Situation A
Jefferson methods, State College has received a grant to compare the effectiveness of innovating teaching methods audio tutorial and computer based using a third group taught through a traditional lecture based technique as a control group. All three groups are composed of randomly selected biology students enrolled in BIO 187L. At the end of the semester, all students will be given Form the B of the Test of Biological Concepts which consists semester, of 250 all multiple-choice items covering the general content of the course.
1. Select and justify your choice of a statistical procedure to test the hypothesis that "there will be no significant differences among the means of the three groups on the test at the end of the course."
2. Investigate "post hoc" or multiple comparisons. Determine under what conditions they have application to the above null hypothesis.
3. If the assumption of random selection equating the three groups for pre-existing knowledge of the discipline is not tenable, determine an alternative strategy to be used including the selection of statistical procedure.

Situation B
The president of Jefferson State College is concerned over the professional environment that exists for the faculty members. In a maturing institution with a maturing faculty, he is seeking new approaches that may stem the tide of "faculty burn-out." In her search she has become interested in exploring the relationship between "burn-out" and tenure status. All professors are either tenured or non-tenured. A newly published faculty inventory can be administered which anonymously identifies each faculty member as "high", "moderate", or "low" in terms of burn-out behavioral characteristics.
1. Select and justify your choice of statistical procedure to test the hypothesis that "there is no relationship between tenure status and burn-out rating."
2. Oops ! Just before you conducted the study, the president found another measure of "burn-out" based on a series of true/false questions which rates the extent of "burn-out" on an interval scale of 0-100. How would this alter the statistical procedure and what alternative would you use?

Situation C
The US Olympic Committee is trying to determine the most effective training methods to be used in training long distance runners. long The two methods are Method A, distance training on alternate days with sprint work on "off" days, or, Method B, long distance training on alternate days with swimming on "off" days. One hundred distance runners from across the nation are assigned at random to carefully controlled plans: Fifty using Method A, fifty using Method B. In August, all 100 runners were assembled in Atlanta for a 10,000-meter race. As: a result of the race, each runner was assigned a rank from 1st to 100th.

1. What statistical procedure could be used to test the hypothesis of no significant statistical difference between the ranks of runners trained through Method A and those trained through Method B? [Hint: Consider the application of non-parametric tests].
2. Suppose that rather than rank the 100 runners on the basis of position of finishing the race, the elapse times for each runner was determined and the mean elapsed time for Method A was compared with the mean elapsed time for Method B. What statistical procedure would be used to make this comparison? What are the advantages and disadvantages of using elapsed times as opposed to ranks?

Situation D
In an experimental design to compare two different instructional modalities in teaching memorization techniques, random sampling was not possible based on practical constraints. In order to compensate for a possible mental ability bias, matched pairs of subjects were selected on the basis of an IQ test administered prior to the treatment. The dependent variable is measured on an interval scale.
1. A t-test may be used to test the equality of means of the two different group's performance on dependent variable measure. Should this t-test of means be an independent or a dependent correlated test? Explain why.
2. Could a subject be its own match in a matched pair design? For example, in Situation D, assume there is no carry-over or practice effect of the two memorization techniques. A random sample is selected and each subject is trained in the use of one technique and is tested. Later each subject is trained in the use of the second technique and is tested using the same or parallel measure. Should the test of differences or means on the dependent variable for each technique use and independent or dependent correlated t-test? How does the design affect the internal validity?

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The relevant test for this test is one way ANOVA, because the test is about more than 2 groups, and we’re testing the hypothesis that all 3 methods are the same, against the alternative that there’s a significant difference between at least one pair of these methods (methods A and B, methods A and C or methods B and C).
In this case we should use a relevant non-parametric...

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