Author: Zhanbii Kadyrkulov

1 Research question

1.1 Is there a difference between women’s and men’s average weekly wages?
1.2 menwage and womwage variables should be collected to answer this research question.

2 Data

library("carData")
mydata <- force(Bfox)

head(mydata)
##      partic  tfr menwage womwage  debt parttime
## 1946   25.3 3748   25.35   14.05 18.18    10.28
## 1947   24.4 3996   26.14   14.61 28.33     9.28
## 1948   24.2 3725   25.11   14.23 30.55     9.51
## 1949   24.2 3750   25.45   14.61 35.81     8.87
## 1950   23.7 3669   26.79   15.26 38.39     8.54
## 1951   24.2 3682   26.33   14.58 26.52     8.84
2.1 Definitions of variables used:

partic - percent of adult women in the workforce tfr - total fertillity rate: expected births to a cohort of 1000 women at current age-specific fertility rates menwage - men’s average weekly wages, in constant 1935 dollars and adjusted for current tax rates womwage - women’s average weekly wages debt - per-capita consumer debt, in constant dollars parttime - percent of the active workforce working 34 hours per week or less

2.2 Definition of the unit of observation and the sample size:

Unit of observation: one person Sample size: 30 people

2.3 Source of the data set:

Source: Fox, B. (1980) Women’s Domestic Labour and their Involvement in Wage Work. Unpublished doctoral dissertation, p. 449.

#####2.4 Basic descriptive statistics

mydata[28, 2] <- 1931

I did this function because in the information for this dataset is written that “The value of tfr for 1973 is misrecorded as 2931; it should be 1931”.

summary(mydata[,c(-1, -2, -4, -5)])
##     menwage         parttime     
##  Min.   :25.11   Min.   : 5.490  
##  1st Qu.:29.24   1st Qu.: 8.688  
##  Median :34.56   Median :10.255  
##  Mean   :35.17   Mean   :10.947  
##  3rd Qu.:40.81   3rd Qu.:13.783  
##  Max.   :48.06   Max.   :16.710

Firstly, to do this analysis, I deleted some rows that are not related to the research questions which are partic, tfr, debt and parttime variables. Then we can see that men’s average weekly wage throughout all the years was 35.17 dollars while women’s was only 10.947 dollars. Another fact that must be mentioned is that the lowest wage of men was 25.11 dollars while women only had 5.49 dollars.

mydata$difference <- mydata$menwage - mydata$womwage

library(ggplot2)
ggplot(mydata, aes(x = difference)) +
  geom_histogram(binwidth = 1, color = "black") +
  xlab("Differences")

We can see from histogram that difference between men and women wages is not normally distributed.

3 Analysis

3.1 Determine which statistical test to use and why

I will use Wilcoxon rank sum test for independent samples ##### 3.2 Evaluate all assumptions The distribution of the variable is not normal in both populations. The data comes from two independent populations. Variable has the same variance in both populations #####3.3 Perform the appropriate statistical test based on the results of the assumption evaluation and its interpretation

H0: There is no difference between men’s and women’s wages H1: there is difference between men’s and women’s wages

shapiro.test(mydata$difference)
## 
##  Shapiro-Wilk normality test
## 
## data:  mydata$difference
## W = 0.91642, p-value = 0.02168

We reject H0 at p-value = 0.03

wilcox.test(mydata$menwage , mydata$womwage,
            paired = FALSE,
            correct = FALSE,
            exact = FALSE,
            alternative = "two.sided")
## 
##  Wilcoxon rank sum test
## 
## data:  mydata$menwage and mydata$womwage
## W = 862.5, p-value = 1.069e-09
## alternative hypothesis: true location shift is not equal to 0

p-value is less than 0.001

3.4 Calculation of the effect size and its interpretation
library(effectsize)
effectsize(wilcox.test(mydata$menwage , mydata$womwage,
                       paired = FALSE,
                       correct = FALSE,
                       exact = FALSE,
                       alternative = "two.sided"))
## r (rank biserial) |       95% CI
## --------------------------------
## 0.92              | [0.85, 0.95]
interpret_rank_biserial(0.92)
## [1] "very large"
## (Rules: funder2019)

We can see that effect size is very large = 0.92

4 Conclusion

Based on the sample data, we find that men’s and women’s weekly wages differ (p < 0.001) and the difference in distribution is very large (r = 0.92).