Holm’s test Hypothesis Testing

Name

Affiliation

Holm’s test Hypothesis Testing

Holm’s test is a stepwise method, also called a sequential rejection method, because it examines each hypothesis in an ordered sequence, and the decision to accept or reject the null depends on the results of the previous hypothesis tests. The Holm’s test is less conservative than the Bonferroni correction, and is therefore more powerful. The Holm’s test uses a stepwise procedure to examine the ordered set of null hypotheses, beginning with the smallest P value, and continuing until it fails to reject a null hypothesis.

Holm’s test.

Suppose we have k = 3 t-tests.

Assume target alpha(T)= 0.05.

Unadjusted p-values are

p1 = 0.001

p2 = 0.013

p3 = 0.074

For the jth test, calculate alpha(j) = alpha(T)/(k – j +1)

For test j = 1,

alpha(j) = alpha(T)/(k – j +1)

= 0.05/(3 – 1 + 1)

= 0.05 / 3

= 0.0167

For test j=1, the observed p1 = 0.001 is less than alpha(j) = 0.0167, so we reject the null hypothesis.

For test j = 2,

alpha(j) = alpha(T)/(k – j +1)

= 0.05/(3 – 2 + 1)

= 0.05 / 2

= 0.025

For test j=2, the observed p2 = 0.013 is less than alpha(j) = 0.025, so we reject the null hypothesis.

For test j = 3,

alpha(j) = alpha(T)/(k – j +1)

= 0.05/(3 – 3 + 1)

= 0.05 / 1

= 0.05

For test j=3, the observed p2 = 0.074 is greater than alpha(j) = 0.05, so we do not reject the null hypothesis.

Recall that the Family-wise error rate (FWER) is the probability that we will get at least one false positive result, P(at least one false positive result).

This shows the null hypothesis was accepted and that career path taking in marketing as an IT professional is the best way to the success of business. The H1 hypothesis was rejected in this case.