# TOST equivalence test in excel

I had a prof once refer to doing science in excel as doing watch repair with oven mitts. Nevertheless, I'm trying...

I'm trying to do a TOST test using excel. I'm basing the equivalence of variances on the excel F-test. If I run both t-tests with a hypothesized mean difference of $$+\Delta$$ and then $$-\Delta$$, with $$\alpha$$ = 0.05, is my final, combined $$\alpha$$ 0.10?

To elaborate: I made three measurements before and after an event. I hope to claim statistically that the event had no effect. I have a measurement uncertainty (0.14) for each measurement, and six values (5.7, 5.8, 5.5 before; 5.6, 5.4, 5.6 after). Because 0.1 is my measurement uncertainty, I thought that it would be a reasonable choice for $$\Delta$$.

For the excel t-test calculator, I provide the values, an anticipated difference in mean (0.14) and $$\alpha$$, and run the calculator twice with the before and after swapped (because excel won't take a negative anticipated difference). I get two t-stats to which to compare to the t critical one tail value. One of these t Stats is -2.47 which is less than -2.13, the t Critical one tail. Is this sufficient to claim equivalence per TOST? What is my final $$\alpha$$ if I ran both of these t-tests with $$\alpha$$=0.05?

• FWIW, note that TOST stands for "Two One-Sided T-tests". Since there is an Excel function for a t-test, you can do this yourself pretty easily. – gung - Reinstate Monica Jun 13 '19 at 19:59
• thanks for the quick response. If I'm understanding correctly (and borrowing heavily from the cross validated page on TOST), I run t-tests in excel hypothesizing a difference of +/- delta, where delta is my chosen limit in the same unit as the mean, I get a t stat to which I can compare to the 't critical one-tail'. I'm not sure I follow the description of alpha: if I run both of these tests with alpha = 0.05, is my overall alpha 0.1? – Nick Jun 13 '19 at 20:19
• I added more info, above. I also found this page, if anyone follows this thread looking for the same thing: daniellakens.blogspot.com/2016/12/… (it says R, but it has an excel spreadsheet, as well). – Nick Jun 13 '19 at 21:55
• Nick, your overall $\alpha$ does not sum the $\alpha$s of these two tests because their $H_{0}$s are non-intersecting. – Alexis Nov 27 '19 at 6:39