Two One-Sided Test (TOST) in Excel

QI Macros Add-in Makes it Easy to Conduct a TOST Test in Excel

When to use a Two One-Sided Test for Equivalence

While measurements at different times or using different formulations can vary, it's often useful to determine if the two measurements produce equivalent results. Traditional hypothesis testing seeks to determine if means are the same or different, but it can have false positives. Equivalence testing determines an interval where the means can be considered equivalent.

The Two One-Sided 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.


Two One-Sided Test Excel Using QI Macros

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.

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

Conduct the Test

Now, conduct a test using S1 and S2 (in that order, E1:F13). Then copy sample 1 in column G:

two one-sided test data example

Run a t-Test Assuming Equal Variances of Sample 1 and 2

Now, select the data and click on QI Macros Menu -> Statistical Tools -> T test two sample Assuming Equal Variances:


QI Macros will prompt for a significance level (default = 0.05 or 0.95 depending on the order of S1 and S2) and hypothesized difference in the means(.8):

significance level prompt in QI Macros statistical software
hypothesized difference in means prompt in QI Macros statistical software

The t test two-sample assuming equal variances macro will perform the calculations and interpret the results for you (one-tailed p value, 0.028 < 0.05):

t test results example in QI Macros statistical software for excel

Repeat the t-Test, but reverse the order of S1 and S2 (F1:G13):


The one-tailed p-value, 0.004 < 0.05, so the means are different:

one tailed p value example in QI Macros software

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.

Learn More...

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