## What is 2 proportions test?

To perform this test, select Stat > Basic Statistics > 2 Proportions.

Use this analysis to:
• Determine whether the proportions of two groups differ
• Calculate a range of values that is likely to include the difference between the population proportions

For example, suppose you wanted to know whether the proportion of consumers who return a survey could be increased by providing an incentive such as a product sample. You might include the product sample with half of your mailings and determine whether you have more responses from the group that received the sample than from those who did not.

## Hypotheses for 2 proportions test

For 2 Proportions, the hypotheses are:
Null hypothesis
 H0: ρ1- ρ2 = d0 The difference between the population proportions (ρ1- ρ2) equals the hypothesized difference (d0).
Alternative hypothesis
Choose one:
 H1: ρ1- ρ2 ≠ d0 The difference between the population proportions (ρ1- ρ2) does not equal the hypothesized difference (d0). H1: ρ1- ρ2 > d0 The difference between the population proportions (ρ1- ρ2) is greater than the hypothesized difference (d0). H1: ρ1- ρ2 < d0 The difference between the population proportions (ρ1- ρ2) is less than the hypothesized difference (d0).

## Methods that Minitab uses to calculate 2 proportions test

Minitab's 2 Proportions test uses a normal approximation by default for calculating the hypothesis test and confidence interval. The normal approximation can be used to approximate the difference between two binomial random variables provided the sample sizes are large and proportions are not too close to 0% or 100%. In addition, when you specify a test difference of zero in the Options sub-dialog box, Minitab does Fisher's exact test, which is exact for all sample sizes and proportions. Fisher's exact test is based on the hypergeometric distribution.

The normal approximation may be inaccurate for small numbers of events or nonevents. If the number of events or nonevents in either sample is less than five, Minitab displays a note. Fisher's exact test is accurate for all sample sizes and proportions.

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