# Calculate p values based on differences between bootstrapped 95% confidence intervals

I have bootstrapped model fits to some data from different three groups, using the $2.5$ and $97.5$ percentiles to generate a $95\%$ confidence interval.

I know that if $95\%$ confidence intervals do not overlap then there there is a significant difference between values of at least $p<0.05$. I would like to calculate the exact $p$ values for pairwise comparisons between the following groups:

           Mean     LowerCI   UpperCI
Group A:  0.05113   0.02279   0.07926

Group B:  0.10979   0.07954   0.14352

Group C:  0.10937   0.09400   0.13040


Any help would be greatly appreciated!

• I see three problems in your suggestion: Firstly, the bootstrap is an asymptotic method (it is not exact). Secondly, bootstrap is primarily about confidence intervals (p values can be obtained under certain assumtions though) and last but not least it would be more natural to base evidence on mean differences instead of group means. – Michael M Nov 21 '13 at 18:57
• This is exactly like another question I just answered on Math.SE: math.stackexchange.com/questions/576048/… – user31668 Nov 21 '13 at 18:57