Question

A review board is evaluating a new drug that might improve a person’s mood. Their hypotheses look like:                    

                                             H₀: The drug does not improve mood

H_a: The drug does improve mood

Why aren’t the hypotheses set up in reverse, with the null being that the drug reduces anxiety?

Answer 1

In testing of hypothesis we test H0 against Ha.

α ( Type I error ) = P(Reject H0 | When H0 is True)

β (Type II error ) = P(Accepting H0 | When H0 is false)

We have to minimise Type I error and Type II error. But, we can't minimise both simultaneously. Thus, we fix β (Type II error ) and try to minimise α ( Type I error ).

For that β (Type II error ) should be less riskier.

In given example,

A review board is evaluating a new drug that might improve a person’s mood. Their hypotheses look like:

H0: The drug does not improve mood

Ha: The drug does improve mood

Here,

β (Type II error ) = P(Accepting H0 | When H0 is false)

  = P(We conclude that the drug does not improve mood given that drug improve mood)

i.e. If drug improve mood but still we accept H0 means, we conclude that drug does not improve mood. Thus we won't use drug. Thus risk is less.

But, If we reverse H0 and Ha means,

H0 : The drug does improve mood (or the drug reduces anxiety)

Ha : The drug does not improve mood (or drug does not reduce anxiety)

Here,

β (Type II error ) = P(Accepting H0 | When H0 is false)

  = P(We conclude that the drug improve mood given that drug does not improve mood)

  = P(We conclude that the drug reduce anxiety given that drug does not reduce anxiety)

i.e. If drug does not improve mood, but still we use it for improving mood since, we accept H0.

i.e. Drug does not reduce anxiety , But still we use it for reducing anxiety. This could be hazardous to human health or it has negative impact or it does't help at all to reduce anxiety.

Thus, we can't use this reversed hypothesis.