Problem Set 4.1: Critical Value

***This was my answer, and my professor said: Be sure to accurately address how k is related to power to complete you response.

Criterion: Explain the relationship between k and power based on calculated k values.

Instructions: Read the following and answer the questions.

Work through the following and write down what you see in the F-table. This will help familiarize you with the table.

The F-table: The degrees of freedom for the numerator (k 1) are across the columns; the degrees of freedom for the denominator (N k) are across the rows in the table. A separate table is included for a .05 and .01 level of significance.

Increasing the levels of the independent variable (k):

Suppose we have a sample size of 24 participants (N = 24). Record the critical values given the following values for k:

.05 .01

k = 2 4.3 7.95

k = 4 3.10 4.94

k = 6 2.77 4.25

k = 8 2.66 4.03

As k increases (from 1 to 8), does the critical value increase or decrease? Based on your answer, explain how k is related to power.

As k increases the critical value decreases. Decreased critical value means the accuracy of the test is also decreased. The implication would be that k is in inverse proportion to the accuracy or power.