Gender in the Workforce

Final Report for Spring 2023 Intro to Data Science

Introduction

1. Research question:

• How has the gender composition of different majors changed over time?
• What factors contribute to the gender pay gap within a particular industry?
• How do the earnings of male and female workers vary within the same major, and what factors might explain these differences?
• Is there a relationship between the percentage of female workers in an major and the average earnings of workers in that major?

2. Why we choose this topic?

• Gender in the workforce is a topic of great social and economic significance, as it directly affects the lives of millions of individuals and has implications for the broader society. While progress has been made towards gender equality in recent years, women continue to face challenges and inequalities in the workplace, including but not limited to, wage disparities and underrepresentation in leadership positions.

• Therefore, analyzing the dataset related to this topic allows us to gain valuable insights into the current state of gender distribution across various job categories in the United States, which can help us identify areas where further progress is needed. Additionally, it can help us examine the impact of gender on earnings and employment status as the information about women’s earnings and employment status from historical data allows us to understand the trends in the past to predict the upcoming possibilities in future dataset. And ultimately, we can identify areas where further progress is needed to achieve gender equality in the workplace.

3. About the dataset:
   

• Our project investigates the main characteristics of occupation in different gender. We will be using the data available at TidyTuesday.

• The Jobs Gender dataset¹, part of the TidyTuesday project, provides valuable insights into the current state of gender distribution across various job categories in the United States. With data spanning multiple industries and job types, this dataset allows for a comprehensive analysis of gender representation in the workforce. There are historical data about women’s earnings and employment status, as well as detailed information about specific occupation and earnings from 2013-2016.

• This dataset was compiled from two sources: the Census Bureau and the Bureau of Labor Statistics. The data is provided as is, and it recognizes the limitations and issues in defining gender as binary. This dataset provides valuable insights into the current state of gender distribution across various job categories in the United States and can be used for further analysis and policymaking to address issues of gender inequality in the workforce.

4. Data dictionary:

Variable	Class	Discription
year	interger	Year
occupation	character	Specific job/career
major_category	character	Broad category of occupation
minor_category	character	Fine category of occupation
total_workers	double	Total estimated full-time workers > 16 years old
workers_male	double	Estimated MALE full-time workers > 16 years old
workers_female	double	Estimated FEMALE full-time workers > 16 years old
percent_female	double	The percent of females for specific occupation
total_earnings	double	Total estimated median earnings for full-time workers > 16 years old
total_earnings_male	double	Estimated MALE median earnings for full-time workers > 16 years old
total_earnings_female	double	Estimated FEMALE median earnings for full-time workers > 16 years old
wage_percent_of_male	double	Female wages as percent of male wages - NA for occupations with small sample size

5. Load the data and take a look at the first 5 rows:

jobs_gender <- read.csv("../data/jobs_gender.csv")
head(jobs_gender,5)

Preliminary Exploratory Data Analysis

• Take a glimpse at the structure of the dataset and the class of each variable:

glimpse(jobs_gender)

## Rows: 2,088
## Columns: 12
## $ year                  <int> 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, …
## $ occupation            <chr> "Chief executives", "General and operations mana…
## $ major_category        <chr> "Management, Business, and Financial", "Manageme…
## $ minor_category        <chr> "Management", "Management", "Management", "Manag…
## $ total_workers         <int> 1024259, 977284, 14815, 43015, 754514, 44198, 10…
## $ workers_male          <int> 782400, 681627, 8375, 17775, 440078, 16141, 7287…
## $ workers_female        <int> 241859, 295657, 6440, 25240, 314436, 28057, 3683…
## $ percent_female        <dbl> 23.6, 30.3, 43.5, 58.7, 41.7, 63.5, 33.6, 27.5, …
## $ total_earnings        <int> 120254, 73557, 67155, 61371, 78455, 74114, 62187…
## $ total_earnings_male   <int> 126142, 81041, 71530, 75190, 91998, 90071, 66579…
## $ total_earnings_female <int> 95921, 60759, 65325, 55860, 65040, 66052, 55079,…
## $ wage_percent_of_male  <dbl> 76.04208, 74.97316, 91.32532, 74.29179, 70.69719…

