Confidence Interval (CI):
Confidence limits are two extremes of a measurement within which 95% observations would lie. These describe the limits within which 95% of the mean values if determined in similar experiments are likely to fall. The value of ‘t’ corresponding to a probability of 0.05 for the appropriate degree of freedom is read from the table of distribution. By multiplying this value with the standard error, the 95% confidence limits for the mean are obtained as per formula below.
Lower confidence limit = mean - (t0.05 × SEM) Upper confidence limit = mean + (t0.05 × SEM) If n > 30, the interval M ± 2(SEM) will include M with a probability of 95% and the interval M ± 2.8 (SEM) will include M with probability of 99%. These intervals are, therefore, called the 95% and 99% confidence intervals, respectively. The important difference between the ‘p’value and confidence interval is that confidence interval represents clinical significance, whereas ‘p’ value indicates statistical significance. Therefore, in many clinical studies, confidence interval is preferred instead of ‘p’ value, and some journals specifically ask for these values. Various medical journals use mean and SEM to describe variability within the sample. The SEM is a measure of precision for estimated population mean, whereas SD is a measure of data variability around mean of a sample of population. Hence, SEM is not a descriptive statistics and should not be used as such. Correct use of SEM would be only to indicate precision of estimated mean of population.