HI6007 Statistics and Research Methods: Use Descriptive Statistics
Questions:
Task:
As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression. These data are available on the website that accompanies this text in the file named medical1. A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are available on the website that accompanies this text in the file named medical2.
|
Florida |
New York |
North Carolina |
Florida |
New York |
North Carolina |
|
3 |
8 |
10 |
13 |
14 |
10 |
|
7 |
11 |
7 |
12 |
9 |
12 |
|
7 |
9 |
3 |
17 |
15 |
15 |
|
3 |
7 |
5 |
17 |
12 |
18 |
|
8 |
8 |
11 |
20 |
16 |
12 |
|
8 |
7 |
8 |
21 |
24 |
14 |
|
8 |
8 |
4 |
16 |
18 |
17 |
|
5 |
4 |
3 |
14 |
14 |
8 |
|
5 |
13 |
7 |
13 |
15 |
14 |
|
2 |
10 |
8 |
17 |
17 |
16 |
|
6 |
6 |
8 |
12 |
20 |
18 |
|
2 |
8 |
7 |
9 |
11 |
17 |
|
6 |
12 |
3 |
12 |
23 |
19 |
|
6 |
8 |
9 |
15 |
19 |
15 |
|
9 |
6 |
8 |
16 |
17 |
13 |
|
7 |
8 |
12 |
15 |
14 |
14 |
|
5 |
5 |
6 |
13 |
9 |
11 |
|
4 |
7 |
3 |
10 |
14 |
12 |
|
7 |
7 |
8 |
11 |
13 |
13 |
|
3 |
8 |
11 |
17 |
11 |
11 |
Required:
- Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?
- Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?
- Use inferences about individual treatment means where appropriate. What are your conclusions?
Answers:
- The relevant descriptive statistics for the participants of the first part of the study which focused on healthy individuals are as outlined below.
From the above it is apparent that the mean depression score is highest in case of New York while the same is i
ndicating the lowest level for Florida.
The relevant descriptive statistics for the participants of the second part of the study which focused on chronically ill individuals with age in excess of 65 years are as outlined below.
In comparison to the first part of the study, the mean depression scores tend to significantly higher for the second part which is noticeable in all the cities thus indicating that it is not linked to parameters related to city and more related with age and the overall health of the individual.
- The analysis of variance needs to be performed for each of the two studies which would involve the use of one factor ANOVA.
Study 1- ANOVA Testing
Null Hypothesis (H0): µFlorida = µNew York = µNorth Carolina and hence there is no significant difference in the means of the depression score witnesses in the given three cities.
Alternative Hypothesis (H1): All the three mean of depression scores witnessed in the three cities are not similar and one of these is atleast significantly different.
The output obtained from excel for the given test is as follows.
The F statistic computed is 5.241 and the corresponding p value is 0.008. Taking 5% significance level, there is sufficient evidence to cause null hypothesis rejection and acceptance of alternate hypothesis. Hence, the average depression score for healthy individuals differs in the three cities considered for the study.
Study 2- ANOVA Testing
Null Hypothesis (H0): µFlorida = µNew York = µNorth Carolina and hence there is no significant difference in the means of the depression score witnesses in the given three cities.
Alternative Hypothesis (H1): All the three mean of depression scores witnessed in the three cities are not similar and one of these is atleast significantly different.
The output obtained from excel for the given test is as follows.
The F statistic computed is 0.714 and the corresponding p value is 0.494. Taking 5% significance level, there is insufficient evidence to cause null hypothesis rejection and acceptance of alternate hypothesis. Hence, null hypothesis cannot be rejected. Hence, the average depression score for old and ill individuals does not significantly differs in the three cities considered for the study.
- The inference that can be drawn from the above analysis is that in case of healthy individuals the mean depression scores that are observed tend to differ which implies that there are certain factors different for these geographies which leads to difference in existence and intensity of depression. However, this is not true for aged and chronically ill people for whom the other aspects become less significant and essentially health and age become the vital factor driving depression incidence and intensity.
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