Under the neutral equilibrium model, the Tajima's D statistic is expected to be zero.
Modification indices are the minimum that the chi-square statistic is expected to decrease if the corresponding parameter is no longer assumed to be fixed at zero [ 28].
Long's test statistic is expected to be χ2 distributed when drift and sampling alone are responsible for the variance among markers.
Thus, even in the case of a non-linear effect, the FBAT CNV statistic is expected to be robust to a range of technical artefacts.
I sought to confirm that the distribution of this statistic was as expected, particularly in the case of small N (few observed substitutions in binding sites) which is typical of real datasets.
We focused our exploration of the Genomic Control method on the Tajima's D statistic, which is expected to approximately conform to a normal distribution whether for a constant-sized or a non-constant-sized population, which we confirmed by examining the real ENCODE data (Supplementary Material, Fig. S2).
The number of polymorphic sites showed a decrease in 10-20% of the original value, which is to be expected given that this statistic is directly dependent on the sample size.
The second estimator of α that we consider is based on the second-order moment statistic D. This statistic is appealing because we can express the expected value of E[ D| N] exactly, whereas E[ D| N] is only available to a first-order approximation.
Although the sensitivity and the C-statistic decreased, which is expected in a replication population that this not identical to the original population, significant association with nephropathy was still observed (χ2 = 17.79, p<0.0001), providing further support for the model.
This statistic is an intermediate between the normal Z-statistic and T-statistic because of the presence of the variance of null features log FC distribution, which is expected to be (almost) independent of the sample size.
This statistic is utterly incomprehensible to me.
