### Description

The confidence interval for the observed difference in the means for two sets of data can be calculated from standard statistical tables and data characteristics (number of values, mean, standard deviation) for the two data sets.

Data assumptions: 2 sets of data with symmetrical distribution

confidence interval for the difference in the means between 2 sets of data =

= ABS((mean first group) - (mean second group)) +/- (factor)

factor =

= (one-sided value of Student's t-distribution) * (pooled standard deviation) * (((1 / (number in first set)) + (1 / (number in second set))) ^ (0.5))

degrees of freedom =

= (number in first set) + (number in second set) - 2

pooled standard deviation =

= ((A + B) / (degrees of freedom)) ^ (0.5)

A = ((number in first set) - 1) * ((standard deviation of first set) ^ 2)

B = ((number in second set) - 1) * ((standard deviation of second set) ^ 2)

where:

• for a 95% confidence interval, the one-tailed value is for 2.5% (F 0.975, t 0.025)

• as the number of values increases, the closer the one-tailed value for t=0.025 approaches 1.96; at 120 degrees of freedom it is 1.98