Suppose you devised a training program to raise student scores on a standardized test, such as ACT, or AIMS (like in Arizona). You first administer the test to a random sample of students, record their scores, administer the training to these students, and then administer the test a second time to each of the same students. For each student you record their score for the second test. (I am deliberately leaving out additional parameters, as you will see why in item b)
a. What would the null and alternate hypothesis be?
b. Assuming there was an increase in scores, do you think that only the training method was responsible? What other factors could explain the changes?
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a. The null hypothesis would be that there is no significant difference in scores between the pre-training and post-training tests. The alternate hypothesis would be that there is a significant increase in scores after the training program.
b. Assuming there was an increase in scores, it is not guaranteed that only the training method was responsible. There could be other factors that could explain the changes in scores. Some possible factors could include:
1. Practice effect: The students could have become familiar with the test format and content through the first administration, leading to improved scores on the second administration simply due to the effect of practice.
2. Test difficulty: The second administration of the test could have been easier compared to the first administration, which would naturally result in higher scores.
3. Random variation: There could be random variation in individual student performance, which could affect their scores on the second administration.
4. Motivation and effort: The students might have been more motivated or put in more effort during the second administration, leading to higher scores.
To account for these additional factors and properly attribute any score changes to the training program, it is important to include a control group that does not receive the training. This allows for comparison between the experimental group (students who received the training) and the control group (students who did not receive the training) to determine the true effect of the training program.