Confidence Intervals: The basics

Interpreting Confidence Intervals

Recall that the purpose of calculating Confidence Intervals (CI) is to obtain an estimate of the population parameter. Ideally, one must take several samples from the population of interest to obtain an accurate estimate of the population parameter. Accordingly, the general interpretation of 95% Confidence Intervals is:

If repeated samples were taken and the 95% confidence interval was computed for each sample (each of which would be different), 95% of the intervals would contain the population mean.

In practice, we often take only one sample and estimate the population parameter from that single sample. As this permits the computation of only one 95% Confidence Interval, one may interpret it as:

There is a 95% probability that the calculated confidence interval (from some future experiment) includes the true value of the population parameter.

It is important to note that the above is a probability statement about the confidence interval, not the population parameter.

Misinterpretations

A 95% confidence level does not mean that

  • There is a 95% probability that the population parameter lies within the interval or
  • There is a 95% probability that the interval covers the population parameter

The population parameter is an unknown constant. Therefore, no probability statement can be made about it. The Confidence interval is related to the reliability of the estimation procedure- it indicates one’s confidence in the estimation procedure.

A 95% confidence level does not mean that 95% of the sample data lie within the confidence interval.

A particular confidence level of 95% calculated from a experiment does not mean that if the experiment were repeated, there is a 95% probability of a sample parameter falling within that interval. (If the study on adult haemoglobin mentioned earlier were repeated, the 95% Confidence Interval (12.3 to 12.8 g/dl) does not mean that there is a 95% probability of a sample parameter falling within 12.3 to 12.8 g/dl.)

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