Question

Dr. Kovaleski is interested in examining whether quantity of sleep impacts problem solving ability. To test problem solving ability, the research team gave participants a puzzle and measured how long it took participants to solve the puzzle in minutes. A group of participants were instructed to sleep 5 hours and then solve the puzzle in the morning. Then the same participants were instructed to sleep 7 hours and then solve a different puzzle in the morning. Then, participants were asked to sleep 9 hours and then solved a third puzzle in the morning.

5 hours	7 hours	9 hours
6	4	6
8	3	1
9	5	3
6	6	6
5	2	1

Answer the following questions and compute the Repeated Measures One Way ANOVA for the data provided above. For this example, assume that alpha is 0.05.

1. What is the Independent Variable? What are the levels of the IV?
2. What is the dependent variable?
3. What are potential confounds and internal validity threats in this design, if any?
4. Given this data, what is your calculated F-value?
5. Given this data, what is your critical value?
6. Given this data, do you need to calculate an effect size? If so, what is the effect size?
7. Given this data, do you need to calculate any Post-hoc tests? If so, which comparisons are significant?

Answer 1

Note: I have used SPSS statistical software, for all the necessary computations

For our given design of experiment, we have

1. Independent Variable: Problem Solving Ability

2. Dependent Variable: Hours of Sleep

3. There can be a lot of potential confounders and threats in this design such as economic status, age, residential area, current educational attainment, access to outside help, e.t.c

4. The calculated F Value:

Within Subjects: 5.352

Between Subjects: 58.616

We can observe the same from the following table:

5. Critical Value :

Within Subjects: 0.082

Between Subjects: 0.002

6. Effect size is defined as a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity. An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population. In that way, effect sizes complement inferential statistics such as p-values. Among other uses, effect size measures play an important role in meta-analysis studies that summarize findings from a specific area of research, and in statistical power analyses. Finally, The larger the effect size the stronger the relationship between two variables. You can look at the effect size when comparing any two groups to see how substantially different they are.

For our given dataset, we have effect size as:

Within Subjects: 0.082

Between Subjects: 0.002

7. Post-Hoc tests are used to tell us which group means are significantly different from other group means. For this design, we have.:

From the above table, we can observe that there is not much difference between the 2nd(7 hours) and 3rd(9 Hours) group statistically. Hence a posthoc analysis for this case would be appropriate.

However, the comparison between the 1st (5 hours ) and 2nd (7 hours) groups are significant statistically,

Finally, we can visualize our entire design as :

Thank You !