Statistical Principles: Confidence Intervals Page 1/3
Researchers evaluated the effectiveness of a standardised consultation for patients with osteoarthritis of the knee compared to usual care. The outcome measures included change in body weight at four months from baseline.
At four months, the standardised consultation group showed greater weight loss than the usual care group (mean 1.11 kg (95% CI 0.70 to 1.52) v 0.37 kg (0.02 to 0.72); P=0.007). 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. (Based on: BMJ 2012;344:e3147)
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Q1. Which of the following statements about confidence intervals do you believe to be true?
The correct answer is a). The estimated range is calculated from a sample of the population data. b) is false. The interval is a measure of precision of the estimate of the population parameter. The normal range gives information about individual values. c) is false. The greater the confidence you require, the wider the confidence interval will be. d) The more observations you include in your sample the smaller the standard error will become and a confidence interval is the estimate ± level of confidence factor * the standard error of the estimate. The ‘level of confidence factor’ depends on the level of confidence required, 90% = 1.68, 95% = 1.96 AND 99% = 2.58.
Q2. Which of the following statements about confidence intervals do you believe to be true?
The correct answers are b), c) and e). a) A confidence interval can be calculated for a small sample using the exact Binomial distribution. It will be very wide if the sample size is small. c) This statement is not strictly true, but the confidence interval is usually interpreted in this way. d) The 95% confidence interval is calculated as the sample proportion ± 1.96 times the standard error of the proportion. The 1.96 is often approximated by 2. The sample proportion ± standard error of the proportion is the 67% confidence interval for the proportion. e) A 95% CI is narrower that a 99% CI. We are accepting less precision for our estimated value because we want to be more certain to include the population estimate in the interval with our 99% interval.
Q3. If the mean value for the weight of 25 men was calculated to be 90 kg with a standard deviation of 10 kg, what would the 95% confidence interval for the mean weight be approximately?
The correct answer is b). The 95% confidence interval is calculated as the sample mean ± 1.96 times the standard error of the mean. The standard error is calculated as the standard deviation divided by the square root of the number of observations in the sample. The 1.96 is often approximated by 2. In our example we would use: 90 ± 2 * 10 / 25 = 90 ± 20 /5 = 90 ± 4, which is 90 – 4 to 90 + 4 or 86 to 94.
Q4. Which the following statements best describes the information provided by the 95% confidence interval for mean weight loss at four months for the standardised consultation group?
The correct answer is c). a) We are trying to estimate the weight loss in population. We know the weight loss in the sample. Our standardised consultation group weight loss is 0.74 Kg greater (1.11-0.37) than in the usual care group. The confidence interval does not describe a range of values for which 95% of the sample members achieved a weight loss. b) The confidence interval does not describe the range of values for individuals within population. The range that 95% of individuals could take is the reference range. c) We are estimating the population parameter using a sample. The population estimate has error associated with it and this is represented by the confidence interval. d) We know the sample weight loss in the standardised group exactly it is 1.11. There is no uncertainty about it.
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