Statistics Data for Assignment
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?
Task :
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:
descriptive statistics
Florida | New York | North Carolina | ||||
Mean | 5.55 | Mean | 8 | Mean | 7.05 | |
Standard Error | 0.478346934 | Standard Error | 0.492041932 | Standard Error | 0.634428877 | |
Median | 6 | Median | 8 | Median | 7.5 | |
Mode | 7 | Mode | 8 | Mode | 8 | |
Standard Deviation | 2.139232523 | Standard Deviation | 2.200478417 | Standard Deviation | 2.837252192 | |
Sample Variance | 4.576315789 | Sample Variance | 4.842105263 | Sample Variance | 8.05 | |
Kurtosis | -1.062192818 | Kurtosis | 0.626431669 | Kurtosis | -0.904925496 | |
Skewness | -0.27355709 | Skewness | 0.625687389 | Skewness | -0.056188269 | |
Range | 7 | Range | 9 | Range | 9 | |
Minimum | 2 | Minimum | 4 | Minimum | 3 | |
Maximum | 9 | Maximum | 13 | Maximum | 12 | |
Sum | 111 | Sum | 160 | Sum | 141 | |
Count | 20 | Count | 20 | Count | 20 | |
Confidence Level(95.0%) | 1.00119164 | Confidence Level(95.0%) | 1.0298556 | Confidence Level(95.0%) | 1.3278749 | |
NOW WHEN WE CONSIDER THE SECOND STUDY
Florida | New York | North Carolina | |||
Mean | 14.5 | Mean | 15.25 | Mean | 13.95 |
Standard Error | 0.708965146 | Standard Error | 0.923024206 | Standard Error | 0.65884668 |
Median | 14.5 | Median | 14.5 | Median | 14 |
Mode | 17 | Mode | 14 | Mode | 12 |
Standard Deviation | 3.170588522 | Standard Deviation | 4.127889737 | Standard Deviation | 2.946451925 |
Sample Variance | 10.05263158 | Sample Variance | 17.03947368 | Sample Variance | 8.681578947 |
Kurtosis | -0.340799481 | Kurtosis | -0.0301367 | Kurtosis | -0.592052134 |
Skewness | 0.280721497 | Skewness | 0.525352494 | Skewness | -0.041733773 |
Range | 12 | Range | 15 | Range | 11 |
Minimum | 9 | Minimum | 9 | Minimum | 8 |
Maximum | 21 | Maximum | 24 | Maximum | 19 |
Sum | 290 | Sum | 305 | Sum | 279 |
Count | 20 | Count | 20 | Count | 20 |
Confidence Level(95.0%) | 1.483881105 | Confidence Level(95.0%) | 1.931911865 | Confidence Level(95.0%) | 1.378981949 |
THE AVERAGE SCORES FOR NEW YORK ARE HIGHER THAN THE FLORIDA AND NORTH , WHICH MEANS THAT THERE IS HIGH RISK OF DISEASES IN NEW YORK AS COMPARED TO OTHER.
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Florida | 20 | 111 | 5.55 | 4.576315789 | ||
New York | 20 | 160 | 8 | 4.842105263 | ||
North Carolina | 20 | 141 | 7.05 | 8.05 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 61.03333333 | 2 | 30.51666667 | 5.240885809 | 0.008139895 | 3.158842719 |
Within Groups | 331.9 | 57 | 5.822807018 | |||
Total | 392.9333333 | 59 |
FOR THE SECOND STUDY –
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Florida | 20 | 290 | 14.5 | 10.05263158 | ||
New York | 20 | 305 | 15.25 | 17.03947368 | ||
North Carolina | 20 | 279 | 13.95 | 8.681578947 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 17.03333333 | 2 | 8.516666667 | 0.714212152 | 0.493906129 | 3.158842719 |
Within Groups | 679.7 | 57 | 11.9245614 | |||
Total | 696.7333333 | 59 |
HYPOTHESIS IS THAT THE DEPRESSION SCORES IN ALL THE THREE GROUPS ARE SAME.
- inferences
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