# 1 Proportion

## Summary

Analyzes the difference between an observed process proportion (defectives) and a specified value.

• Is the process proportion defective significantly different from a specified value such as a previously known defective proportion or a nominal specification?
When to Use Purpose
Pre-project Verify the process is producing output significantly different from expectations (in this case, that usually means a higher-than-expected defect rate), which validates the need for an improvement project.
Mid-project Test whether the proportion defective changed significantly when an input is controlled at a new setting or a previously uncontrolled setting is now controlled.
Mid-project Verify changes from the pre-project standard, throughout the course of making improvements.
End of project Verify the proportion defective from the controlled improved process is different from the pre-project proportion defective. Of course, this step assumes one of the goals of the project was to reduce the proportion defective.

### Data

Discrete Y at exactly two levels (also called binary or binomial data). You can enter the raw data into a single column in Minitab where each row represents one observation. Or, you can enter summarized data (the number of items sampled and the number of defectives observed) in the 1 Proportion dialog box.

## How-To

1. Verify the measurement system for the Y data is adequate.
2. Develop a data-collection strategy (who should collect the data, as well as where and when; how many data values to collect; the data’s precision how to record the data; and so on).
3. Collect process data and enter the values into a single column in a Minitab worksheet. When you enter raw data, you can use any coding cheme, as long as you only use two values. By default, Minitab defines the higher numeric value, or the text value closer to the end of the alphabet, as the event (defect). For example, you can enter the data as 0 for good and 1 for defective or Normal/Problem. If you like, you can change the value order Minitab uses to define defectives.
4. Enter the test proportion (a standard or benchmark proportion) to compare the process data against.
5. Determine your hypothesis. You are often trying to prove the alternative hypothesis (Ha) with the data. In a 1-proportion test, the alternative hypothesis tests whether the process proportion defective is greater than, less than, or not equal to the benchmark value. The null hypothesis (Ho) is the opposite of the alternative hypothesis
6. You can also perform the test without the actual data if you know the number of items sampled and the number of defective items.

## Guidelines

• Develop a sound data collection strategy to ensure 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, which means the data must meet the following assumptions:
• Each test result has exactly two possible outcomes.
• The probability of a particular outcome is constant for all trials.
• The trials are independent of each other.
• The 1-proportion test can also be used to generate a confidence interval for a proportion. For example, if you make 2,518 units and 239 are defective, you can use this test to state with 95% confidence that the defect rate is between 8.37% and 10.70%.
• By default, Minitab uses the exact method to perform the test and calculate the confidence interval. Minitab also provides a normal approximation method; however, this method is not recommended because it is not as accurate as the exact method.
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