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 (TOST) Test uses two t-tests assuming equal variances with a hypothesized mean difference (u1-u2 = 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.

equivalence test data

Run an Equivalence (TOST) Test Using QI Macros

Select the data within your Excel spreadsheet, click on the QI Macros menu > Statistical Tools > F and t Tests and select Equivalence (TOST) Test:

QI Macros f and t test menu in Excel

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

enter significance level

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

hypothesized difference in means prompt in QI Macros statistical software

Calculation used:

hypothesized mean difference formula

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.

Define the two null and alternate Hypotheses for equivalence:

  • The null hypothesis H01 is that the mean difference (x1-x2) <= 0.8
  • The alternative hypothesis H11a is that the mean difference > 0.8
  • The null hypothesis H02 is that the mean difference (x1-x2) >= 0.8
  • The alternative hypothesis H12a is that the mean difference < 0.8

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