Calculation of 95% Confidence Interval for means

As 95% Confidence Intervals are commonest in medical literature, I will describe the calculation of 95% Confidence Intervals here.

To calculate 95% Confidence Intervals (CI) for a population mean we need the following:

Sample mean (m)

Standard Error (SE)

The appropriate value from the t distribution with (n-1) degrees of freedom (1.96 (generally rounded up to 2) for 95% CI)

95% CI = m- 2SE to m+ 2SE

Example:

A researcher measured the haemoglobin of 25 volunteers and found that the mean haemoglobin was 12.5 g/dl, with a standard deviation of 1.5 g/dl. What is the 95% confidence interval?

Solution:

Confidence interval for a sample mean is calculated using the formula

95% CI = m- 2SE to m+ 2SE

Here,

Sample mean = 12.5

Standard Error = Standard Deviation / ÖSample size

Therefore, SE = 1.5/Ö25 = 1.5/5 = 0.3

Substituting

95% CI = 12.5 – 0.3 to 12.5 + 0.3

95% CI = 12.2 to 12.8 g/dl