RBH-1
Module: Accuracy and Precision, Confidence Intervals
Instructions: Please write down your answers in this document. Take care that you save the
copy of the document on your local PC BEFORE you start writing. At the end of the practical
send the document to ibz@mefst.hr.
Exercises
1. What is the standard error of the following measures:
a) Mean cholesterol levels in 30-60 year olds recruited from GP practices in
northern Croatia where:
M=5.1 mmol/L
Sample size=1600
SD=2.3 mmol/L
b) The proportion of women with breast cancer in women in a small town in Croatia
where:
Number of cases of women with skin cancer=30
Number of women in a study sample=5700
c) Mean blood glucose levels on ward where:
M= 5.1 mmol/L
SD= 2.3 mmol/L
Sample size= 16
2. As the size of a random sample increases
a) The standard deviation decreases
b) The standard error of the mean decreases
c) The mean increases
d) The range may increase
e) The precision of my parameter estimate increases
3. Assuming normal distribution of variables calculate the confidence intervals for the
following datasets:
a) The 95 per cent confidence interval (CI) for the forced expiratory volume
(FEV1) of children with asthma, where the mean is 1.47 L, the standard
deviation is 0.34 L and the sample size is 1089
b) The 99 per cent CI for the proportion of babies born with birth defects to
mothers who had an infection during pregnancy, where the number of babies
with birth defects is 7 and the total number of babies in the study is 43. (NB:
In the normal distribution, 99 per cent of the data lie within 2.58 standard
deviations of the mean.)
4. Suppose that we want to estimate the average height of Dalmatian males. By using a
simple random sampling, you chose 1000 males from a population of 1,000,000
males and you measured their height. Mean height was 180 cm, and standard
deviation was 30 cm. What was 95% confidence interval for mean?
(A) 180 + 1.86
(B) 180 + 3.0
(C) 180 + 5.88
(D) 180 + 30
(E) None of the above
5. The famous newspaper has chosen a random sample of 1600 readers from their
subscribers’ list of 100,000 subscribers. Examinees were asked if they think the
coverage of local news should be reduced. Forty percent of the sample agreed with
the reduction. What is 99% confidence interval for readers which voted in favour of
reduction?
(A) 0.30 to 0.50
(B) 0.32 to 0.48
(C) 0.35 to 0.45
(D) 0.37 to 0.43
(E) 0.39 to 0.41
Based on the data presented make the editor’s decision: PRO or CON of reduction?
6. A 95 percent CI for a mean
A. Is narrower than a 99 percent CI
B. Is a useful way of describing the precision of a study
C. Includes 95 percent of the observations in a study
D. Will include the population mean 95 percent of the time in repeated
samples
7. Brain tissues of 9 patients with schizophrenia were sampled. For each patient, the
concentration of the particular enzyme was determined. Enzyme levels were also
determined in 9 controls. Following statistics were calculated: mean of 𝑥̅ 1 = 39.8
mmol/L and standard deviation s1 = 8.16 mmol/L in the control group, and 𝑥̅ 2 = 35.5
mmol/L, and s2 = 6.93 mmol/L in the patient groups. What can you conclude about
difference in enzyme activity between the control and the patient group? Calculate
and elaborate your conclusion.
8. Researchers evaluated the effectiveness of standardized consultations for patients
with osteoarthritis of the knee. Standardized consultations involved three goal
oriented visits, which comprised education about osteoarthritis and treatment
management, as well as information on physical exercises and weight loss. A cluster
randomized controlled trial was used. Control treatment was usual care. Participants
were recruited from primary care. Inclusion criteria included age 45-75 years and a
diagnosis by a rheumatologist of osteoarthritis of the knee according to the American
College of Rheumatology clinical and radiological definition. Main outcome measures
included change in body weight at four months from baseline.
In total, 336 patients were included, with 154 allocated to standardized
consultation and 182 to usual care. At four months, the standardized consultation
group showed greater weight loss than the usual care group: mean 1.11 kg (95% CI
0.70 to 1.52) vs. 0.37 kg (0.02 to 0.72). The authors concluded that, compared with
usual care, a structured consultation programme for patients with osteoarthritis of
the knee resulted in significantly greater short term weight loss.
Which one of the following statements best describes the information
provided by the 95% confidence interval for mean weight loss at four months for the
standardized consultation group? Elaborate your choice.
a) 95% of sample participants in the standardized consultation group achieved a
weight loss between 0.70 kg and 1.52 kg
b) 95% of the population would achieve a weight loss between 0.70 kg and 1.52 kg if
they received a standardized consultation
c) There is a probability of 0.95 that the population mean weight loss at four months
with standard consultation would be between 0.70 kg and 1.52 kg
d) There is a probability of 0.95 that the sample mean weight loss for the
standardised consultation group was between 0.70 kg and 1.52 kg
9. Researchers investigated whether antidepressant drug prescribing and referrals to
specialist services for depression by general practitioners were associated with
patients’ scores on depression severity questionnaires measured at the start of
treatment. Anonymised data from the medical records of 38 general practices were
investigated. The nine item patient health questionnaire (PHQ-9) was used in 1658
patients and the depression subscale of the hospital anxiety and depression scale
(HADS) was used in 548 patients.
The distribution of HADS questionnaire scores for the sample was approximately
normal, whereas the PHQ-9 scores were negatively skewed. The mean PHQ-9 score
was 15.5 (standard deviation 6.0) and the mean HADS score was 11.1 (4.6). It was
reported that patients with higher depression severity scores were more likely to
receive prescriptions for antidepressants and be referred to specialist services.
However, other factors were independently associated with treatment and referral,
including patient age and concurrent physical illness and geographical area.
Which of the following statements, if any, are true? Explain your choice.
a) The normal distribution approximated by the HADS scores can be uniquely
described by the sample mean and standard deviation
b) The normal distribution approximated by the HADS scores is symmetrical about
the sample mean value
c) For the distribution of PHQ-9 scores, the tail on the right was longer than the tail
on the left
d) The sample mean PHQ-9 score was smaller than the median PHQ-9 score
10. Among the British respondents in the National Child Development Study, those who
are vegetarian at age 42 have significantly higher childhood general intelligence than
those who are not vegetarian at age 42. (Childhood general intelligence was
measured with 11 different cognitive tests at three ages before 16.) Vegetarians
have the mean childhood IQ of 109 (n=175) whereas meat eaters have the mean
childhood IQ of 100.9 (n=6,531). Authors claim that the difference is large and highly
statistically significant and present figure below to substantiate their findings. Data
presented in this excercise do include all data which are presented in a paper. Do you
think their findings are valid? Explain