# 2 Proportions

## Summary

Analyzes observed differences in the process proportion defective at two settings of an input. Use the 2-proportions test when the data from the process are discrete and have exactly two levels (for example, pass or fail) and the factor being evaluated has exactly two levels (for example, fast or slow, before or after). You must collect a sample at each level of the input variable.

• If I change an input from one level to another, does the process proportion defective stay the same or does it change?
• Is the process proportion defective the same before and after a change has been made to the process?
When to Use Purpose
Mid-project Fixing an input at two different settings (levels) helps to determine which inputs have significant influence on the proportion defective of the output.
End of project Verify a significant reduction in the process proportion defective results from the implemented improvements. Of course, this step assumes one of the goals of the project was to reduce the proportion defective.

### Data

Discrete Y at two levels (for example, good or bad), a single X at two levels.

## How-To

1. Verify the measurement systems for the Y data and the input X are adequate.
2. Develop a data collection strategy (who should collect the data, as well as where and when; how many data values are needed; the preciseness of the data; how to record the data, and so on).
3. Use one of three methods to enter the data in Minitab:
• Enter results (for example, pass or fail) in two columns, one for each factor level.
• Enter results (for example, pass or fail) in one column with the factor level in a second column.
• Use summarized data (the most common approach) by entering the number of trials and number of events (for example, pass) for both factor levels directly in the Minitab dialog box.
4. Determine the hypotheses. The alternative hypothesis (Ha) is what you are trying to prove with the data. The alternative hypothesis for the 2-proportions test is whether the two proportions are not equal or if one is greater or less than the other. The null hypothesis (Ho) is the opposite of the alternative hypothesis.

## Guidelines

• Develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• Use Minitab’s Power and Sample Size command to determine the sample size necessary to detect the smallest difference of interest with sufficient power.
• The data must fit a binomial distribution:
• Each test result has exactly two possible outcomes.
• The probability of a particular outcome is constant.
• The trials are independent of each other.
• Use this test to generate a confidence interval for the differences in the proportions.
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