A two-factor ANOVA: the null hypotheses, interpretation, and assumptions A fourt

Question

A two-factor ANOVA: the null hypotheses, interpretation, and assumptions A fourth-grade teacher suspects that the time he administers a test, and what sort of snack his students have before the test, affects their performance. To test his theory, he assigns 90 fourth-grade students to one of three groups. One group gets candy (gummy bears) for their 9: 55 AM snack. Another group gets a high-protein snack (tofu) for their 9: 55 AM snack. The third group does not get a 9: 55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10: 00 AM (right after snack), 11: 00 AM (an hour after snack), and 12: 00 PM (right before lunch). Suppose that the teacher uses a two-factor, independent-measures ANOVA to analyze these data. Without post hoc tests, which of the following questions can be answered by this analysis? Check all that apply. Do students who are tested at 12: 00 PM score lower than students who are tested at 10: 00 AM? Do students who eat a candy snack score higher than students who have a protein snack? Does the effect of the type of snack depend on the timing of the test? Does the type of snack (or lack of snack) affect student performance on the test? In the following table are the mean test scores for each of these nine different combinations of snack type and test timing. The following graph shows the mean test scores for the treatment conditions. Use this graph and the data matrix to answer the following questions. Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. mu_10: 00 AM = mu_11: 00 AM = mu_12: 00 PM mu_candy = mu_protein = mu_no snack There is no interaction between the type of snack and the time of test Which of the following statements must the teacher assume in order to believe that the results of his two-factor ANOVA are valid? Check all that apply. The populations defined by the nine treatment conditions have equal means regardless of snack type or test time. The test scores within each of the nine samples (one for each treatment condition) are independent. The populations defined by the nine treatment conditions have different variances depending on type of snack and test time. The populations defined by the nine treatment conditions are normally distributed.

Explanation / Answer

Ans: Part I>> a c d

Part II>>a c

Part III>>a b d

n.b Two-way ANOVAs are also called factorial ANOVA. Factorial ANOVAs can be balanced (have the same number of participants in each group) or unbalanced (having different number of participants in each group). Not having equal size groups can make it appear that there is an effect when this may not be the case. There are several procedures a researcher can do in order to solve this problem:

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