Statistics with ANOVA

These questions relate to the article from the American Journal of Nursing posted to Blackboard: “Increasing the Safety-Promoting Behaviors of Abused Women”.

IMPORTANT NOTES

 “Expected Length of Answer” values are intended as GUIDELINES only. They represent the approximate length of my “solution” answer. No points will be deducted based on word counts.

 Please carefully read the note at the end of Question 1, and apply it to all remaining questions!

1. (6 points) The primary response variable for this study is the number of safety-promoting behaviors indicated by each participant out of a possible 15 behaviors (listed in the table on page 42). The authors will treat this variable as interval-ratio in using ANOVA methods. Do you agree with the assessment of this variable as representing interval-ratio data? Explain why or why not. Expected length of answer: 50-100 words.

PLEASE NOTE: For the remainder of this assignment, you should assume that we have decided to accept the treatment of this variable as interval-ratio and appropriately measured – whether or not you had misgivings about this when answering this first question. Please do NOT answer any of the questions 2-14 by arguing that the response isn’t interval-ratio, as that answer will not receive credit.

2. (6 points) In their description of the measurement instrument (number of safety-promoting behaviors) on page 43-44, the authors mention an adjustment to the measurement. What was the adjustment and why (from a statistical perspective) was the adjustment necessary? Expected length of answer: 50-100 words.

3. (6 points) Explain why it was necessary for this study to be approved by an Internal Review Board prior to the collection of data. Expected length of answer: 30-50 words.

4. (6 points) This study utilized repeated measures. Identify the repeated measures factor and explain the benefits that come from including that factor in our RM-ANOVA model. Expected length of answer: 50-100 words.

5. (6 points) In addition to the RM-factor, two other factors are being examined. Identify both of these factors as well as the levels associated with each factor. Expected length of answer: 30-50 words.

6. (4 points) How many observations were taken in this study? Expected length of answer: <20 words.

7. (10 points) The results of three significance tests are described in the bullet points on page 47. Briefly explain what these results represent and how they should be used to guide the rest of the analysis (be specific). Note: I am asking for YOUR analysis which may or may not be the same as the authors. Expected length of answer: 100-150 words.

8. (8 points) Based on information within the paper, I would guess that their Tukey “minimum significant difference” was around 1.00. Identify evidence from the paper that indicates the authors actually did performed pairwise-comparisons (which indirectly allowed me to make this reasonable guess at the MSD). Also indicate whether these comparisons examined main effects or interaction. Expected length of answer: 50-100 words.

9. (4 points) An interaction plot is shown on the top of page 48. There is something intentionally misleading about this plot. Identify this issue, explain why it is misleading, and indicate what should be done to correct the problem. Expected length of answer: <20 words.

PLEASE NOTE: While they did something slightly inappropriate here, the plot itself may still be interpreted like most interaction plots we have seen before – which we will do in problems 10-11. The answers to Questions 10 and 11 should NOT be addressing the issue identified in #9.

10. (12 points) Using my proposed Minimum Significance Value of 1.00 as factual, give a complete statistical interpretation of the interaction plot. Expected length of answer: 100-150 words.

11. (8 points) Consider the first paragraph of their discussion (page 48). They claim the intervention to be effective. Is this supported by the statistical analysis? Justify your answer completely. Expected length of answer: 50-100 words.

12. (8 points) What pairwise comparison adjustment was made by this study? Do you believe the appropriate method was chosen? Either make an argument in favor of the method they used or argue for another method of your choosing. Expected length of answer: 100-150 words.

13. (EC 2 points) There were 75 subjects in the intervention group and 74 subjects in the control group. How many degrees of freedom will remain for error in a model that contains the repeated measures component indicated in question 4 as well as the two factors (and their interaction) indicated in question 5? Expected answer: one number, with some reasonable justification as to how you arrived at it.

14. (EC 2 points) On page 43 in the “More on Methods” box, the authors mention having used analysis of covariance for part of their analysis. This is a fairly useful topic we will not have time to discuss in this class. Briefly explain what an analysis of covariance adds (over and above a regular ANOVA) and indicate why it was used in this particular study.