• Check and clean the dataset:

# check for NA value in the dataset
colSums(is.na(jobs_gender))

##                  year            occupation        major_category 
##                     0                     0                     0 
##        minor_category         total_workers          workers_male 
##                     0                     0                     0 
##        workers_female        percent_female        total_earnings 
##                     0                     0                     0 
##   total_earnings_male total_earnings_female  wage_percent_of_male 
##                     4                    65                   846

#replace NA value by mean of the column's value in the dataset
jobs_gender <- jobs_gender %>% 
  mutate(total_earnings_male=ifelse(is.na(total_earnings_male),mean(total_earnings_male,na.rm=TRUE), total_earnings_male),
         total_earnings_female=ifelse(is.na(total_earnings_female),mean(total_earnings_female,na.rm=TRUE), total_earnings_female),
         wage_percent_of_male=ifelse(is.na(wage_percent_of_male),mean(wage_percent_of_male,na.rm=TRUE), wage_percent_of_male))

head(jobs_gender,5)

• Uni-variate summary statistics and data visualizations:

# Summary Statistics
summary(jobs_gender)

##       year       occupation        major_category     minor_category    
##  Min.   :2013   Length:2088        Length:2088        Length:2088       
##  1st Qu.:2014   Class :character   Class :character   Class :character  
##  Median :2014   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :2014                                                           
##  3rd Qu.:2015                                                           
##  Max.   :2016                                                           
##  total_workers      workers_male     workers_female    percent_female  
##  Min.   :    658   Min.   :      0   Min.   :      0   Min.   :  0.00  
##  1st Qu.:  18687   1st Qu.:  10765   1st Qu.:   2364   1st Qu.: 10.73  
##  Median :  58997   Median :  32302   Median :  15238   Median : 32.40  
##  Mean   : 196055   Mean   : 111515   Mean   :  84540   Mean   : 36.00  
##  3rd Qu.: 187415   3rd Qu.: 102644   3rd Qu.:  63327   3rd Qu.: 57.31  
##  Max.   :3758629   Max.   :2570385   Max.   :2290818   Max.   :100.00  
##  total_earnings   total_earnings_male total_earnings_female
##  Min.   : 17266   Min.   : 12147      Min.   :  7447       
##  1st Qu.: 32410   1st Qu.: 35711      1st Qu.: 29364       
##  Median : 44437   Median : 46837      Median : 40903       
##  Mean   : 49762   Mean   : 53138      Mean   : 44681       
##  3rd Qu.: 61012   3rd Qu.: 64846      3rd Qu.: 53613       
##  Max.   :201542   Max.   :231420      Max.   :166388       
##  wage_percent_of_male
##  Min.   : 50.87      
##  1st Qu.: 82.86      
##  Median : 84.03      
##  Mean   : 84.03      
##  3rd Qu.: 86.77      
##  Max.   :117.40

From the summary statistics, we can see that the dataset covers 2,088 rows of occupations and it was collected between 2013 and 2016. There is few notable statistics in the summary above: the total number of workers in the dataset ranges from 658 to 3,758,629 with a mean of 196,055. The percentage of female workers in the dataset ranges from 0% to 100%, with a mean of 36%. This indicates that there is some variation in gender representation across different occupations. Also, the percentage of the male wage that the female wage represents ranges from 50.87% to 117.40%, with a mean of 84.03%. This suggests that, on average, female workers earn about 84% of what male workers earn in the same occupation. However, it’s worth noting that there is likely a lot of variation in this figure across different occupations.

The below data visualizations are formed based on all 2088 rows in the dataset, including duplicated occupations. Detailed exloratory data analysis on different occupations will be analysed in the final write-up data project.

