Posted: November 28th, 2022

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Part 1

- A researcher computes a one-way within-subjects ANOVA, thus:
- Which of the following is a source of variation that is measured using the one-way within-subjects ANOVA?
- A researcher observed the mating behavior of 10 porpoises in five different social conditions. What are the degrees of freedom between-groups for a one-way within-subjects ANOVA?
- A researcher measures the time it takes eight participants to complete three successive tasks. What are the degrees of freedom between-persons for a one-way within-subjects ANOVA?
- A researcher recorded the shooting percentage of 28 professional basketball players in each of four quarters in a game. What are the degrees of freedom error for a one-way within-subjects ANOVA?
- Which source of variation is computed using a one-way within-subjects ANOVA, but not a one-way between-subjects ANOVA?
- A one-way within-subjects ANOVA is typically associated with ______ power than the one-way between-subjects ANOVA.
- Which of the following is an assumption for the one-way within-subjects ANOVA, but not for the one-way between-subjects ANOVA?
- Which of the following post hoc tests can be used with the related samples t-test, following a significant the repeated-measures ANOVA?
- If the experimentwise alpha for three tests is .05, then what is the value reported in two decimal places for testwise alpha?
- If both the Greenhouse-Geisser and the Huynh-Feldt corrections lead to significant results we should

Part 2

Please use the data (Quiz 5B.RM ANOVA,sav) under Resources for Quizzes > Quiz 5 for this quiz. We will run the repeated-measures (RM) ANOVA step by step, solving problems while checking your understanding.

The procedure for the inferential statistical analyses is always same;

For Step 2, let’s set the criteria for a decision: we will use to evaluate significance of the statistical test. For Step 3, we need to evaluate assumptions. There are FOUR ASSUMPTIONS to be met to conduct an RM ANOVA. List them all to match with the description.

In the RM ANOVA, the assumptions for the third and the fourth in the list in **QUESTION 3 **are together called **______**. Satisfying this condition is very important because the violation of this assumption will artificially increase the value of between-groups variances and as a result, it will increase the likelihood to commit a **_____.**

To run the repeated-measures ANOVA, go to Analyze >> General Linear Model >> Repeated Measures…. When a new window shows up, you will see factor1 as a default for Within-Subject Factor Name. As we have one factor, type the factor name, SEASON, and then specify a number, 4, in Number of Levels and then click Add and then Define.

For Step 4, in the SPSS output, find the results from Tests of Within-Subjects Effects. As Mauchly’s test of Sphericity is significant and the epsilon is all smaller than ___, so we will use Greenhouse-Geisser’s correction for degrees of freedom. Therefore, we can describe the results as below. As usual, report the values in three decimal places.

As there are significant mean differences in depression across seasons, post hoc tests are necessary to determine which pair or pairs of group means significantly differ. Because we have 4 sets of repeated data or 4 groups, we need to make multiple pairwise comparisons using a post-hoc test to determine which mean or means are different significantly from the rest.

In the SPSS output, find the results from Estimates, Pairwise Comparisons, and Profile Plots. Which choice is the most appropriate statement about the results?

For a RM ANOVA, the two measures of effect sizes are partial eta-squared (η2p) and partial omega-squared (ω2p). Report partial eta-squared in the results from Tests of Within-Subjects Effects of the SPSS output. As usual, report the values in three decimal places.

As partial eta-squared (η2p) tends to overestimate effect size, we usually report partial omega-squared (ω2p), which is more conservative measure of effect size. To compute partial omega-squared, we need to identify the four values below in Tests of Within-Subjects Effects of the SPSS output and manually calculate the partial omega-squared (ω2p).

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