Comparing individual confidence intervals of two population means is an incorrect procedure for determining the statistical significance of the difference between the means. We show conditions where confidence intervals for the means from two independent samples overlap and the difference between the means is in fact significant.
Ryan, George W. and Leadbetter, Steven D.
"On The Misuse Of Confidence Intervals For Two Means In Testing For The Significance Of The Difference Between The Means,"
Journal of Modern Applied Statistical Methods: Vol. 1
, Article 56.
Available at: http://digitalcommons.wayne.edu/jmasm/vol1/iss2/56