The 2-proportion z-test is a statistical procedure used to compare the proportions of two independent groups. This test is used when the researcher wants to know if there is a significant difference between the two groups, specifically if one group is significantly higher than the other.
This test can be used in various situations, such as comparing the success rate of two treatments or comparing the proportions of Males vs Females who responded positively to a survey question.
How the 2-Proportion Test Works
The 2 proportion z-test works by first calculating what is known as the pooled proportion. This is done by taking the sum of the successes of both groups and dividing it by the sum of the number of observations in both groups.
Once we have the pooled proportion, we can calculate the standard error. The standard error tells us how much variation we should expect from our sample statistic; in this case, it will tell us how much variation we should expect from our pooled proportion.
Once we have both values, we can calculate a z-score. The z-score tells us how many standard deviations are from our sample statistic’s mean. In this case, it will tell us how many standard deviations away from 0.5 our pooled proportion is.
Depending on whether our null hypothesis is that there IS a difference or there IS NO difference, our alternative hypothesis will be directional or non-directional, respectively. If our alternative hypothesis is directional, we will look for a z-score that falls into either the upper or lower tail depending on the direction we are testing for. For example, if we are testing to see if Group 1 has a higher success rate than Group 2, we would be looking for a z-score that falls into the upper tail.
However, if our alternative hypothesis is non-directional, we will look for a z-score that falls into either extreme of the distribution. In other words, we would be looking for a z-score that falls below -1.96 OR above 1.96.
Conclusion:
The 2 proportion z-test is a helpful statistical procedure that can be used to compare two proportions and determine if there is a significant difference between them. This test can be used in various situations and can help researchers understand whether one group is significantly higher than another.
