A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The test was carried out with a power of 85%.  Assuming that this study was well designed and carried out properly, do you believe that there really is no significant difference in blood pressure?  Explain your answer.

 

Answer:

Explain:

This question is more of an interpretational question wherein we need to see or rather verify if there is any semblance of significance of the dataset given that it was observed that there was no significance as per test of hypothesis.

Now lets think,

what has occurred?

We have conducted a hypothesis testing on a sample of size 36. We found that there was no significance.

Clearly , this was a test of significance for type I error. (checking of null hypothesis).

However there is another way to check the same .

This is done through test of significance of alternate hypothesis assuming null hypothesis is not correct.

This is called as test for type II error..

Note that we are given with the power of the test.

The power of a binary hypothesis test is the probability that the test rejects the null hypothesis (H₀) when a specific alternative hypothesis (H₁) is true.

Mathematically we can describe it as:

power =Pr(Reject Ho | H₁ is true) (pr =probability)

In light of the definition of power and its value we can now say that,

There is a 85 % probability of rejecting the null hypothesis given that the alternate hypothesis which is opposite assumption of null hypothesis is true.

Conversely we can say that there is 15 % chance that the we should accept the null hypothesis given that the alternate hypothesis is true.

This is a significant value (>5% or 0.005)

Hence even if the type I error testing gives a result of no significance, the power test (type II error ) signifies otherwise.

Footnote: Most researchers assess the power of their tests using π (power of the test) = 0.80 as a standard for adequacy. This convention implies a four-to-one trade off between β-risk and α-risk. (β is the probability of a Type II error, and α is the probability of a Type I error; 0.2 and 0.05 are conventional values for β and α).