Questions:
Question 1
The variable ‘anticlot’ indicates the type of anticlotting drug prescribed to the patients.Produce the relevant graph and table to summarise the ‘anticlot’ variable and write a report describing this variable in the style presented in the course materials.
Question 2
The age of patients in years is provided in the data file. Produce the relevant graph and tables to summarise the ‘age’ variable and write a report describing this variable in the style presented in the course materials.
Question 3
Current research indicates that the number of everyday life stressors has risen in the last decade. Hospital records for 2014 show that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission. The researchers have suggested, that due to increasing stress, the percentage of Australians admitted to hospital for suspected myocardial infarction who have normal blood pressure at the time of admission is now lower than this.
Conduct a Binomial Test using the ‘bp ’ variable to test the researchers’ hypothesis. Produce the relevant output and write a Binomial test report based on your output in the style presented in the course materials.
Question 4
Due to federal cuts to the Government Health System, the researchers predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.
Conduct a OneSample ttest using the ‘los’ variable to test this prediction. Produce the relevant output and write a Onesample ttest report based on your output in the style presented in the course materials.
Question 5
The researchers have also claimed that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not. Conduct an Independent samples ttest using the ‘los’ and ‘diabetes’ variables to investigate this claim. Produce the relevant output and write an Independent samples ttest report based on your output in the style presented in the course materials.
Answers:
Question 1
The variable ‘anticlot’ indicates the type of anticlotting drug prescribed to the patients.
Produce the relevant graph and table to summarise the ‘anticlot’ variable and write a report describing this variable in the style presented in the course materials.
Solution
In this question, the study sought to understand the most frequent type of anticlotting drug prescribed to the patients. Table 1 below gives the frequency distribution of the various types of anticlotting drugs prescribed to the patients. It can be seen that the most prescribed drug is Aspirin (42%, n = 844) while the least prescribed drug is Warfarin (7%, n =148). 22% (n = 442) of the patients did not receive any drug prescription while 27% (n = 544) of the patients were
prescribed for Heparin.
Table 1: Type of anticlotting drug prescribed



Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Aspirin 
844 
42.2 
42.7 
42.7 
Heparin 
544 
27.2 
27.5 
70.2 

Warfarin 
148 
7.4 
7.5 
77.7 

None 
442 
22.1 
22.3 
100.0 

Total 
1978 
98.9 
100.0 


Missing 
System 
22 
1.1 


Total 
2000 
100.0 


The above results can also be visualized in the bar chart presented in figure 1 below;
Figure 1: Bar chart of anticlotting drugs prescribed to the patients
Question 2
The age of patients in years is provided in the data file.
Produce the relevant graph and tables to summarise the ‘age’ variable and write a report describing this variable in the style presented in the course materials.
Solution
The average age of the patients in years was found to be 63.45 years with oldest patient being 95 years old while the youngest patient was 45 years old.
Table 2: Descriptive statistics

Age in years 

N 
Statistic 
1995 
Range 
Statistic 
50 
Minimum 
Statistic 
45 
Maximum 
Statistic 
95 
Mean 
Statistic 
63.45 
Std. Deviation 
Statistic 
8.216 
Variance 
Statistic 
67.507 
Skewness 
Statistic 
.243 
Std. Error 
.055 

Kurtosis 
Statistic 
.401 
Std. Error 
.110 
The normality test for the variable “Age in years” showed that the variable does not come from a normally distributed dataset (p < 0.001).
Table 3: Tests of Normality
Tests of Normality 


KolmogorovSmirnov^{a} 
ShapiroWilk 

Statistic 
df 
Sig. 
Statistic 
df 
Sig. 

