1)
Median [Min, Max] 9.50 [6.00, 24.0] 8.00 [1.00, 53.0] 8.00 [1.00, 53.0]
NPubs
Mean (SD) 13.8 (11.5) 19.6 (13.7) 18.7 (13.5)
Median [Min, Max] 11.0 [1.00, 38.0] 16.0 [1.00, 50.0] 16.0 [1.00, 50.0]
Ncits
Mean (SD) 42.9 (14.9) 41.9 (15.8) 42.0 (15.6)
Median [Min, Max] 47.5 [19.0, 60.0] 36.0 [14.0, 83.0] 36.5 [14.0, 83.0]
Salary
Mean (SD) 88500 (18000) 94900 (12900) 93900 (13800)
Median [Min, Max] 90600 [62900, 110000] 95600 [70000, 126000] 95600 [62900, 126000]

Task 2.4: Determine whether the disciplines differed between male and female associate professors:

table(assoc.P$Sex, assoc.P$Discipline)
##         
##           A  B
##   Female  4  6
##   Male   22 32
fisher.test(assoc.P$Sex, assoc.P$Discipline)
## 
##  Fisher's Exact Test for Count Data
## 
## data:  assoc.P$Sex and assoc.P$Discipline
## p-value = 1
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.1795097 4.6576966
## sample estimates:
## odds ratio 
##  0.9701586
  • As the expected number of female professors in the Theoretical discipline (Discipline = A) is 4.06 (the observed number = 4)< 5, a Fisher’s exact test is used.
  • There is no evidence (P = ~1.0) that the disciplines differed between male and female professors.