I can't figure out why you didn't just use the correlation coefficients for these studies?
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Is there a reference or a reason you calculated the coverage using the F distribution, etc. for these statistics rather than just using the Fisher transform on the correlation coefficient?
Lines 551 to 694 in c15f3f0
| ### study 12 | |
| df1.or[1] <- 2 | |
| df2.or[1] <- 92 | |
| F.or[1] <- 3.13 | |
| df1.rep[1] <- 2 | |
| df2.rep[1] <- 232 | |
| F.rep[1] <- 1.63 | |
| ### study 13 | |
| df1.or[2] <- 2 | |
| df2.or[2] <- 68 | |
| F.or[2] <- 41.59 | |
| df1.rep[2] <- 2 | |
| df2.rep[2] <- 68 | |
| F.rep[2] <- 41.603 | |
| ### study 17 | |
| df1.or[3] <- 2 | |
| df2.or[3] <- 76 | |
| F.or[3] <- 8.67 | |
| df1.rep[3] <- 1.58 | |
| df2.rep[3] <- 72.4 | |
| F.rep[3] <- 19.48 | |
| ### study 22 | |
| df1.or[4] <- 3 | |
| df2.or[4] <- 93 | |
| F.or[4] <- 5.23 | |
| df1.rep[4] <- 2.33 | |
| df2.rep[4] <- 90 | |
| F.rep[4] <- 0.38 | |
| ### study 43 | |
| df1.or[5] <- 2 | |
| df2.or[5] <- 64 | |
| F.or[5] <- 10.17 | |
| df1.rep[5] <- 2 | |
| df2.rep[5] <- 72 | |
| F.rep[5] <- 1.97 | |
| ### study 46 | |
| df1.or[6] <- 21 | |
| df2.or[6] <- 230025 | |
| F.or[6] <- 118.15 | |
| df1.rep[6] <- 21 | |
| df2.rep[6] <- 455304 | |
| F.rep[6] <- 261.93 | |
| ### study 50 | |
| df1.or[7] <- 2 | |
| df2.or[7] <- 92 | |
| F.or[7] <- 4.36 | |
| df1.rep[7] <- 2 | |
| df2.rep[7] <- 103 | |
| F.rep[7] <- 2.601 | |
| ### study 55 | |
| df1.or[8] <- 2 | |
| df2.or[8] <- 54 | |
| F.or[8] <- 3.19 | |
| df1.rep[8] <- 2 | |
| df2.rep[8] <- 68 | |
| F.rep[8] <- 0.3 | |
| ### study 64 | |
| df1.or[9] <- 2 | |
| df2.or[9] <- 76 | |
| F.or[9] <- 21.57 | |
| df1.rep[9] <- 2 | |
| df2.rep[9] <- 65 | |
| F.rep[9] <- 0.865 | |
| ### study 80 | |
| df1.or[10] <- 2 | |
| df2.or[10] <- 43 | |
| F.or[10] <- 3.36 | |
| df1.rep[10] <- 2 | |
| df2.rep[10] <- 67 | |
| F.rep[10] <- 1.7 | |
| ### study 86 | |
| df1.or[11] <- 2 | |
| df2.or[11] <- 82 | |
| F.or[11] <- 4.05 | |
| df1.rep[11] <- 2 | |
| df2.rep[11] <- 137 | |
| F.rep[11] <- 1.99 | |
| ### study 117 | |
| df1.or[12] <- 18 | |
| df2.or[12] <- 660 | |
| F.or[12] <- 16.31 | |
| df1.rep[12] <- 18 | |
| df2.rep[12] <- 660 | |
| F.rep[12] <- 12.98 | |
| ### study 132 | |
| df1.or[13] <- 3 | |
| df2.or[13] <- 69 | |
| F.or[13] <- 5.15 | |
| df1.rep[13] <- 1.48 | |
| df2.rep[13] <- 41.458 | |
| F.rep[13] <- 1.401 | |
| ### study 139 | |
| df1.or[14] <- 3 | |
| df2.or[14] <- 9 | |
| F.or[14] <- 8.5 | |
| df1.rep[14] <- 3 | |
| df2.rep[14] <- 12 | |
| F.rep[14] <- 13.06 | |
| ### study 140 | |
| df1.or[15] <- 2 | |
| df2.or[15] <- 81 | |
| F.or[15] <- 4.97 | |
| df1.rep[15] <- 2 | |
| df2.rep[15] <- 122 | |
| F.rep[15] <- 0.24 | |
| ### study 142 | |
| df1.or[16] <- 2 | |
| df2.or[16] <- 162 | |
| F.or[16] <- 192.89 | |
| df1.rep[16] <- 2 | |
| df2.rep[16] <- 174 | |
| F.rep[16] <- 252.83 | |
| ### study 143 | |
| df1.or[17] <- 4 | |
| df2.or[17] <- 108 | |
| F.or[17] <- 3.67 | |
| df1.rep[17] <- 4 | |
| df2.rep[17] <- 150 | |
| F.rep[17] <- 0.58 | |
| ### Added later, after reviews, before re-submitting to Science [July 16, 2015] | |
| ### study 25 | |
| df1.or[18] <- 3 | |
| df2.or[18] <- 48 | |
| F.or[18] <- 9.14 | |
| df1.rep[18] <- 3 | |
| df2.rep[18] <- 59 | |
| F.rep[18] <- 5.681 |
For these statistics, the standard error of the Fisher transformed correlation statistic cannot be calculated, hence coverage cannot be calculated using this statistic. Therefore, we used the noncentral distribution of the F and chi2 statistic, of which the distribution is known exactly
Can you point me to the reference where the transform for the F + chisq2 statistic with multiple dof can be transformed into a correlation coefficient and the reference where you can calculate the standard error for the cases where there is only a single dof test? Thanks
Please see the Appendix of the paper for more information.
Ok. It wasn't clear there. There was no reference. Thanks.