What should the null hypothesis be?

[Tyto alba]

Homework Statement

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)

Homework Equations

What should the Ho and H1 be?

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).

 

[vbrasic]

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.

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.

 

[Tyto alba]

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

 

[vbrasic]

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

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.

 

[Mark44]

Test the prediction that the antipsychotic drug is significantly more ffective in preventing relapse than placebo.

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

 

[vbrasic]

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

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

 

[Mark44]

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

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