## Question

Part I

A NP researcher randomly sampled 100 women aged 50-65 years and measured their minutes of exercise in the past week, BMI, and depression. Depression was measured using a Likert type scale consisting of 20 items. The summation score ranged from 20 to 100 and the higher the score, the higher the level of depression. The Pearson correlation coefficients (r’s) are summarized in the following table. For the analyses, the significance level was set at 0.05

(α = 0.05).

Table 1: Correlation among minutes of exercise, BMI and depression

Exercise in past week (minutes) BMI

BMI -0.25

Depression score -0.33* 0.12

*p < 0.05

1. Write a

a. research and

b. null hypotheses regarding the relationship between exercise and depression.

2. Based on the test statistics in table 1, what is your conclusion regarding your research hypothesis? (Hint: discuss both the magnitude and direction of the relationship).

3. What proportion of variance is shared by minutes of exercise and depression among women 50-65 years of age?

4. For the relationship between minutes of exercise and BMI,

a. what was the estimated power of the statistical test? (Using the power table on page 202, table 9.1, Polit 2010).

b. What was the risk that a type II error was committed?

5. If -0.25 is a good estimation of population correction, what sample size would be needed to achieve power of 0.80 at a significance α=0.05?

PART II.

Using the “Data”, file

a). select two variables with nominal or ordinal level measurements, and perform the descriptive statistics (frequency and percentage). [Please select only dichotomous variables from the following list: poverty, smoker, PoorHealth].

b). perform the bi-variate descriptive statistics using crosstabulation.

c). Hand calculate the ARs, ARR, RR, and OR. Show all your calculations.

d). Perform a chi-square analysis.

e). Using APA format, write a full report with the following sections:

1. Introduction: Describe your research question and hypothesis. Include the variables, measurement levels, the bivariate research question, and the hypothesis [for example, the event of adverse risk (using your variable name here, for instance, alcohol usage) will be higher/or lower in the risk exposed group (i.e., marijuana use) compare to the non-exposed group (non-users of marijuana)].

2. Method: Include the sample description (sample size, eligibility criteria) and statistical methods used for data analysis. (The sample information can be found in “Polit Dataset Description” in SPSS Data Sets folder).

3. Results: Include frequencies and percentages for the two variables, crosstabulation results, risk indexes (ARs, ARR, RR, and OR), and chi-square test results. Include a summary table for the results and write your interpretation. (Attach SPSS outputs).

4. Discussion: Write a report including summary and interpretation of the findings reported in the previous sections relative to the research questions you posed in your introduction.

Part III

Run a one-way ANOVA using the dataset “Data”. The Dataset contains 462 cases from the original PolitDatasetA. Two variables will be used for this analysis: Satisfaction and Houseproblem.

The variable Houseproblem is created using the variable housprob, a summary index of eight variables about current housing problems for the women in this sample—for example, whether or not they had their utilities cut off, had vermin in the household, had unreliable hear, and so forth. The variable housprob is a count of the total number of times the women said “yes” to these eight questions. The variable housprob is recoded into Houseproblem based on number of housing problems. The coding for Houseproblem is: 1=no housing problems, 2=one housing problem, and 3= two or more housing problems.

Satisfaction measures the overall satisfaction with material sell-being. This variable is a summated rating scale variable for women’s responses to their degree of satisfaction with four aspects of their material sell-being—their housing, food, furniture, and clothing for themselves and their children. Each item was coded from 1 (very dissatisfied) to 4 (very satisfied), so the overall score for the four items could range from a low of 4 (4 X 1) to 16 (4 X 4). Higher score indicates greater satisfaction. This scale has an internal consistency Cronbach’s alpha of 0.90. The content validity and construct validity have been established in previous research.

For this analysis, use the variable Houseproblem as the independent (group) variable and variable Satisfaction as the outcome variable. To run the one-way ANOVA, click Analyze → Compare Means → Oneway. In the opening dialogue box, move Satisfaction into the Dependent List and Houseproblem into the slot for Factor. Click the Options pushbutton, and click Descriptives and Homogeneity of Variance, then continue. Next, click the Post Hoc pushbutton and select LSD. Click continue, then OK, and answer the following questions using compete sentences:

1. What are the mean levels of satisfaction in the three groups? Report the mean, SD, minimum, maximum and sample size in a table.

2. Write a research question.

3. Write the research hypothesis (Ha) and the null hypothesis (Ho).

4. What was the value of the F statistic and its p-value?

5. Can the null hypothesis be rejected?

6. What were the degrees of freedom?

7. According to the LSD test, were any group means significantly different from any others? If yes, which ones?

8. Write a paragraph summarizing all the results.

9. Attach the relevant SPSS printouts.

## Solution Preview

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1. Write aa. research and

We want to see whether there is any statistically significant linear association between variables minutes of exercise in the past week, BMI, and depression.

b. null hypotheses regarding the relationship between exercise and depression.

Null Hypothesis (Ho): There is no statistically significant linear association between variables exercise and depression. (ρ=0).

Where ρ= population correlation coefficient between exercise and depression.

2. Based on the test statistics in table 1, what is your conclusion regarding your research hypothesis? (Hint: discuss both the magnitude and direction of the relationship).

We can see that the correlation coefficient between exercise and depression is -0.33 with p-value less than 0.05, so we can conclude that there is a statistically significant linear association between variables exercise and depression. We can see that the correlation coefficient is negative, it means that there is a negative relationship between these two variables. We can say that if one variable is increasing, the other variable is decreasing. For example, if depression is increasing, the minutes of exercise in the past week is decreasing and vice-versa. The value 0.33 is lies between 0.2 and 0.4, so we can say that there is a weak relationship between exercise and depression....

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