A confidence interval is a range of values that is used to estimate an unknown population parameter with a certain level of confidence. It is a way to express the uncertainty around an estimate of a population parameter, such as the mean.
For example, in a study investigating the effectiveness of a new physiotherapy treatment for lower back pain, the researchers might collect data from a sample of patients and calculate the mean pain reduction for the treatment group. A 95% confidence interval for the mean pain reduction would be a range of values within which the true population mean pain reduction is expected to fall with a 95% probability. This means that if the same study is conducted 100 times, about 95 studies will have the true population mean within their 95% confidence interval.
A typical example would be:
“The results show a mean VAS reduction in pain at four weeks of 2.3 (95% CI 1.8 – 2.8).”
The confidence interval is calculated based on the sample statistics and the level of confidence desired (commonly 95% or 99%). It is important to note that a confidence interval does not indicate whether the null hypothesis is true or false, but it provides an interval of values that’s likely to include the true population parameter with a certain level of confidence.
A narrow confidence interval indicates that the sample mean is a more precise estimate of the population mean, while a wide confidence interval indicates that the sample mean is less precise. In general, larger sample sizes tend to result in narrower confidence intervals, and thus more precise estimates of population parameters.
It is important to note that one cannot say that there is a 95% chance that the true population mean lies within a given interval of a certain paper. It will simply be the case, or not. However, if this study is repeated an infinite number of times, the true mean will be found within the generated intervals 95% of the time.
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