# Histogram of totall earnings across all occupations
ggplot(data = jobs_gender) +
  geom_histogram(mapping = aes(x = total_earnings), fill = "steelblue", bins = 30) +
  labs(title = "Distribution of the total earnings across all occupations", x = "Total earnings", y = "Count")

This data visualization is a histogram of total earnings, showing the distribution of total earnings through all 2088 occupations in the dataset. The histogram is constructed using 30 bins and a bluesteel fill color. This histogram showed a right-skewed pattern with the range of total earnings from 17266 to 201542. It can be observed that nearly the majority of the occupations earn from above 25000 to over 50000, with the center of the histogram at around 30000 (or 30000 is the earning that nearly 330 occupations are at). And there are just few occupations that can earn above 100000 in a year, which also shows that the values are slightly spread out.

# Bar chart of major categories
ggplot(data=jobs_gender) +
  geom_bar(mapping = aes(x=major_category),fill='steelblue') +
  labs(title="Number of occupations in each major category", x = "Major Category", y = "Number of occupations") + coord_flip()

The graph above shows that there are 8 different types of major categories in this dataset. The categories are sorted in alphabetical order on the x-axis. And the distribution of number of occupations per major category ranges from over 110 to nearly 450 occupations. In detail, Production, Transportation, and Material Moving has most occupations with nearly 450 while Healthcare Practitioners and Technical has the least occupations of over 110.

• Bi-variate and/or multivariate data visualizations and summary statistics if applicable:

# Scatter plot matrix of earnings and percent female
ggplot(data = jobs_gender) +
  geom_point(mapping = aes(x = total_earnings, y = percent_female), alpha = 0.4, color = "steelblue") +
  geom_smooth(mapping = aes(x = total_earnings, y = percent_female),method = "lm", se = FALSE, color='red') + labs(title = "Relationship between earnings and percent female", x = "Total earnings", y = "Female percent")

## `geom_smooth()` using formula = 'y ~ x'

The bi-variate data visualization above demonstrates a scatter plot of relationship between earnings and percent female with the best fit line. The best fit line slopes downward, which suggests a negative relationship, meaning that as one variable increases, the other tends to decrease. Also, from the plot, the points on the scatterplot are moderately clustered around the line and tend to spread out at the higher total earnings. This suggests a moderate relationships between total earnings and percent of female. And there seems to be hardly any outliers in the plot.

# Box plot of wage percent of male by major category
ggplot(data = jobs_gender) +
  geom_boxplot(mapping = aes(x=major_category,y=wage_percent_of_male),fill='steelblue') +
  labs(title = "Wage percent of male by major category",x= "Major category", y = "Wage percent of male") + coord_flip()

From the given boxplot, we can notice that Production, Transportation, and Material Moving and Natural Resources, Construction, and Maintenance ’s box plots are shorter (nealy none) and have more outliers than other categories. This mean that these two categories have the data less spread out and more variable than the others, interpreting that the distribution of wages for those category is highly skewed and that there are some high earners who are making significantly more than the typical earners in those category. Moreover, observing other categories, the positions of the boxplots quite overlap with each other, which means that the medians are similar. The whiskers of Management, Business, and Financial and Education, Legal, Community Service, Arts, and Media are longer than the others, which may indicate that the data are more variable in these 2 categories.

• Narrative about what you observe in the exploratory data analysis and what you learn about the data from the exploratory data analysis:

From the above exploratory data analysis, we can see that:

• The dataset covers 2,088 rows of occupations and was collected between 2013 and 2016.
• Total number of workers in the dataset ranges from 658 to 3,758,629 with a mean of 196,055.
• Percentage of female workers in the dataset ranges from 0% to 100%, with a mean of 36%.
• Percentage of the male wage that the female wage represents ranges from 50.87% to 117.40%, with a mean of 84.03%.
• The histogram of total earnings is right-skewed with a center around 30,000 and a range of 17,266 to 201,542. The majority of occupations earn from above 25,000 to over 50,000, and only a few earn above 100,000.
• The distribution of occupations across eight major categories shows that The Production, Transportation, and Material Moving category has the most occupations (nearly 450) while the Healthcare Practitioners and Technical category has the least (over 110).
• The scatter plot that shows a moderate negative relationship between total earnings and percent of female indicates that the best-fit line slopes downward, and there are few outliers. The points are moderately clustered around the line and tend to spread out at higher total earnings.
• The boxplot of Wage percent of male by major category indicates that Production, Transportation, and Material Moving and Natural Resources, Construction, and Maintenance categories have shorter boxplots with more outliers than other categories, indicating the data is less spread out and more variable. Management, Business, and Financial and Education, Legal, Community Service, Arts, and Media have longer whiskers, suggesting the data is more variable in these categories.

