Your reproducible lab report: Before you get started, download the R Markdown template for this lab. Remember all of your code and answers go in this document:

download.file("https://github.com/GarciaRios/govt_3990/raw/gh-pages/Labs/lab6/lab6.Rmd", destfile = "lab6.Rmd")

American salaries

Since 2005, the American Community Survey polls ~$3.5 million households yearly. We will work with a random sample of 2000 observations from the 2012 ACS. You have already worked with this dataset once, as part of your application exercise. In this lab you get a chance to work with it a little more extensively.

load(url("https://github.com/GarciaRios/govt_3990/raw/gh-pages/Labs/lab6/acs.RData"))

Below is the codebook for this dataset:

Note that this dataset contains some people who are not in the labor force or not employed.

  1. What percent of the original sample (acs) are employed?

First, let’s subset the dataset for those who are employed. We will call this new dataset acs_emp, short for “employed”. Remember that we use the filter function for subsetting the data based on attributes stored in a variable.

acs_emp <- acs %>%
  filter(employment == "employed")

Next let’s take a look at the income distribution by gender. The first step would be to create a visualization:

ggplot(acs_emp, aes(y = income, x = gender))+ 
  geom_boxplot()

We can also obtain summary statistics such as means and standard deviations and sample sizes.

acs_emp %>%
  group_by(gender) %>%
  summarise(xbar = mean(income), s = sd(income), n = n())
  1. At a first glance how do the average incomes of males and females compare? Make sure to include the visualization and the summary statistics in your answer, and discuss/ interpret them.

Before you proceed, make sure to load the inference function. You might have this function already loaded in your console’s enviromment from last time, but not that in order to create a fully reproducible lab report you need to load it in your markdown document as well.

load(url("https://github.com/GarciaRios/govt_3990/raw/gh-pages/Labs/lab5/inference.RData"))

  1. Construct a 95% confidence interval for the difference between the average incomes of males and females using the inference function, and interpret this interval.

  2. Based on this interval is there a statistically significant difference between the average incomes of men and women? Why, or why not?

  3. What is the significance level for the equivalent hypothesis test that evaluates whether there is a significant difference between average incomes of men and women.

  4. Conduct this hypothesis test using the inference function, and interpret your results in context of the data and the research question. Do your results from the confidence interval and the hypothesis test agree?

Confounding variables

There is a clear difference between the average salaries of men and women, but could some, or all, of this difference be attributed to a variable other than gender? Remember that we call such variables confounding variables. We will evaluate whether hrs_work is a confounder for the relationship between gender and income. But before we do that, let’s first convert the hrs_work variable to a categorical variable (with levels "full time" or "part time") so that we can use methods we have learned so far in the course to run the analysis. (Later in the course we will learn how to work with numerical explanatory variables in a regression model setting.)

Recoding variables

We want to create a new variable, say emp_type, with levels "full time" or "part time" depending on whether the employee works 40 hours or more per week or less than 40 hours, respectively. Remember, we create a new variable with the mutate function.

acs_emp <- acs_emp %>%
  mutate(emp_type2 = case_when(hrs_work >= 40 ~ "full time", 
                              TRUE ~ "part time"))

Again, the case_when() function has three arguments: a logical test for various elements, the value that will assigned when the condition is met, and the values for the remaining elements of test. In this case, emp_type will be coded as "full time" for observations where hrs_work is greater than or equal to 40, and as "part time" otherwise.

To find out what percent of the sample is full vs. part time for men and women, we turn to count() and/or group_by:

acs_emp %>%
  group_by(gender) %>%
  count(emp_type) %>% 
  mutate(pct = prop.table(n))

Here we first grouped the data by the gender variable and generated counts of each employment type using our new variable (emp_type), then we calculated proportions of full and part time employees by group, in this case gender using that total count (n).

  1. Create a bar plot of the distribution of the emp_type variable, and also include the summary statistics you calculated above in your answer. What percent of the sample are full time and what percent are part time employees?

  2. Are females more heavily represented among full time employees or part time employees?

On your own

  • Create two subsets of the acs_emp dataset: one for full time employees and one for part time employees. No interpretation is needed for this question, just the code is sufficient.

  • Use a hypothesis test to evaluate whether there is a difference in average incomes of full time male and female employees. If the difference is significant, also include a confidence interval (at the equivalent confidence level) estimating the magnitude of the average income difference.

  • Use a hypothesis test to evaluate whether there is a difference in average incomes of part time male and female employees. If the difference is significant, also include a confidence interval (at the equivalent confidence level) estimating the magnitude of the average income difference.

  • What do your findings from these hypothesis test suggest about whether or not working full or part time might be a confounding variable in the relationship between gender and income?

  • What type of a test would we use to compare the average salaries across the various race / ethnicity groups in this dataset? Explain your reasoning.

  • Conduct this hypothesis test using the inference function. Note that the response variable is income and the explanatory variable is race. You will need to figure out the remaining arguments for the function. Use a trial-and-error approach, and let the errors inform you as to what else needs to be specified, and how. (Note: Use the dataset containing records from all employes participants: acs_emp) Write your hypotheses, and interpret your conclusion in context of the data and the research question. Note that the inference function by default uses a significance level of 0.05 for the ANOVA, and will run pairwise t-tests and report p-values for them if the ANOVA is significant. (Note also that you can change the significance level by setting sig_level equal to some other value.)

  • Pick another numerical variable from the dataset to be your response variable, and also pick a categorical explanatory variable (can be one we used before). Conduct the appropriate hypothesis test, using the inference function, to compare means of the response variable across levels of the explanatory variable. Make sure to state your research question, and interpret your conclusion in context of the dataset. Note that you can use the complete acs dataset, the subsetted acs_emp dataset, or another subset that you create.