Age in years 
.055 
1995 
.000 
.989 
1995 
.000 
a. Lilliefors Significance Correction 
A boxplot was drawn to see the distribution of the dataset. A number of outliers were observed in the dataset further suggesting that the dataset is not symmetrical.
Figure 2: Boxplot for age in years
However, the histogram presented below suggests that the dataset seems to be normally distributed since the graph is almost symmetrical and in the shape of a bellshaped curve.
Figure 3: Histogram for age in years
Question 3
Current research indicates that the number of everyday life stressors has risen in the last decade. Hospital records for 2014 show that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission. The researchers have suggested, that due to increasing stress, the percentage of Australians admitted to hospital for suspected myocardial infarction who have normal blood pressure at the time of admission is now lower than this.
Conduct a Binomial Test using the ‘bp ’ variable to test the researchers’ hypothesis. Produce the relevant output and write a Binomial test report based on your output in the style presented in the course materials.
Solution
In this question, we conducted a Binomial test using the ‘bp’ variable to test the researchers’ hypothesis that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission (Howell, 2007). The hypothesis set to be tested was;
Table 4: Descriptive Statistics
Descriptive Statistics 


N 
Mean 
Std. Deviation 
Minimum 
Maximum 
Blood pressure 
1996 
.79 
.411 
0 
1 
Table 5: Binomial Test
Binomial Test 


Category 
N 
Observed Prop. 
Test Prop. 
Exact Sig. (1tailed) 

Blood pressure 
Group 1 
Normal 
1568 
.79 
.74 
.000 
Group 2 
Nonnormal 
428 
.21 



Total 

1996 
1.00 


From table 5 above, we can clearly see that the proportion of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission is 79% for the sample data provided. Binomial test that was conducted revealed that there is significant evidence that the proportion of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission is greater than 74%. The claim by the researchers that the proportion is lower than 74% is therefore not significantly valid.
Question 4
Due to federal cuts to the Government Health System, the researchers predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.
Conduct a OneSample ttest using the ‘los’ variable to test this prediction.
Produce the relevant output and write a Onesample ttest report based on your output in the style presented in the course materials.
Solution
The aim of this question was to test the claim that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.
Hypothesis
Using onesample ttest, we tested the above claim at 5% level of significance (John , 2006).
Table 6: OneSample Statistics



N 
Mean 
Std. Deviation 
Std. Error Mean 
Length of stay 
1995 
5.54 
1.439 
.032 
Table 7: OneSample Test



Test Value = 5.5 

t 
df 
Sig. (2tailed) 
Mean Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Length of stay 
1.112 
1994 
.266 
.036 
.03 
.10 
The mean length of stay was found to be 5.54. Results from the onesample ttest revealed that there is no evidence predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014 (p > 0.05).
Question 5
The researchers have also claimed that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not.
Conduct an Independent samples ttest using the ‘los’ and ‘diabetes’ variables to investigate this claim. Produce the relevant output and write an Independent samples ttest report based on your output in the style presented in the course materials.
Solution
In this question we tested the claim that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not. The hypothesis is;
Where is the average length of stay in hospital for patients who have a history of diabetes while is the average length of stay in hospital for patients who do not have a history of diabetes.
To test this claim, independent ttest was conducted at 5% level of significance. Results are given the tables below.
Table 8: Group Statistics
Group Statistics 


History of diabetes 
N 
Mean 
Std. Deviation 
Std. Error Mean 
Length of stay 
No 
1780 
5.52 
1.374 
.033 
Yes 
214 
5.68 
1.899 
.130 
Table 9: Independent Samples Test 


Levene's Test for Equality of Variances 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Length of stay 
Equal variances assumed 
32.045 
.000 
1.572 
1992 
.116 
.164 
.104 
.368 
.040 
Equal variances not assumed 


1.223 
240.51 
.223 
.164 
.134 
.427 
.100 
An independent samples ttest was performed to compare the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not (Zimmerman, 2007). There was no significant difference in the length of stay for the two groups of patients. The length of stay for those with history of diabetes (M = 5.68, SD = 1.90, N = 214) was not significantly different to those with no history of diabetes (M = 5.52, SD = 1.37, N = 1780), t(1992) = 1.57, p > .001, onetailed.
References
Howell, D. C. (2007). Statistical methods for psychology.
John , R. A. (2006). Mathematical Statistics and Data Analysis.
Zimmerman, D. W. (2007). A Note on Interpretation of the PairedSamples t Test. Journal of Educational and Behavioral Statistics, 22(3), 349–360.
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