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# Paired Sample Equivalence Test Help

This test is used to determine if there is a practical difference between two averages when the samples are not independent – they are paired.   For example, you might want to compare two test methods.  You test the same sample in each test method.  So, the samples are not independent.  Each sample is tested in each test method.

One average is considered the reference average.  The other average is considered the test average.  The difference being examined is the test average minus the reference average.  You must define a range of values that are considered to be the “same” as the reference average.  You use your knowledge of the process to determine this.  This test can be two-sided or one-sided.

The example below demonstrates how to do this test.  You can download the data at this link.

A company is looking at purchasing a new gas analyzer.  The current gas analyzer is considered to be the reference.  As long as the new gas analyzer is within 3 ppm for a certain component, it will be considered the same.  Twenty gas samples were split and tested in each analyzer. The steps to perform the analysis with the SPC for Excel software are given below.

1. Enter the data into a worksheet as shown below. The data must be in columns.  One column represents the test data; the other column, the reference data.  The software assumes that the first column is the test data, but it does not have to be.

2. Select the data above (including the heading).

3. Select “Equivalency Tests” from the “Statistical Tools” panel in the SPC for Excel ribbon.

4. Select the “Paired Samples Equivalence Test.” The input form below is shown.

#### Paired Samples Equivalence Test Output

The output from the example data is shown below.  A new worksheet is added to the workbook.  The LEL = -3 and the UEL = 3 in this example.  The alternate hypothesis chosen was Lower Equivalence Limit <  Average – Target < Upper Equivalence Limit.

An explanation of terms is given below the output.  In addition to the output table, the program displays charts that help interpret the results.

The chart below is also created. This makes it easy to see if the confidence interval for the difference is within the equivalence interval.

There are also two charts – one for the test data and one for the reference data –  to look for possible outliers.  If the program detects possible outliers, they will be in red and a message will be printed on the worksheet.

There are also one chart that plots the difference.

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