That doesn't actually have a large effect. An example in numpy: In [14]: x = norm(0.0,1).rvs(100000) In [15]: mean(x[where(x > 2.0)]) Out[15]: 2.37

That doesn't actually have a large effect. An example in numpy: In [14]: x = norm(0.0,1).rvs(100000) In [15]: mean(x[where(x > 2.0)]) Out[15]: 2.3774795090391301 In [16]: y = norm(0.5,1).rvs(100000) In [17]: mean(y[where(y > 2.0)]) Out[17]: 2.4372124830289557 I.e., a difference in the mean of 0.5 sigma corresponds to 0.06 in Graham's test statistic. Graham is a little bit off - a better place to look for bias is the bottom of the accepted distribution than at the mean.