Statistics Data for Assignment

Question

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:

  1. Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?
  2. Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?
  3. 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.

 

  1. inferences
THE TREATMENT MEANS SHOWS THAT NEWYORK HAS HIGHEST SCORES OF DEPRESSION AMONG THE THREE WHICH MEANS THAT NEWYORK NEEDS ATTENTION AT THE EARILIEST. ALSO NORTH CAROLINA IS ALSO NEEDING ATTENTION. THE FLORIDA HAS LOWEST MEAN SCORES AMONG THE THREE.
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