# 9.8 In a study of 10 new producers of iron supplements, nine contrasts in the mean iron level in the supplements were constructed by the quality control department for comparing various characteristics of the producers.a. In order to achieve an experimentwise error rate of .05, what value should be selected for the value of aI?b. What is the critical value for the F statistic for testing the nine contrasts if there were six samples of the supplement taken from each of the 10 producers?

Question

9.8

In a study of 10 new producers of iron supplements, nine contrasts in the mean iron level in the supplements were constructed by the quality control department for comparing various characteristics of the producers.

a. In order to achieve an experimentwise error rate of .05, what value should be selected for the value of aI?

b. What is the critical value for the F statistic for testing the nine contrasts if there were six samples of the supplement taken from each of the 10 producers?

check_circle

Step 1

Part (a):

The experiment-wise error rate is the probability of committing one or more Type I error, while making several comparisons in an experiment.

Suppose an experiment is performed with j contrasts, with αe denoting the experiment-wise error rate. If α1 denotes the comparison-wise error rate, then the relationship between the two error rates is αe = 1– (1 – α1)j.

In case the contrasts are independent of each other (orthogonal), the above relationship holds. In case the contrasts are not independent, αe ≤ 1– (1 – α1)j.

In this case, j = 9, αe = 0.05. Thus, the value of α1 is calculated as follows:

Step 2

Part (b):

The F-statistic is used here for pairwise comparisons. Thus, the numerator degrees of freedom would always be 1.

If there are k treatments each with n observations, then the denominator degrees of freedom of the F-statistic is (nkk).

Now, 6 samples are taken from each of 10 producers. Thus, total sample size is nk = 60. Here, k = 10. Thus, the denominator degrees of freedom is 60 – 10 = 50.

The level of significance for the critical ...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Statistics 