Research question 1: How has the gender composition of different majors changed over time?

• How many industries in the dataset and what are they?

#distinguish the major
jobs_gender %>% distinct(major_category)

• Create a dataset grouped by major category and year with the mean of female percent

# Group the data by major category and year, and calculate the mean percentage of female workers
jobs_gender_df1 <- jobs_gender %>%
  group_by(major_category, year) %>%
  summarize(mean_percent_female = mean(percent_female))

## `summarise()` has grouped output by 'major_category'. You can override using
## the `.groups` argument.

jobs_gender_df1 

• Visualize the data of percent_female in many major categories over time:

#Visualize the data of percent_female in many major categories over time
jobs_gender_df1 %>% ggplot() +
  geom_col(aes(x = year, y = mean_percent_female, group = major_category, fill = major_category)) +
  labs(x = "Year", y = "Percentage of female workers", 
       title = "Percent of female in 8 major categories over time",
       caption = "Data Source: [1]") + theme_bw()

• From the stacked bar chart above, it can be seen that the overall percentage of female in all industries increased gradually from 2013 to 2016 in which 2016 witness the largest percent of female throughout the industries. In detail, all major categories in the stacked bar chart show no specific trends of increasing or decreasing as most of them remain stable over the time. The female percent of Natural Resources, Construction, and Maintenance is the least compared to other industries over time with around 5.6%. Meanwhile, Healthcare Practitioners and Technical has the most percent of female in the industry with around 65% throughout the 4 years.

Final Conclusion and Answer to the Research Question:In short, it could be said that the female percent in each major category stay nearly the same from 2013 to 2016 in which Natural Resources, Construction, and Maintenance has the least and Healthcare Practitioners and Technical has the most female workers among the 8 major categories.

Research question 2: What factors contribute to the gender pay gap within a particular industry?

For this question, we will pick Natural Resources, Construction, and Maintenance as the industry to analyze. From question 1’s answer, it can easily be seen that this industry has the least female percent among all major categories. Therefore, we want to see if female_percent will influence the pay gap between genders along with other factors in this major category or not.

We gonna check how much is the gap between total earnings of female and male first:

Scatterplots of total earnings for male and female workers within the Natural Resources, Construction, and Maintenanceindustry:

#create a dataset with major_category Natural Resources, Construction, and Maintenance
jobs_gender_df2 <- jobs_gender %>% 
  filter(major_category == "Natural Resources, Construction, and Maintenance")

#Scatterplot of total earnings for male workers within Natural Resources, Construction, and Maintenance:
jobs_gender_df2 %>% ggplot() +
  geom_point(aes(x=total_earnings,y=total_earnings_female,color = total_earnings_female)) + 
  geom_smooth(aes(x=total_earnings,y=total_earnings_female),method="lm",se=FALSE,color="red") +
  labs(x="Total earnings", y = "Total earnings of female",
       title = "Relationship between total earnings and total earnings of female",
       caption = "Data Source: [1]")

## `geom_smooth()` using formula = 'y ~ x'

#Scatterplot of total earnings for male workers within Natural Resources, Construction, and Maintenance:
jobs_gender_df2 %>% ggplot() +
  geom_point(aes(x=total_earnings,y=total_earnings_male,color = total_earnings_male)) + 
  geom_smooth(aes(x=total_earnings,y=total_earnings_male),method="lm",se=FALSE,color="red") +
  labs(x="Total earnings", y = "Total earnings of male",
       title = "Relationship between total earnings and total earnings of male",
       caption = "Data Source: [1]")

## `geom_smooth()` using formula = 'y ~ x'

• When plot total_earnings_female and total_earnings_male with total_earnings with the best fit line, it can easily be seen that the data in total_earnings_female is a little bit widespread while that of total_earnings_male is clustered together. Also, the range of total_earnings_female is from around 5000 to over 110000 with the highest 160000. Meanwhile, the range of total_earnings_male is from around 20000 to 90000 with the higest 90000. Moreover, from the best fit lines of the two graph, we can see that the best fit line of total_earnings_female seems to increase slower than the line of total_earnings_male.

