# Gender change in Irish political representation

## Estimating the effect of the gender quota: The initial question

A gender quota for candidates was imposed in the 2016 Irish election (see e.g., http://www.thejournal.ie/readme/gender-quota). The question arises whether it had an impact. As a first pass consider the following table:1

           |        gender
dail |         f          m |     Total
-----------+----------------------+----------
2011 |        21        145 |       166
|     12.65      87.35 |    100.00
-----------+----------------------+----------
2016 |        32        116 |       148
|     21.62      78.38 |    100.00
-----------+----------------------+----------
Total |        53        261 |       314
|     16.88      83.12 |    100.00


This is clearly a big rise. Is it statistically significant?

# Pollsters’ 3% Margin of Error

The 3% margin of error often quoted in polling has the following logic. It uses a sample size of 1000, and calculates a confidence interval as follows: $$\hat \pi \pm 1.96 \times SE$$ where $$\hat\pi$$ is the sample proportion, and SE, the standard error, is the standard deviation divided by the square-root of the sample size.