Predicting ten-year stroke risk using age, blood pressure, and smoking status

SPSS Data Analysis

American Heart Association Prediction of Stroke Risks

Over a ten-year study, the American Heart Association collected data on age, blood pressure level, and smoking information in order to calculate the risk of strokes within the sample population. Within the context of this study, risk is interpreted by the probability (times 100) that the patient will have a stroke over the next ten-year period. With those who smoke, there is a dummy variable assigned to correlate the data. In this case a 1 indicates a smoker, and 0 indicates a nonsmoker.

Data Set

Risk

Age

Blood Pressure

smoking.302

With the equation formulated earlier that computes the overall numeric risk value being Y = a + b1*X1 + b2*X2 + b3*X3, we can now begin to plug in both the computed constant and coefficients along with new independent variables of an individual not included in the original data set. The equation with the constant and coefficients included, the final equation to be used with new variable sets is Y = -93.401 + .697x1 + 0.553x2 + .302x3. Here, we must first define the variables used in the regression analysis. Variable 0 represented the age of each individual within the data set, Variable 2 represented blood pressure, and variable 3 represented smoking habits. Variable 1 is equated to the dependent variable, or numeric risk value, and so is represented as Y. Thus, with a 68-year-old man who smokes and has a blood pressure of 175, shows an equation to:

Y=-93.401 + .697 (age) + .553 (blood pressure) + .302 (smoking)

Y = -93.401 + .697 (68) + .553(175)+ .302(1)

Y=-93.401 + 47.396 + 96.775+ .302

Y=51.072

Here then, the risk level is at 51.072, and can then be rounded down to 51. The individual in question here then has a risk factor of 51 in terms of his risk for having a stroke within the next ten years, meaning that the base probability is estimated at .51072. It is clear that the man's blood pressure and smoking habits are the two independent variable factors that play the most significant role in formulating such a high risk of stroke within the next ten years in comparison to the other individuals within the original data set.

Question 2

A. Fuel Additives and Mileage

Data Table

Sample a

Sample B

17.3

18.7

18.4

17.8

19.1

21.3

16.7

21

18.2

22.1

18.5

18.7

17.5

19.8

20.7

20.2

Data Rank

Rank a

Rank B

2

8.5

6

4

10

15

1

14

5

16

7

8.5

5

11

13

12

Data Set

Sum

Mean

17.9571429

5.14285714

Variance

0.6795238

2.2641071

Rank Sum

Rank Mean

4.9

11.3

Combined Sum

Combined Median Rank

8.1

Testing commenced on two separate fuel additives in order to test their differing effect on the mileage of the cars. One sample included seven cars, and the other nine cars. Their mileage per gallon can then be used to determine if there is a significant difference between the two additives in terms of mileage information. The two sets of data represent comparable observations and measurable central tendencies. Both include the mileage of vehicles which were used as sampling for the fuel additives in question. Additionally, each sample test is independent of the other and the observations in each sample itself are also independent of each other. Thus, the Mann-Whitney statistical test proves a viable option to compare the two sets of data from the two different and independent fuel additives. The Mann-Whitney test allows for the observation of one sample population in regards to how it fairs in comparison to another sample population, where the variances are equal amongst both sample groups.

Thus, the following equation can be implemented within the computation of the Mann-Whitney statistical test.

UA= nanb +na (na+1) -- TA

2

na= 7 (critical values for U)

nb= 9

TA= the sum of the ranks of Sample a

nanb +na (na+1) = the maximum value of TA

2

With these values, the following computations were made, including the value of U, P (1), and P (2), which can then be analyzed to show if there is a significant difference between the two additives and how they affect the mileage rate of the vehicles they are used in.

Ranks

fuel additives (per m)

N

Mean Rank

Sum of Ranks

gas mileage additive 1

7

4.86

34.00

additive 2

9

11.33

Total

16

Test Statisticsb

gas mileage

Mann-Whitney U

6.000

Wilcoxon W

34.000

Z

-2.701

Asymp. Sig. (2-tailed)

.007

Exact Sig. [2*(1-tailed Sig.)]

.005a

a. Not corrected for ties.

b. Grouping Variable: fuel additives (per m)

P (1)

0.004

P (2)

0.008

With the two P. values being so far apart, as well as the variance of the two groups being of significant value, around 2 whole values, it is clear that there is a significant difference to be noted between the two sample groups. Through the analysis of both the variance and the computations worked out through the Mann-Whitney test, it is clear that Sample B. has a higher rate of miles per gallon than the vehicles tested in Sample a. Here, the significant difference can then be interpreted that the fuel additive used within the context of Sample B. is more effective in terms of increased mileage within its test vehicles.

