# Stats help - please!

#### HGHG

##### New Member
Hi all,

I am writing a project proposal: randomized, placebo-controlled crossover trial, I will be investigating treatment vs air. Participants will be asked to inhale the treatment or high-flow air (placebo). In this case, would a one-tailed test or a two-tailed test be more appropriate? Furthermore, the primary endpoint will be the time to onset of pain relief - which would be the best statistical tests?

My statistical competency is not so great. I, therefore, appreciate the help and do let me know if more info is required.

Thank you in advance.

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#### obh

##### Well-Known Member
What is your alternative hypothesis (H1)?
I would assume that you expect the treatment to reduce the "time to onset of pain relief"?

#### HGHG

##### New Member
That's correct, I expect treatment to render a reduced time to onset of pain relief compared to placebo.

Thank you.

#### obh

##### Well-Known Member
So this is only one direction, meaning one tail.
If H1 will be that the treatment changes the time (for good or for bad) you would choose the two tails, but this Is not the case.

What is the sample size?
Does the time distribution is normal? symetrical?

#### HGHG

##### New Member
Great. Through some learning of mine, I have seen that one tail may be questionable for some research, is this correct?

I am yet to work out the sample size, I was hoping to do this once I know what tests and tail to go ahead with.
Yes, the time distribution is normal.

Thanks again,

#### Karabiner

##### TS Contributor
Do not use a one-tailed test if a result in the unexpected direction could be of theoretical and/or practical interest.
I.e. there are only very rare situations in which one-tailed tests are justified. Yours is none of them, AFAICS.

I doubt a little bit that time-to-onset is normally distributed (in each group, by the way), since "time" has a
natural zero point and is notoriously right skewed. But anyway, perhaps time to onset could be analysed
using a survival analysis method, e.g. Cox regression.

With kind regards

Karabiner

#### HGHG

##### New Member
Do not use a one-tailed test if a result in the unexpected direction could be of theoretical and/or practical interest.
I.e. there are only very rare situations in which one-tailed tests are justified. Yours is none of them, AFAICS.

With kind regards

Karabiner
Dear Karabiner,

In the case of my question, do you then advise using a two-tailed test? Thank you for help!

#### obh

##### Well-Known Member
The difference between one tail and two tails is big, as in one tail the significance level is only on one side of the distribution. so it likes a two-tail with a double significance level.

If you are clueless about how the treatment will influence you should use the two tails.
But if you have the prior knowledge that the treatment won't increase the time to pain relief, and the only two options ares that the treatment will reduce the time or that it won't influence the time, I believe you should use the one tail.

It is correct that the default distribution for time may not be normal, and that the distribution is blocked by zero from the left.
But if the standard deviation is small relative to the average it may still be similar to normal.
For example, if the pain relief time is between 40 min to 60 min the zero-edge will not influence dramatically. and if you are interested in the average statistic, the CLT will do the job.

I assume the distribution of "onset of pain relief" depends on two random variables: the absorption rate, and the personal sensitivity to the medicine.
So I don't really know the distribution, please let us know your finding ...

#### hlsmith

##### Less is more. Stay pure. Stay poor.
@obh you make good points, but if the placebo really does not have an effect - I would imagine their times could be crazy long for a few people. I would also second the use of two-tailed approaches. It is the standard cautious approach.

Will subjects be blinded to treatment? The order of the treatments may need to be controlled for in the model, if subjects don't sustain timely alleviation of pain during first treatment - they could be tipped off to expect better results by the second treatment. Also, will both treatments be provided the same day or will time elapse between treatments?

#### obh

##### Well-Known Member
Hi @hlsmith

It probably won't be normal... at least the placebo treatment. I thought only of the treatment.
But the best way is to look at your data ...

Correct if you are not sure, it is better to be cautious and use the two-tailed approach.
If you compare two drugs A and B and you try to prove that drug B is better, there is always the risk that drug B is worse. So I believe in this case it is better to use the two-tailed approach. (although some think otherwise, depend if you care on not for the other direction)

In this case, it seems that you compare treatment to no treatment. So if you have any suspicion that the treatment may do the opposite job, delay the pain relief, you should use the two-tailed approach. But if you know for sure that the treatment may not delay the pain relief, it seems to me right to use the one tail, or do you believe that we should delete the one tail approach from all the statistics books ...?
(not talking about some tests that have only one tail option)

#### hlsmith

##### Less is more. Stay pure. Stay poor.
If you think about it, what we are talking about here is a superior test and if you go to the web and search images of superior test they all typically have two-tails and potentially a threshold for significance as well.

#### obh

##### Well-Known Member
I assume you relate to the first example I wrote ( compare two drugs A and B)
In this case, drug B might be better than A, or worse. So clearly you should use the two-tailed approach.

But in the current example, as I understand the question, I assume that the treatment might only improve the pain but won't do the opposite.
Of course, if my assumption is not correct then it should be the two-tailed approach.