# What should the null hypothesis be?

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1. Apr 4, 2017

### Tyto alba

1. The problem statement, all variables and given/known data

In a study of effecftiveness of an antipsychotic drug, patients are treated with the antipsychotic drug and were compared to those receiving a placebo.
In terms of the number relapsing, 698 of 1068 patients were released after taking the placebo while 639 out of 2,127 relapsed after taking the antipsychotic drug,
Test the prediction that the antipsychotic drug is significantly more ffective in preventing relapse than placebo.(Have to apply Chi-square)

2. Relevant equations

What should the Ho and H1 be?

3. The attempt at a solution

As I know, the Ho should be that the observed data follows some theoretical model and any deviation(which will almost always be) is due to chance. But here since we have no theoretical model to compare our data with I have thought in this way:

Since H1 is often the hypothesis that the scientist is trying to prove and the Null could be set as what might be needed to disprove1?

So,

Ho= The effect of antipsychotic drug and the placebo is the same, any deviation/difference is due to chance.
Ha= The effect of antipsychotic drug and the placebo is not the same and the drug is significantly more effective.

1 This is what I presume, tell me if it isn't right (ideally with citation).

2. Apr 4, 2017

### vbrasic

Note that these two possibilities do not encompass all possible outcomes. The null hypothesis, $H_0$, you've proposed is $E_{drug}=E_{placebo}$, where $E$ is simply the efficacy of the drug/placebo, while your alternative hypothesis, $H_a$ states, $E_{drug}>E_{placebo}$. What about if the drug is less effective? You haven't accounted for that possibility within your hypotheses.

3. Apr 4, 2017

### Tyto alba

Should this be a two-tailed test? Is there an authentic source online to learn it?

4. Apr 4, 2017

### vbrasic

A two-tailed test is of the form $\mu\neq\mu_0$. That is, you want to test whether or not the mean efficacy of the placebo is greater than or less than the mean efficacy of the placebo. In your case however, you only care if the drug performs better than the placebo (not worse).

I recommend reading this. It's a webpage from a chemistry course taught at the University of Toronto.

5. Apr 4, 2017

### Staff: Mentor

I disagree with vrbasic's recommendation. Based on what I quoted, the null hypothesis should be H0: Effdrug ≤ Effplacebo and the alternate hypothesis, Ha should be Ha: Effdrug > Effplacebo. This would be a one-tailed test.

6. Apr 4, 2017

### vbrasic

That is precisely what I was suggesting... I don't think it should be two-tailed. Sorry for any miscommunication.

7. Apr 4, 2017

### Staff: Mentor

Sorry, what you wrote was clear enough -- I simply misunderstood it.