It can be concluded that there is a significant difference between the earnings of male and female workers. Female workers seem to have a wider range of earnings than male workers, with some females earning significantly less and others earning significantly more than the male workers. Also, the two best fit lines indicate that male workers have higher earnings than female workers on average as total_earnings_female increases at a slower rate than the line for total_earnings_male.

Now, we will go deep into analysing which factors contributing to this pay gap by using linear regression model on both outcome variables with some predictor variables:

For this analyzing, we take into accounts all other variables to be the predictor variables except for total_earnings,total_earnings_female and total_earnings_male (2 of them are the main outcome variables, and the other is the sum of these 2 variables). After regarding the fact that there are too many occupations and total_workers is the sum of workers_male and workers_female, we decide to eliminate occupation, workers_female and workers_female out of the predictor variables. Therefore, the predictor variables for the linear models are year, minor_category, total_workers, percent_female, and wage_percent_of_male.

Linear regression model with total_earnings_female as the response variable:

female_model <- lm(total_earnings_female~
                     year+minor_category+total_workers+percent_female+wage_percent_of_male, 
                   data = jobs_gender_df2)
summary(female_model)

## 
## Call:
## lm(formula = total_earnings_female ~ year + minor_category + 
##     total_workers + percent_female + wage_percent_of_male, data = jobs_gender_df2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -29512  -8675   -684   4277 116037 
## 
## Coefficients:
##                                                       Estimate Std. Error
## (Intercept)                                         -3.468e+05  1.397e+06
## year                                                 1.742e+02  6.944e+02
## minor_categoryFarming, Fishing, and Forestry        -9.581e+03  3.495e+03
## minor_categoryInstallation, Maintenance, and Repair -1.611e+03  1.632e+03
## total_workers                                       -1.110e-02  3.898e-03
## percent_female                                      -1.057e+02  1.088e+02
## wage_percent_of_male                                 4.608e+02  1.752e+02
##                                                     t value Pr(>|t|)   
## (Intercept)                                          -0.248  0.80413   
## year                                                  0.251  0.80207   
## minor_categoryFarming, Fishing, and Forestry         -2.742  0.00646 **
## minor_categoryInstallation, Maintenance, and Repair  -0.987  0.32445   
## total_workers                                        -2.848  0.00468 **
## percent_female                                       -0.972  0.33181   
## wage_percent_of_male                                  2.631  0.00893 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13960 on 321 degrees of freedom
## Multiple R-squared:  0.09427,    Adjusted R-squared:  0.07734 
## F-statistic: 5.569 on 6 and 321 DF,  p-value: 1.646e-05

The factors (or variables) in the model that contribute to total_earnings_female are:

• minor_categoryFarming, Fishing, and Forestry: being in this occupation category is associated with a decrease in earnings compared to other categories.
• total_workers: an increase in total workers is associated with a decrease in earnings.
• wage_percent_of_male: an increase in the wage percent of male workers is associated with an increase in female earnings.

The other variables in the model, year and percent_female, do not appear to be significant contributors to female earnings.

However, it is worth noting that the R-squared value of 0.09427 indicates that the model explains only about 9.4% of the variance in the outcome variable, which is relatively low. This indicates that these variables explain only a small proportion of the variation in total earnings of male workers.

Check the assumptions of female_model:

par(mfrow=c(2,2))
plot(female_model)

• Linearity: Based on the Residuals vs Fitted scatterplot, we can see that it does not look linear as the residuals seem not to be randomly scattered around zero, most of the data clustered in a point.

• Independence: We can assume that the observations are independent as long as each earnings with other predictor variables are likely to be unique and not influenced by the presence of other data.

