OBJECTIVE
Verify
whether two proportions are significantly different.
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.
TEMPLATE