Department of Health Management and Health Economics
Faculty of Medicine
University of Oslo
English
Written exam 7th of February 2014, 9:00am - 1:00pm
HMET4100 – Fundamentals of statistics
All written exam resources and a calculator Citizen SR-270x are allowed
Results will be made available within 3 weeks, see the board at the Department
of Health Management and Health Economics, Forskningsveien 3A. The results
will also be posted on Studentweb.
The receiving day of the results is the day the results are posted on the board at
the Department. Appeals must be submitted within three weeks of this date.
The Written Exam consists of 4 pages including this.
Remember to write down your candidate number so this is easily accessible
when the results become available.
Exam HMET4100 February 2014
Maximum score is 50 points. The exercises are based on hypothetical data.
The number of points for each question is given in parentheses below. All written material,
like textbook, handouts and written notes, and a calculator are allowed. Suggested solutions
will be posted on the website after the exam.
A ward at a hospital considers replacing the treatment they are using by a new treatment. You
are given the task to do a randomized study on whether the new treatment works better than
the old one. 80 patients get the new treatment, and 80 other patients get the old treatment. In
the group getting the new treatment, 33% are cured, whereas only 24% are cured in the group
using the old treatment.
a) (10p) Formulate a null hypothesis and an alternative hypothesis. Do a test on whether
there is a difference in the effect of the two treatments. Choose significance level 5%.
What is your conclusion? Do you think the result would have been more or less
significant if the percentages were the same, but there were three times as many
patients in each group (no calculations needed)? Explain your answer.
b) (5p) Also, calculate the 95% confidence interval for the difference in proportions
between the two groups. Explain how you can see from the confidence interval
whether there is a significant difference or not.
c) (4p) In the report to the hospital, one of your colleagues formulate the conclusions of
the test in the following way (you can assume that the calculations are correct): 33% of
the patients in the new treatment group were cured (95% confidence interval: 22.7%43.3%), and 24% of the patients in the old treatment group were cured (95%
confidence interval: 14.6%-33.3%). This is not significant, with p-value>0.05. Explain
why it is better to give a single confidence interval for the difference, as in b), rather
than presenting separate confidence intervals for each proportion as above.
d) (8p) Originally, the hospital also included a third group in the study, who was given
placebo. Even though the results from this group were not included in the final report,
you can see the results from the three-group comparison above. What was the
proportion of cured patients in the placebo group, and how many patients were
included in that group? Explain the relationship between the value 22.579 and the pvalue in the second table above (i.e. is there any connection between them?). What is
the alternative hypothesis for that test in the situation described here? What is the
advantage of doing a three-group comparison first, before doing all pairwise
comparisons when there are many groups?
In order to decide whether they should change to the new treatment or not, the hospital also
wants an analysis of the costs. The mean cost per patient in the new treatment group was
55000 kroner, whereas the mean cost per patient in the old treatment group was 54300 kroner.
The pooled sample variance sp2 was 5074000 kroner.
e) (8p) Formulate a null hypothesis and an alternative hypothesis. Do a t-test on whether
there is a difference in costs between the two treatments (You will not find the exact
number of degrees of freedom in the table in Newbold, just use an approximate
number). Choose significance level 5%. What is your conclusion?
f) (6p) Above is the SPSS output of a two sample t-test. What is the meaning of the
Levene’s test in the table? Interpret the Levene’s test p-value, and explain what this
means. Which line should be read in the t-test part of the table?
g) (2p) Above are the histograms of the costs in the treatment groups. Using the
histograms, discuss the validity of the t-tests done in e) and f).
h) (7p) Above is the output of another non-parametric test of the data. Which test is this?
What is the conclusion of this test? Do you think the conclusion from this test is more
valid or less valid than the test in f)? Based on the results from the entire exercise,
would you recommend that the hospital switch to the new treatment? Explain how you
arrived at your answer.