• Normality: Based on the Normal Q-Q plot, the plot shows that the residuals are likely to be normally distributed. The points seem to be near to the line except for the last part where the data is gradually distant from the line. Also, from the Shapiro-Wilk test, as p-value < .05 (2.2e-16 < .05), we reject the null hypothesis and there is evidence to suggest that the residuals are not normally distributed. The normality assumption is likely to be broken.

shapiro.test(summary(female_model)$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  summary(female_model)$residuals
## W = 0.83743, p-value < 2.2e-16

• Homoscedasticity:From the Breusch-Pagan test, as p-value > .05 (0.2038 > .05), we fail to reject the null hypothesis that the variance of the residuals is constant.

bptest(female_model)

## 
##  studentized Breusch-Pagan test
## 
## data:  female_model
## BP = 8.4992, df = 6, p-value = 0.2038

Based on the assessment of the assumptions, it may not be appropriate to use a linear model for this data. The linearity and normality assumptions appear to be violated. A nonlinear model or a different type of regression model may be more appropriate for this data. It’s also possible that further data cleaning or transformation may be necessary before building a regression model.

Linear regression model with total_earnings_male as the response variable:

male_model <- lm(total_earnings_male~
                     year+minor_category+total_workers+percent_female+wage_percent_of_male, 
                   data = jobs_gender_df2)
summary(male_model)

## 
## Call:
## lm(formula = total_earnings_male ~ year + minor_category + total_workers + 
##     percent_female + wage_percent_of_male, data = jobs_gender_df2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -24373  -7547  -2173   6626  43669 
## 
## Coefficients:
##                                                       Estimate Std. Error
## (Intercept)                                         -1.252e+06  1.197e+06
## year                                                 6.436e+02  5.951e+02
## minor_categoryFarming, Fishing, and Forestry        -9.541e+03  2.995e+03
## minor_categoryInstallation, Maintenance, and Repair  1.789e+03  1.399e+03
## total_workers                                       -7.860e-03  3.341e-03
## percent_female                                      -6.561e+01  9.321e+01
## wage_percent_of_male                                 1.830e+01  1.501e+02
##                                                     t value Pr(>|t|)   
## (Intercept)                                          -1.046  0.29645   
## year                                                  1.081  0.28032   
## minor_categoryFarming, Fishing, and Forestry         -3.185  0.00159 **
## minor_categoryInstallation, Maintenance, and Repair   1.279  0.20192   
## total_workers                                        -2.353  0.01925 * 
## percent_female                                       -0.704  0.48202   
## wage_percent_of_male                                  0.122  0.90308   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11970 on 321 degrees of freedom
## Multiple R-squared:  0.09813,    Adjusted R-squared:  0.08127 
## F-statistic: 5.821 on 6 and 321 DF,  p-value: 8.949e-06

Based on the coefficients of the model, the variables that have a significant effect on the total earnings of male workers are:

• minor_category: Male workers in the “Farming, Fishing, and Forestry” category earn about 9,541 less than those in the reference category, which is “Management, Business, and Financial Operations” category. On the other hand, male workers in the “Installation, Maintenance, and Repair” category earn about 1,789 more than the reference category.
• total_workers: An increase of one worker is associated with a decrease of $7.86 in total earnings of male workers.
• wage_percent_of_male: An increase of one percentage point in the wage of male workers is associated with an increase of $18.30 in total earnings of male workers.

However, it’s worth noting that the R-squared value of the model is low (0.09813), which indicates that these variables explain only a small proportion of the variation in total earnings of male workers.

Check the assumptions of male_model:

par(mfrow=c(2,2))
plot(male_model)

• Linearity: Based on the Residuals vs Fitted scatterplot, we can see that it does not look linear as the residuals seem to clustered a lot at the end of the graph, and at the beginning of the graph, the dât are just a little.

• Independence: We can assume that the observations are independent as long as each earnings with other predictor variables are likely to be unique and not influenced by the presence of other data.

