question about null hypothesis??

here is my question:
in my minor thesis, based on my theoretical framework, i have a hypothesis that stated that: "the score of group A is the same as group B".
so if that was my alternative hypothesis? what would be my null hypothesis?
would my Ho be: "the score of group A is not the same as group B"? or should i say "different" or "there's difference between.." instead?

is that okay to state " not the same as..", "different" in Ho?
cos I usually see "different" in alternative hypothesis.

i'm pretty confused right now
thank u very much for your help :)
No. You can't have "is not the same as" or "different" as your null hypothesis. It sounds like what you really want to do is "equivalence testing". This looks to be a decent explanation of why you don't want to do "standard" significance testing and a brief explanation of equivalence testing:
if i cant have "is not the same as" or "different" as my null hypothesis, so what should my null hypothesis be like?
in my minor thesis, I compared the score of episodic memory between deaf and normal children.
my data distribution is not normal, so i used mann-whitney to compare, and it means I used median instead of mean.
there was no significant difference between the 2 groups (median score of deaf group=8; median score of normal group=9;p=0,256)
but from what i've read in your link, if i accept my hypothesis (deaf group score is the same as normal group score) based on that significance test, my conclusion is invalid.

it said i your link there's way to ask about equivalence and express the results as p value, but it's complicated. or it said that I could use CI.
but I didnt see any confidence interval in mann-whitney test.

so do u know, what test should I use? and u should know beforehand that I'm no expert and I cant understand a really difficult statistical things.
thank u so much for ur help :)


TS Contributor
Your sample size is much too small for equivalence testing.
To support the hypothesis that 2 populations differ only to a
neglible or practically unimportant degree requires large

Even if you would consider a medium (0.5 standard deviations)
difference between the two populations as equivalent, and
would also accept an extremely low statistical power (50%),
you would still need a sample size of about n=90.

Kind regards

dear karabiner,
so what should I do?
how about I make my hypothesis -> null hypothesis,
and because the mann-whitney test showed that there was no significant difference between the 2 groups,
i would say that I rejected my alternative hypothesis, and accept my null hypothesis (the score is the same).
is that ok? really, I couldn't think of anything else.
thank u for your help sir


Ambassador to the humans
The problem is that just because you fail to reject the null hypothesis doesn't mean you have evidence that the null hypothesis is true.

Ho: I did not just stick my tongue out at you
Ha: I just stuck my tongue out at you

You have no evidence to reject the null hypothesis here but it was true. Do you see the problem with saying that the null is true just because you didn't reject it?
dear dason,
yeah, I see.
but you said that I should do equivalence testing, and then karabiner said I couldnt do it because my sample size is too small (it's true, there's only 15 subjects per group). so I dont have any other options.
do you have any suggestions?
thank you sir!


TS Contributor
As usual in this forum (funny enough, as it's one of the most improtant informations),
you didn't mention your sample size in the beginning, so the impossibility of proper
equivalence testing was revealed only by your second posting. The size of your study
is simply much too small for making strong inferences about deaf and non-deaf children
in general. What you can do, you can report your results and note hat your study was
underpowered (had only small chances to detect differences, and no chances to reliably
support the assumption of equivalence), whatever the reason for that was.

Kind regards