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Exercise

Comparing two proportions

When we deal with categorical data, our parameter of interest is a sample proportion. An example of a sample proportion could be the proportion of people that are left wing voters. Imagine that we want to compare the proportion of males that are left wing voters to the proportion of females that are left wing voters. In this case our two groups are independent. To do the above analysis, we usually use a Z test.

Before we do a Z test however to see whether the difference between two proportions is meaningful, we usually calculate 2 things:

  1. The difference between the two sample proportions
  2. The standard error

The difference between the two sample proportions is easily calculated with the following formula: \(p1 - p2\). The formula for the standard error is a little bit trickier as it involves the calculation of pooled estimate \(\hat{p}\). You can calculate \(\hat{p}\) with the following formula: \(\hat{p} = (p1 + p2) / (n1 + n2)\). Here, \(p1\) stands for the number of successes in group 1, \(p2\) for the number of successes in group 2, \(n1\) for the sample size of group 1 and \(n2\) for the sample size of group 2.

Instructions

100 XP
  • In this exercise we have a sample of 100 males with a proportion of left wing voters of 0.6 and a sample of 150 females with a proportion of left-wing voters of 0.42. Calculate the difference between the male and the female sample proportion and store it in the variable difference
  • Calculate the pooled estimate \(\hat{p}\) and store it in a variable called pooled pooled