• Normality: Based on the Normal Q-Q plot, the plot shows that the residuals are likely to be normally distributed. The points seem to be near to the line except for the last half part where the data is gradually distant from the line. Also, from the Shapiro-Wilk test, as p-value < .05 (1.386e-07 < .05), we reject the null hypothesis and there is evidence to suggest that the residuals are not normally distributed. The normality assumption is likely to be broken.

shapiro.test(summary(male_model)$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  summary(male_model)$residuals
## W = 0.96165, p-value = 1.386e-07

• Homoscedasticity:From the Breusch-Pagan test, as p-value < .05 (0.002774 < .05), we reject the null hypothesis that the variance of the residuals is constant and conclude that there is evidence of heteroscedasticity in the data.

bptest(male_model)

## 
##  studentized Breusch-Pagan test
## 
## data:  male_model
## BP = 19.996, df = 6, p-value = 0.002774

Based on the violation of multiple assumptions, it may not be appropriate to use a linear model for this data. The linearity and homoscedasticity assumptions seems to be violated. Other models may be more appropriate.

Final Conclusion and Answer to the Research Question:

Based on the analysis, the following factors contribute to the gender pay gap within the Natural Resources, Construction, and Maintenance industry:

• minor_category: Workers in the “Farming, Fishing, and Forestry” category earn less than those in the reference category, which is the “Management, Business, and Financial Operations” category. This difference is more pronounced in male workers than female workers.

• total_workers: An increase in total workers is associated with a decrease in earnings.

• wage_percent_of_male: An increase in the wage percent of male workers is associated with an increase in female earnings.

It is worth noting that both two model only explains about 9.4% and 9,8% of the variance in the outcome variable, which are relatively low. This indicates that these variables explain only a small proportion of the variation in total earnings of both female and male workers.

Additionally, it may not be appropriate to use a linear model for this data because the linearity and normality assumptions appear to be violated. A nonlinear model or a different type of regression model may be more appropriate for this data. It’s also possible that further data cleaning or transformation may be necessary before building a regression model.

Research question 3: How do the earnings of male and female workers vary within the same major, and what factors might explain these differences?

• What is the median earnings by major category for male and female workers?

#Median of total earnings by major category for male and female workers
earnings_by_occ_gender <- jobs_gender %>%
  group_by(major_category) %>%
  summarise(median_earnings_male = median(total_earnings_male),
            median_earnings_female = median(total_earnings_female))

• The difference in median total earnings between male and female workers

# Calculate the difference in median earnings between male and female workers 
earnings_by_occ_gender <- earnings_by_occ_gender %>%
  mutate(median_earnings_diff = median_earnings_male - median_earnings_female)

• Visualize the data of earnings_by_occ_gender in all major categories

ggplot(data = earnings_by_occ_gender)+
  geom_col(mapping = aes(x = major_category, y = median_earnings_diff), fill = "orange")+
  labs(title = "Median Earnings Difference by Major Category",
       x = "Major Category", y = "Median Earnings Difference", caption = "Data Source: [1]") +
  coord_flip()

Final Conclusion and Answer to the Research Question:

• The resulting plot display the difference in median earnings between male and female workers for each major category.
• Based on the plot, it can be clearly seen that salaries of men are always higher than that of women. Moreover, the largest pay differences based on gender are in the major categories of “Management, Business, and Financial”, followed by “Engineering” and “Computers & Mathematics”, which are about $15,000 and $12,500 on average, respectively. In contrast, the lowest wage difference between gender can be found in the major categories of “Natural Resources, Construction, and Maintenance”, followed by “Service”, which between $2000 and $3000 on average.
• This is because much of the gender pay gap has been explained by measurable factors such as educational attainment, occupational segregation and work experience. According to The U.S. Census Bureau’s most recent analysis²,in 2021, full-time, year-round working women earned 84% of what their male counterparts earned, on average.
• According to a Pew Research Center survey conducted in October 2022³, other factors that are difficult to measure, including gender discrimination, may also contribute to the ongoing wage discrepancy.
• Parents with children younger than 18 in the household are more likely than those who don’t have young kids at home (48% vs. 40%) to say a major reason for the pay gap is the choices that women make about how to balance family and work. On this question, differences by parental status are evident among both men and women⁴.

Research question 4: Is there a relationship between the percentage of female workers in an major and the average earnings of workers in that major?

Based on the result from the research question 3, the largest pay differences based on gender are in the major categories of “Management, Business, and Financial”. Therefore, for this analyzing, we want to explore if there is any relationship between the percentage of female workers in the major categories of “Management, Business, and Financial” and the average earnings of workers in that major.

