# Sample size in equivalence trial?

#### merisslian

##### New Member
Hey all,

For my thesis I need to calculate the sample size for an equivalence trial with four groups (the score on four equivalent forms in order to prove they are indeed equivalent). The study is done before with only one of the four forms, they found a mean = 19.8, SD = 2.0, tolerance = 1SD. I use an ANOVA to see whether they're significantly different.

Unfortunately, all I can find is programs for two groups or formulas I don't understand like this http://www.mddionline.com/article/determining-sample-size-testing-equivalence and this http://www.biostat.uzh.ch/teaching/master/previous/methods2008-1/4a_Equivalence.pdf (slide 17)..

For example the following:

n=2((Z1-a+Z1-b/2)^2)/((Delta-SD)^2)

This doesn't help me a lot, as I have no clue how to get Z(1-a)..

Anyone who could help me please?
Thanks a lot!!

#### rogojel

##### TS Contributor
hi,
if you use R you might want to look at the daewr package which has a function FPower1 for sample sizes of one way ANOVA. Other SWs will have their own variants.

regards

#### rogojel

##### TS Contributor
I ran the function and assuming that the tolerance = 1SD is the smallest difference between the average of two groups where you will call them different the results look like this:

Code:
> power=Fpower1(alpha=0.05, nlev=4, nreps=2:25, Delta=2, sigma=2)
> power
alpha nlev nreps Delta sigma      power
[1,]  0.05    4     2     2     2 0.07785485
[2,]  0.05    4     3     2     2 0.11297917
[3,]  0.05    4     4     2     2 0.15072795
[4,]  0.05    4     5     2     2 0.19041991
[5,]  0.05    4     6     2     2 0.23147661
[6,]  0.05    4     7     2     2 0.27335307
[7,]  0.05    4     8     2     2 0.31554916
[8,]  0.05    4     9     2     2 0.35761767
[9,]  0.05    4    10     2     2 0.39916772
[10,]  0.05    4    11     2     2 0.43986506
[11,]  0.05    4    12     2     2 0.47943046
[12,]  0.05    4    13     2     2 0.51763677
[13,]  0.05    4    14     2     2 0.55430516
[14,]  0.05    4    15     2     2 0.58930083
[15,]  0.05    4    16     2     2 0.62252853
[16,]  0.05    4    17     2     2 0.65392793
[17,]  0.05    4    18     2     2 0.68346914
[18,]  0.05    4    19     2     2 0.71114838
[19,]  0.05    4    20     2     2 0.73698386
[20,]  0.05    4    21     2     2 0.76101206
[21,]  0.05    4    22     2     2 0.78328422
[22,]  0.05    4    23     2     2 0.80386327
[23,]  0.05    4    24     2     2 0.82282102
[24,]  0.05    4    25     2     2 0.84023576
So, you would need about 20-25 measurements per group to be reasonably sure you did not miss an effect that is important.

I hope this helps

#### merisslian

##### New Member
Thanks a lot, this is great! Just what I was looking for!