B. Exercise and Calories Burnt

Data Table

Swimming

Tennis

Cycling

Data Rank

Rank a

Rank B

Rank C

8

9

5

4

14

1

11

13

3

6

10

7

12

15

2

Data Set

Sum

2040

Mean

Variance

Rank Sum

41

61

18

Rank Mean

8.2

12.2

3.6

Combined Sum

Combined Median of Ranks

8

Three separate exercises were observed three times a week for forty minutes each session. The data here shows the number of calories burnt by each different activity within that context of forty minute work outs three days a week. By using the Kruskal -- Wallis test, the data can help determine if there was a significant difference between the three activities and corresponding calorie burnt data. The test itself requires a measured independent variable, and one nominal variable with one measurement variable. In the contest of this analysis, the ranked data is the set being computed. It also depends on the fact that the K. samples are random and independent, coming specifically out of a larger sample population. Additionally, all populations within the two sample sets are expected to have normal distribution and similar variances. Here the equation for analysis is as follows, with a=0.05.

SSbg (R)=n (mean of the group -- combined mean)

H= SSbg (R)

N (N=1)/12

Ranks

Activities

N

Mean Rank

calories burned swimming

5

8.20

Tennis

5

12.20

cycling

5

3.60

Total

15

Test Statisticsa, b calories burned

Chi-Square

9.260

df

2

Asymp. Sig.

.010

a. Kruskal Wallis Test

b. Grouping Variable: Activities

H=

9.26

df=

2

P=

0.0098

Within this data set, the sample sizes are at the 5 limit mark to create the notion that the distribution of H. is closely corresponding to the approximation of df, where df=k-1. Thus, with the computed analysis, it is clear that one sample population does show a significant difference the other two. It can be assumed that Cycling is significantly different in terms of how many calories it burns compared to the other two sample groups. It is significantly lower in terms of how many calories it burns within the context in comparison to the other sampled activities of swimming and tennis. Swimming and Tennis are much closer, with less of a significant difference between them, showing much more correlation in regards to the amount of calories burned within the workout regime setting. Based on the analysis, however, it is clear hat Tennis burns the most calories out of the two listed activities with less of a significant difference. .

Question 3

Quality of Inpatient Treatment

In thus data set, forty patients represent the sample set to be used to determine the correlation between the number of visitations and perceived quality of the care based on the opinion of the patient. The patients were divided into visitor categories, in which 1=frequent, 2=occasional, and 3=rare. Then, treatment was valued between the scale of 1=good, 2=fair, and 3=poor. A Chi-square Test was then performed on the data set to determine if there was a significant difference between the number of visits and the perceived quality of care within the given set of surveyed patients.

Data Set

Chi-Square Test Results

Test Statistics

visitors treatment

Chi-Square

.050a

.650a

df

2

2

Asymp. Sig.

.975

.723

a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 13.3.

visitors

Observed N

Expected N

Residual

frequent

13

13.3

-.3

occasional

13

13.3

-.3

rare

14

13.3

.7

Total

40

treatment

Observed N

Expected N

Residual

good

11

13.3

-2.3

fair

14

13.3

.7

poor

15

13.3

1.7

Total

40

The data analysis using the Chi-Square Test clearly shows a significant difference between the three categorized groups of patients. The sample size for frequent patients and medium frequency patients was thirteen variables. The sample size for patients who rarely needed care within the hospital setting was set at fourteen variables. Each was analyzed in comparison to each other utilizing the principle equations within the Chi-Square Test. It is clear here that the null hypothesis was true in this case. Through the analysis, it was observed that there were significant differences between all three groups. With this analysis, it was clear that the higher duration spent in care signified a pre-determined rating of its healthcare quality. Sample a, the patients who were frequently being cared for by hospital staff showed a mean perceived care rating of 1.38. Sample B, patients who needed occasional care had a different mean of a 2.08 perceived care rating. Those who rarely entered the hospital setting showed a mean perceived rating as 2.86. Thus, the findings of the analysis shows that those patients who are need of care more often are less satisfied with the type of care they receive. This may be on the increased demands of these patients or the frustration of the frequency of visits. Whatever the base cause, it is clear that frequent patients are the most unsatisfied in terms of their perceived care. Patients who occasionally needed care had an improved perception of the hospital care setting, however, this rating was still set at fair. It was only Sample C, or the patients who rarely needed hospital care who were the most satisfied with the type of care they were receiving. Although not fully satisfied, this was the closest population of a satisfied care rating. This may be based on the notion that they are not used to typical care standards based on their low frequency of visits, and so do not know what negative elements to look for within their care setting. With this analysis, the hospital can now look to improve the care strategies used for more frequent or long-term patients, as this is the population who is the most dissatisfied, as well as the population most encountered within the day-to-day hospital setting.