Significance of difference in means In “A Comparative Study of Nursing Home Residents …”, Aigner et al. write (p. 20)

Acute visits were significantly higher for the nurse practiticoner/physician team at 3.0 visits per year (± 2.4) versus 1.2 visits per year (± 1.5) for the physician-only group (P <0.0001)

Furthermore, (p. 19)

The statistical analysis was performed using the chi-squared or Fisher exact test for comparisons of percent and Student t test for comparison of means

I always thought that if confidence intervals overlap by that much, differences can’t be significant. Am I wrong?
Aigner, M. J., Drew, S., & Phipps, J. (2004). A comparative study of nursing home resident outcomes between care provided by nurse practitioners/physicians versus physicians only.  Journal of the American Medical Directors Association, 5(1), 16-23.
 A: The data aren't normal. I presume that the number of acute visits is an integer, i.e. you can't visit a patient 1.5 times. You either visit them once or twice. 
As an example, here are some data:
Mean: 3.2 sd: 2.142
8 8 4 1 2 2 0 2 5 2 3 3 3 1 5 4 4 1 4 2

and 
Mean:1.25 sd: 1.164
4 0 4 1 1 2 0 1 2 2 1 2 1 0 0 0 1 1 1 1

If you performed a t-test, you would get p=0.001
A: They're probably not confidence intervals for the mean, but rather standard deviations from the data, just reported weirdly.  
This interpretation is supported by the very confused presentation of results in the second quote.  Fisher's exact test is a) not the same as a chi-squared test, b) almost certainly inappropriate given most sampling schemes (both margins are seldom fixed).  And if they used both we'd want to know why.  Neither test compares percentages, although probably results are ultimately reported in percentages.  Finally, applying Students t with such low counts seems risky at best.
From the other side of the paywall its hard to say more, but I think you're seeing a weak analysis ambiguously presented.
