# 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 (*u*_{1}-*u*_{2} = 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 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

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

Input your data into an Excel spreadsheet.

Click and drag over the data to select it and then click on QI Macros Menu -> Statistical Tools -> f and t tests -> 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:

QI Macros t test two-sample macro will perform the calculations and interpret the results for you. The one-tailed p value of 0.028 < 0.05.

### Repeat the t-Test, but reverse the order of S1 and S2:

Copy column A to column C, then select B1:C13.

Click on QI Macros -> Statistical Tools -> f and t tests -> t test assuming equal variances.

Answer the prompts with the same values.

The one-tailed p-value of 0.004 < 0.05.

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.

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