Question

What is always true of the familywise error​ rate? Choose the correct answer below. A. It is larger than the significance level for any one of the individual tests. B. It is dependent on the sample size. C. It is smaller than the significance level for any one of the individual tests. D. It is the same as the significance level for any one of the individual tests.

Answer 1

A.

Explanation:

Let's make a short definition to clarify the answer:

The FWER (Familywise Error Rate) is understood as that probability of making erroneous discoveries or how multiple hypothesis tests are understood: Type I errors.

Basically the formula tells us that:

`FWER\leq 1-(1-\alpha_(\pi))^(k)`

Where:

`c` = number of comparision

and

`\alpha_(\pi)` = 'Error for individual tests'

In this way it is directly intuited that when making comparisons the number of the rate increases considerably (This due to the exponent k)

With one comparison, our probability of getting a false significant result in the long run is 5%, and our probability of getting a nonsignificant result is 95% (1 - .05) ^ 1.

If there is no real effect and we make ten independent comparisons, the probability of obtaining at least one erroneous result increases to 40%. With 13 independent comparisons, it is 50%, and with 20 comparisons, it is 64%. That is a high probability of finding a significant result that could be pure noise.

As you can see, the result increases independently of the sample size, and will always be greater than making a single comparison. Never less than or equal.