Statistics - Hypothesis Testing Projects

Part B: Proposed Research The researcher is working on a proposal to the Grant Foundation in order to

Part B: Proposed Research

The researcher is working on a proposal to the Grant Foundation in order to fund the experiment. To strengthen the proposal, the researcher wants to include some pilot data to show that the new "innovative" instructional method is superior to the old "traditional" method. The Foundation has a strict policy to not consider proposals which use the sign test. The researcher proposes a stratified design (like that mentioned in part A6) so that the data are matched-pairs. Prior to the experiment the researcher decides to use the Wilcoxon Matched-Pairs test using scores obtained with Instrument II.

The pilot study was implemented over a summer term in which there were 20 students participants. Recognizing that a small sample size will limit power, the researcher decides on an α of 0.10. The pilot study returned the following difference scores.

d = New Method Scores – Old Method Scores

8.2
-5.5
12.1
1.6
-3.4
5.5
10.0
-3.1
6.7
2.9

B1 Is the new method different than the old method? Conduct the Wilcoxon Matched-Pair Test.

Part C: The Main Experiment

Based on the results of the pilot study, and recognizing that the Foundation does not have ‘deep pockets,’ the researcher proposed a study involving 40 students using Instrument II. The Foundation has expressed an interest in more students receiving the new method than the old. Accommodating this means the data will no longer be matched-pairs. The Foundation recommends that 15 of the 40 students be randomly assigned to the "traditional" method and the rest to the "innovative" method. The scores are in the following table. As the researcher expects to be defending these results, an α of 0.05 is selected.

Old Method	New Method

53.0	74.4	75.2
27.2	92.3	90.7
75.1	77.6	76.6
23.9	72.0	50.4
73.4	93.1	60.7
26.3	83.4	81.2
57.4	66.5	92.5
54.8	87.3	56.9
77.4	46.4	76.5
47.1	63.9	53.4
24.5	83.4
24.2	75.2
68.5	82.6
56.7	75.9
52.1	81.5

C1 Is the new method better? Conduct the appropriate Wilcoxon Test.

Part D: Follow Up

Finally, after numerous publications demonstrating the efficacy of the new "innovative" method of statistics instruction, a larger Foundation funds research using the more accepted Instrument III. Since it is a costly instrument, they opt to keep the sample sizes as small as possible.

D1 Is the new method better than the old method? Assuming that the scores of Instrument III are normally distributed, conduct the appropriate test on the following data. State any assumptions you may have made.