#Filter the dataset to include only this major category:
df_4 <- filter(jobs_gender, major_category == "Management, Business, and Financial")
#Calculate the correlation coefficient between the percent_female and total_earnings variables
cor <- cor(df_4$percent_female, df_4$total_earnings)
print(cor)

## [1] -0.2954133

A correlation coefficient of -0.2954133 suggests a negative relationship between the percentage of female workers in the “Management, Business, and Financial” major category and the average earnings of workers in that major. A negative correlation coefficient means that as the percentage of female workers in the major category increases, the average earnings tend to decrease.

• Visualize the relationship between these two variables

ggplot(data = df_4) +
  geom_point(mapping = aes(x = percent_female, y = total_earnings)) +
  labs(x = "Percentage of female workers", y = "Average earnings", title = "Relationship between the percentage of female workers and the average earnings of workers in the major categories of Management, Business, and Financial")

Final Conclusion and Answer to the Research Question:

• A negative correlation coefficient -0.2954133 means that as the percentage of female workers in the major category increases, the average earnings tend to decrease.
• The scatter plot can also provide insight into the relationship between the variables. Looking at the scatter plot, we can see that the data points are spread out and do not form a clear linear pattern. However, we can still observe that there is a general trend of decreasing average earnings as the percentage of female workers increases.

Conclusion

• Overall, based on the above analysis results, it can be summed up that the dataset analyzed indicates that a gender pay gap exists across various industries, with men consistently earning higher salaries than women. The largest pay differences between gender are found in the major categories of “Management, Business, and Financial”, followed by “Engineering” and “Computers & Mathematics”, while the lowest pay differences are found in the major categories of “Natural Resources, Construction, and Maintenance”, followed by “Service”. Factors contributing to the gender pay gap include the measurable factors of educational attainment, occupational segregation, work experience, total workers, and the wage percent of male workers, but other difficult-to-measure factors such as gender discrimination may also contribute to the ongoing wage discrepancy. Additionally, the percentage of female workers in a major category is negatively correlated with average earnings, but the low explanatory power of the regression models suggests that further research is needed to better understand the factors driving the gender pay gap.

• For future work:

  • Future work could involve collecting more comprehensive and detailed data on the factors that contribute to the gender pay gap, including information on specific jobs or occupations within each major category, as well as data on race, ethnicity, and disability status.
  • It could be valuable to explore potential interventions or policy changes that could help to reduce the gender pay gap in different industries and job categories.

• Commentary of limitations: we can see that there are some limitations to this dataset:

  • The dataset only includes information from the United States, so the conclusions may not be generalizable to other countries.
  • The dataset does not include information on other potential factors that could contribute to the gender pay gap, such as race, ethnicity, or disability status, gender discrimination and the impact of family and work balance, may contribute to the ongoing wage discrepancy and require further investigation.
  • The variables included in the dataset explain only a small proportion of the variation in total earnings of both female and male workers, indicating that other important factors may not have been measured.
  • The violation of some of the assumptions of the linear model used in the analysis is a limitation of this dataset. Specifically, the linearity and normality assumptions appear to be violated, which may lead to biased results or incorrect conclusions. This suggests that a nonlinear model or a different type of regression model may be more appropriate for this data. Additionally, further data cleaning or transformation may be necessary before building a regression model. Therefore, the conclusions drawn from the linear regression models should be interpreted with caution.

Data Sources and Works Cited

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1. Data Source: https://github.com/rfordatascience/tidytuesday/tree/master/data/2019/2019-03-05 posted by TidyTuesday who collected it from Census Bureau and Bureau of Labor here and here in March 2019.↩︎

2. Carolina Aragão. (2023). Gender pay gap in U.S. hasn’t changed much in two decades. Pew Research Center.↩︎

3. Carolina Aragão. (2023). Gender pay gap in U.S. hasn’t changed much in two decades. Pew Research Center.↩︎

4. Carolina Aragão. (2023). Gender pay gap in U.S. hasn’t changed much in two decades. Pew Research Center.↩︎