# Equivalence Test in Excel

## When to use an Equivalence Test

Traditional t-tests determine if *means* are different, but they can have false positives. Equivalence testing determines an interval where the means can be considered *equivalent*.

The Equivalence Test uses two t-tests assuming equal variances with a hypothesized mean difference (*u*_{1}-*u*_{2} = interval).

**Note:**Excel does not do equivalence tests; QI Macros adds this functionality.

### Equivalence Test Example

Adhesive tape is measured immediately after production and 24 hours later. Are the measurements equivalent at these two different points in time. If they are, one measurement can be eliminated, saving time and money.

#### Run an Equivalence-Test Using QI Macros

Select the data within your Excel spreadsheet, click on QI Macros menu, Statistical Tools and select Equivalence test.

QI Macros will prompt for a significance level (default = 0.05 or 0.95):

Along with the hypothesized mean difference (**Note:** this difference will set the range acceptable for equivalence):

*Calculation used:*

The Equivalence test will perform the calculations and interpret the results for you.

If both p-values are less than 0.05, the means are equivalent.

#### Now here's where it gets interesting...because the one-tailed p-values are both less than 0.05... ** the means can be declared ***equivalent*. So, we can eliminate one of the tests.

*equivalent*

**Define the two null and alternate Hypotheses for equivalence:**

- The null hypothesis H
_{01}is that the mean difference (x1-x2) <= 0.8 - The alternative hypothesis H
_{11}a is that the mean difference > 0.8 - The null hypothesis H
_{02}is that the mean difference (x1-x2) >= 0.8 - The alternative hypothesis H
_{12}a is that the mean difference < 0.8

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