My research study compares the effectiveness of two different interventions to a control group, for a total of three groups. I would like my hypothesis to state both treatments will be equally effective. However, in my text, and the million hours I've spent on Google, it states that this would be a null hypothesis. That being said, I've also seen "no difference in treatments" hypothesized before. My question is, if my hypothesis is "equally effective"/"no difference in treatments", would my null hypothesis be "one interention is more effective than the other" or would I have 2 different null hypothesis that state each one is more effective than the other.

Either way, would this make a difference on whether or not I should choose a one-tailed or two-tailed test? If I have 2 different null hypothesis, each stating that one intervention is more effective (or better) than the other, wouldn't the standard advice be to use a one-tailed test because it's one directional? :confused:

My research study compares the effectiveness of two different interventions to a control group, for a total of three groups. I would like my hypothesis to state both treatments will be equally effective. However, in my text, and the million hours I've spent on Google, it states that this would be a null hypothesis. That being said, I've also seen "no difference in treatments" hypothesized before. My question is, if my hypothesis is "equally effective"/"no difference in treatments", would my null hypothesis be "one interention is more effective than the other" or would I have 2 different null hypothesis that state each one is more effective than the other.

Either way, would this make a difference on whether or not I should choose a one-tailed or two-tailed test? If I have 2 different null hypothesis, each stating that one intervention is more effective (or better) than the other, wouldn't the standard advice be to use a one-tailed test because it's one directional? :confused:

Hey stucky, just to clarify, I'm assuming that you're hypothesising that your two treatments will be equally effective - but both more effective than the control condition? (sort of a mix between a null hypothesis and a research hypothesis!)

Putting aside the better-than-control question, what it sounds like what you want to do is confirm a null hypothesis. This is actually absolutely alright - you don't need to reword the hypothesis in reverse or anything! BUT - confirming a null hypothesis requires MUCH higher statistical power than a usual study that tries to confirm an alternative hypothesis. This is because failing to find a stat sig difference could be both a result of no real difference OR insufficient power. Thus, lower statistical power increases the chance of Type 1 error, which is unacceptable, whereas the usual case of low power increasing the chance of Type 2 error is usually considered acceptable.

Jacob Cohen's written some great resources on the topic of confirming a null hypothesis... it actually isn't possible to show that there are exactly NO differences of course, but you can show, for instance, that the groups are no more than 10% of an SD apart (i.e. minimally different), or some other chosen level.

That makes a lot more sense, plus the higher statistical power needed and reasons behind this is probably why it wasn't mentioned in my primer text. I've heard of Cohen a couple of different times. I'll have to check it out.

Thank you so much for your feedback. It's much appreciated.

No worries at all :) Yep - the issue is often ignored, a lot of people think that a study showing no statistically significant differences is sufficient evidence that no differences exist, when this isn't really true at all! Jacob Cohen is great, I chuckle away merrily at his dry statistician's humour. A great start to his stuff is the link below (which also touches on your issue):

http://www.personal.kent.edu/~dfresco/CRM_Readings/Cohen_1990.pdf

I must say though, if the practicalities of our harsh world require it, a rather easier option would be to perform a lower-power study that might end up with a result something like this: "both treatment conditions were found to be more effective than control. Statistically significant differences were not found between the two treatment conditions, although this may have been the result of insufficient statistical power."

[This would just involve simple between-groups comparisons between the three groups with usual null-hypothesis testing methods: the fact that you'd rather like one of the null hypotheses not to be refuted wouldn't change the technique or terminology.]

Doing this, you won't have provided definitive evidence that the two treatments are equal, but you can show (hopefully) that they're both better than control, and perhaps not too different to each other in their effectiveness. It's the easy way out, but could be more practical than acquiring hundreds or thousands of participants in order to show decidedly that the treatment conditions are only minimally different in effectiveness.

Well, enough from me - good luck whichever way you go!