## About this lesson

The One-Sample and Two-Sample Test of Proportions are used with discrete data. These tests determine whether the percentage of a particular attribute being studied is similar to or different from the selected target value. These tests are illustrated using both Excel and Minitab.

## Exercise files

Download this lessonâ€™s related exercise files.

Test of Proportions.xlsx11 KB Test of Proportions - Solution.docx

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## Quick reference

### Test of Proportions

The Test of Proportions is for data sets with discrete data. The tests compare the percentage of a particular attribute found in the data against either a known target or the percentage of that attribute in another data set.

### When to use

Use the Test of Proportions with discrete data, such as yes/no, true/false, or on/off. It is often used to determine if two data sets are different; either to discover an underlying root cause or as a before after test during the improve phase.

### Instructions

The Test of Proportions is a simple test to determine if the percentage of an attribute in a data set is statistically different from a target percentage or from another data set. It is used both when determining cause and effect relationships and for determining the benefit of a solution implementation during the improve phase.

The One-Sample Test of Proportions tests the data set percentage against a known or target percentage. The Two-Sample Test of Proportions tests the percentages of each sample against each other.

Excel:

- Excel cannot perform the One-Sample Test of Proportions
- Excel requires several steps to perform the Two-Sample Test of Proportions.
- Ensure your discrete data is converted to integers – on=1, off=0
- Use the VAR function to find the variance for each of the data sets
- In the Data Analysis Menu, use the Z Test: Two Samples for Means function.
- Enter the data ranges and the variance values.
- Excel will calculate both a one-sided tail and two-sided tail P Value. The one-sided tail is for the Hypothesis test of greater than or less than. The two-side test is for the Hypothesis test of equal to or not equal to.

Minitab:

- Minitab calculates the One-Sample Test of Proportions
- Stat > Basic Statistics > 1 Proportion
- Enter the column with your data and enter your target percentage.
- Click on the Hypothesis test box
- Select the Option button to change the Alternative Hypothesis to a greater than or less then condition.

- Minitab calculates the Two-Sample
- Stat > Basic Statistics > 2 Proportion
- Select the format of your data (all data in one column or in two columns)
- Select your data columns
- Select the Option button to change the Alternative Hypothesis to a greater than or less than condition.

### Hints & tips

- Minitab and Excel calculate slightly different P Values – but the difference is very small.
- The data values must be in integer format for Excel, but the data can still be text data in Minitab.
- The difference between one-sided tail and two-sided tail is based upon the Bell-shaped Curve. When the Hypothesis test is “equal to” or “not equal to” the test must consider both the upper portion of the curve and the lower portion of the curve. When the Hypothesis test is “greater than” or “less than,” only one side of the Bell-shaped curve must be checked.

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