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Question

For this set of exercises, we examine the data from a2014 PNAS paper that analyzed success rates from funding agencies in the NetherlandsExternal link http://www.pnas.org/content/112/40/12349.abstract

and concluded:

"our results reveal gender bias favoring male applicants over female applicants in the prioritization of their "quality of researcher" (but not "quality of proposal") evaluations and success rates, as well as in the language used in instructional and evaluation materials."

A response was published a few months later titledNo evidence that gender contributes to personal research funding success in The Netherlands: A reaction to Van der Lee and EllemersExternal link http://www.pnas.org/content/112/51/E7036.extract

, which concluded:

However, the overall gender effect borders on statistical significance, despite the large sample. Moreover, their conclusion could be a prime example of Simpson's paradox; if a higher percentage of women apply for grants in more competitive scientific disciplines (i.e., with low application success rates for both men and women), then an analysis across all disciplines could incorrectly show "evidence" of gender inequality.

Who is right here: the original paper or the response? Here, you will examine the data and come to your own conclusion.

The main evidence for the conclusion of the original paper comes down to a comparison of the percentages. The information we need was originally in Table S1 in the paper, which we include indslabs:

library(dslabs)

data("research_funding_rates")

research_funding_rates

Question

Construct a two-by-two table of gender (men/women) by award status (awarded/not) using the total numbers across all disciplines.

1. What is the number of men not awarded?
2. What is the number of women not awarded?

Question

Use the two-by-two table from Question 1 to compute the percentages of men awarded versus women awarded.

1. What is the percentage of men awarded? - Report a percentage between 0 and 100.
2. What is the percentage of women awarded? - Report a percentage between 0 and 100.

Question 3

Run achi-squared test

• On the two-by-two table to determine whether the difference in the two success rates is significant.

(You can usetidy()to turn the output ofchisq.test()into a data frame as well.)

1. What is the p-value of the difference in funding rate?