Thursday, April 18, 2019

44. TEST OF PROPORTIONS


OBJECTIVE
Verify whether two proportions are significantly different.


DESCRIPTION

This test has the same purpose as a t-test but is applied to compare proportions, that is, when elements can take the value of 0 or 1. For example, we can compare the conversion rate of two advertising campaigns (two-sample test of proportions) or compare the improvement in patients who received a new drug compared with the average improvement of these patients.

As in the t-test, we need to specify our hypothesis and, based on that, run either a two-tailed t-test or a one-tailed t-test (see 43. t-TEST); the only difference is that instead of using means we use proportions. We then need to specify the required significance level (α) and the hypothesized difference between the proportions.
Other differences from the t-test is that we resolve the test by calculating the z-critical value instead of the t-critical value and that the calculation is slightly different because we use proportions instead of means, variances, and standard deviations. In addition, we have to check that the number of events (conversions) and the number of “no events” (users who did not buy) are at least 10.


ONE-SAMPLE

The boss of a company claims that 80% of people are very satisfied with their working conditions. Our null hypothesis is that the satisfaction is equal to 80%, and our alternative hypothesis is that the satisfaction rate is different from 80%. The HR department decides to survey 100 employees, with a result of 73%. At the 0.05 level of significance, we fail to reject the null hypothesis, so we cannot state that the satisfaction of our survey is significantly different from 80%. In Figure 47 we can see that the confidence interval (95%) includes 80%.



Results of a One-Sample Test of Proportions



TWO-SAMPLE

A company has started a new online marketing campaign and wants to compare it with a standard online marketing campaign. The goal is to increase the conversion rate of online users, and the conversion rates of the two campaigns are compared using a proportion test. The results are not presented here, since this test is explained in more detail in chapter 45. A/B TESTING.


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