# R - what is magnitude of region of similarity (epsilon) when using tost() from equivalence package

I have two vectors:

library(equivalence)
a <- c(32, 18, 23,  4,  9, 19, 34, 22, 24, 26,  8, 10, 18)
b <- c(28, 32, 20, 10,  7, 31, 18, 25, 22, 28, 10,  9, 21)
tost(a, b, epsilon=5)


Now when I use tost() (from following library: http://cran.r-project.org/web/packages/equivalence/equivalence.pdf), what exactly does the epsilon=5 mean? Does it mean one of them can have mean $5\%$ higher of lower, or is it not $\%$ and is just $\pm5$?

I can't find anything concrete on that. Does it have another name?

• What package is that function from? How can we determine how it works if you don't even tell us what it is? – gung - Reinstate Monica Nov 10 '16 at 23:53
• Added additional information. It's from package equivalence (cran.r-project.org/web/packages/equivalence/equivalence.pdf) – Matjaz Muhic Nov 11 '16 at 11:25
• The other functions in that package seem to use standard deviation units for the margin. You can always look at the source code for a definitive answer of course. R is open source. – mdewey Nov 11 '16 at 14:30
• @mdewey that's true. :/ – Matjaz Muhic Nov 12 '16 at 22:38

I think it is a synonym to the equivalence margin. Because there is no exact equivalence it is a range of the similarity.

Here is a article which describes the Equivalence and Noninferiority Testing.

EDIT: For the hypothesis testing it is necessary to set a acceptable range of unequality. The deviation of the equal margin can be in positive and negative direction. So the 5 means it is 5% higher or lower. I am not sure about the edit, it would be nice if somebody verify this...

Thanks

• Can you give more details here rather than just a link? – mdewey Nov 8 '16 at 12:24

I was also wondering if an epsilon of 2 sets a margin of 2 above and 2 below or a margin of 1 above and 1 below for a total rang of 2. As I couldn't find the answer nor understand the R code I contacted directly the author of the package "equivalence", professor Robinson, who very kindly answered:

An epsilon of 2 sets margin for 2 above and 2 below.