New protocol for care of patients following their first myocardial infarction (MI) is proposed

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

 

 1.    A new protocol for care of patients following their first myocardial infarction (MI) is proposed.

A study is conducted to directly compare the standard care to the new protocol using a randomised trial. The number of patients under each type of care and the number who were readmitted to hospital within 6 weeks are recorded in the table below.

Treatment	Number of patients	Number readmitted to hospital within 6 weeks
Standard Care	125	16
New Protocol	125	11

 a. Based on the given information, is there a significant reduction in the readmission rate under the new protocol?

 

Carry out an appropriate hypothesis test (by hand) showing all steps.

[Hint: Let be the population proportion of patients under the Standard Care who were readmitted to hospital within 6 weeks.

Text Box: 1a. /6Let be the population proportion of patients under the New Protocol who were readmitted to hospital within 6 weeks.]

b. Text Box: 1b. /3Calculate a 95% confidence interval for given the information in the table above. Write a statement to interpret the interval in context.

c. Text Box: 1c.i. /1i. State the margin of error of the 95% confidence interval for in terms of a percentage.

ii. Text Box: 1c.ii. /2If a follow-up study required that the estimate of be determined within 1.5% (instead of what was obtained in c.(i)) with 95% confidence, determine the sample size required for the follow-up study.

iii. Comment on your result in c(ii) with reference to the sample size of n=125 used in the original study.Text Box: 1c.iii. /1

Question 1 total =13 marks

2. An individual's critical flicker frequency is the highest frequency at which the flicker in a flickering light source can be detected. At frequencies above the critical frequency, the light source appears to be continuous even though it is actually flickering. This investigation recorded critical flicker frequency (in cycles/sec) and iris colour of the eye for 19 subjects.

The data is in the SPSS file Flicker.sav.

Data source: http://www.statsci.org/data/general/flicker.html

We would like to determine if the mean critical flicker frequency is different for different eye colours.

In your answers to the following questions, you may paste the results from SPSS into your answer but you must refer to and interpret the relevant output in your answer.

a. Create a side-by-side boxplot and a table of the means and standard deviations of the critical flicker frequencies given eye colour. Paste the results here and comment on each.

Text Box: 2a. /4

b. Use an appropriate statistical test to test if there is sufficient evidence to believe that the population mean critical flicker frequency is different for different eye colours.

Include all the steps as demonstrated in lectures. Use the notation as given in lectures.

Text Box: 2b. /6

c. What are the assumptions and requirements for inference using the technique in Part (b)? Do any of them appear to be violated? Which ones?

Text Box: 2c. /5[Hint: you will need to obtain the residuals.]

d. Text Box: 2d. /3Use the appropriate procedure to produce (experimentwise) 95% confidence intervals for the difference in population mean critical flicker frequency for each pair of eye colours, properly adjusted for multiple comparisons/testing. Which, if any, of the eye colours' mean critical flicker frequencies appear to be significantly different?

e. Perform an appropriate non-parametric statistical test to the test performed in (b).

Text Box: 2e. /6State the hypotheses, paste in the SPSS results, and state test statistic, the degrees of freedom and the decision of the test.

f. Text Box: 2f. /2Compare the p-values produced for the test in (b) and the test in (e). With regard to power, which test has the higher power? Explain your answer.

Question 2 total =26 marks

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