# Fisher's exact test and non-inferiority / equivalence

#### tim_k

##### New Member
I have some data (multiple choice question scores for two groups of medical students exposed to an experimental and standard type of anatomy teaching). It's ordinal data (scores out of 10). I'd like to test whether the experimental type of teaching is equivalent (i.e. not inferior) to the standard teaching type. An acceptable delta (error) would be one mark in the MCQ test.

Now I am not the greatest statistician in the world - I understand how to show superiority with Fisher as applied to contingency tables but really am not sure what I'm doing with equivalence. Do I do two one-tailed Fishers? Or one two-tailed but somehow altered to have a null hypothesis in which there IS a difference? I'd be really grateful if someone could give me concrete steps as to how to calculate this - I've googled it like crazy and only confused myself further.

Tim

#### Karabiner

##### TS Contributor
Why Fisher's exact test? Since you have ordinal data you normally
would use Mann-Whitney U-test to compare groups. Maybe the
scale could be treated as interval, which would make calculations
easier.

Regarding "equivalence testing", for me it appears that there are
a lot of decent introductory explainations on the web.

With kind regards

K.

#### tim_k

##### New Member
Thanks Karabiner. Based on your comments I've given the problem a great deal more thought / googling and have tried a few things in SAS and SPSS.

The data are interval and non-normally distributed. I want to show non-inferiority of the treatment. If the data were normally distributed, I'd perform the equivalence testing in SAS based on two one-sided t tests, and just take the p-value for the non-inferiority direction (delta being 1 point in the 10 point MCQ scores). I need a way of calculating a Wilcoxon / Mann-Whitney U equivalent to the TOST t-test. This can't be too exotic a requirement as many clinical trials with ordinal level outcome data would use this statistic. Does anyone know where I could find this, or at least a clear, step-by-step way of calculating it.

Please be kind with me, I'm only a dumb neurosurgeon!

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#### Karabiner

##### TS Contributor
If your sample size is large enough (> 50 or so), then you don't
need an U-test, t-test will perform well.
Please be kind with me, I'm only a dumb neurosurgeon!
I guess I wouldn't enter a neurosurgery forum
and ask for a step-by-step explanation
of how to perfom a minimal invasive
procedure for correcting lumbar hernias.

With kind regards

K.

#### tim_k

##### New Member
Yep, sample size is 80+ so I'll stick to the t-test. Thank you for your help, really - a straightforward solution wasn't available elsewhere.

"I guess I wouldn't enter a neurosurgery forum
and ask for a step-by-step explanation
of how to perfom a minimal invasive
procedure for correcting lumbar hernias."

Of course not. Neurosurgeons do brain and spine. For a lumbar hernia repair you'd
want to ask a general surgeon. But if you wanted to know about microdiscectomies, I can't think where else you'd post other than a neurosurgery forum (the orthopods may beg to differ), nor why you'd expect a frosty response.