Simulation and Analysis of Gender Discrimination in Promotion Decisions Assignment

Assignment Task

Preparation

• Create a script to put the code you will use to complete this practice (name it gender- R ). It is always a good idea to include some comments in the beginning explaining what the script is about, the author and the date.
• Create an object named id and assign it the number in your student id, g., if your students id is a12345 , id should be 12345.
• This assignment can be done in If that is your case, create an id2 object for a second student. The work should be submitted by the first student only.

Tasks

Consider the case study presented in OpenIntro Slides 4th Edition (chapter 2, slide 40 onwards). We want to decide between:

Independence hypothesis - the variables gender and promotion decision are indepen- dent, that is, women and men have the same probability of being promoted and the difference observed in the 1972 study was due to chance;

Alternative hypothesis -  the variables gender and promotion decision are dependent, that is, in the 1972 study discrimination against women was

1. As described in the slides, using a normal deck of 52 cards1, we can easily run a simulation to observe what would happen if the independence hypothesis is

• Remove the aces from the deck, leaving only 48
• The 24 red cards will represent women and the 24 black cards will represent
• Shuffle the 48 cards and draw 35 cards at random (these will be promotions).
• Count and record how many women and men promoted (make sure the sum is 35).
• Repeat the simulation 100 times (shuffle/draw/count) and write down the

If this whole process seems tedious, you can use R to generate random observations. It can be done easily, but you must research the correct way to do it.

2. Create a CSV file (csv) with the collected data. The following procedure is sug- gested:

• Create an “empty” data frame with 4 variables to place the results: auth (name of authors), sim_num (number the simulations from 1 to 100), pw (number of women promoted) and pm (number of men promoted).
• Insert the results of the simulations into the table. You can use R to easily edit data with the edit()
• Check for errors by making sure the total number of promotions always equals
• Save the data in a CSV

The following code (which should not be included in the script to be submitted) is one of the possibilities:

3. Your script should contain:

• A comment with the name of the
• Code to read the created data
• Code to calculate the statistics about promotions to support your
• Code to build the graphics for analysis: a stacked dot diagram2, similar to Figure 1, a box plot similar to Figure 2, and a scatter plot with the raw results similar to Figure 3.
• Code needed for any other analysis or graphic you decide to

4. Write a text document (e.g. Word) with 2 or 3 paragraphs with your conclusions and Specifically:

• Which of the two hypotheses do you think is more plausible for the 1972 study? Do you think gender discrimination is more likely or can the results obtained in the study be explained by chance?
• Don’t forget to include and comment the graphics created in your document (you can copy and paste from RStudio).
• Also don’t forget to identify the authors at the top of the

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