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# One Sample Equivalence Test Help

This test is used to determine if there is a practical difference between an average and a target value.  The user must determine a range of values that are considered to be insignificant when compared to the target value.   You use your knowledge of the process to determine this range of values, which is also is called the equivalence interval.  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 chemist is evaluating the density of a potential new product.  The existing product as a density of 5.5 and the chemist wants the density of the new product to be the same.  The target value for the new product is 5.5.  The chemist is willing to have the new product’s density vary from +/- 0.3 of the target value.  The equivalence interval is then -0.3 to 0.3.  The chemist takes 29 random samples of the new product and measures the density of each sample.  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 one column.

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 “One Sample Equivalency Test.” The input form below is shown.

#### One Sample Equivalence Test Output

The output from the example data is shown below.  A new worksheet is added to the workbook.  The target value is 5.5, the LEL = -0.3 and UEL = 0.3 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 two charts to help interpret the results.

The output tells you the conclusion from the test.

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 is also a chart of the 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.

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