Percentage Points of the Incomplete Beta Function

Abstract

for N=10(1)50, X=1(1)N, and a=.005, .010, .025, and .050, where Ip(X, Y) is Karl Pearson's incomplete beta function ratio.' Values of p for which Ip(X, Y) =.005, 010, .025, .05, .10, .25, .50 have been given by Thompson2 in terms of the arguments vP =2 Y and V2 =2X. The entries in the present table were obtained by inverse linear interpolation of the logarithms of the accumulated frequencies found in Pearson's Tables of the Incomplete Beta Function and by interpolation with Lagrangian coefficients of Thompson's percentage points of the incomplete beta function. For values of p> .2000 these two methods of interpolation gave results which agreed within two units in the fourth significant figure, in spite of the fact that for v2>30 in Thompson's tables double interpolation was employed. Thompson's tables for p .2000 the data were smoothed by taking fourth differences, staying within the limits set by these two methods of interpolation. The data are therefore felt to be accurate within ? 1.5 in the last significant figure. Since binomial sums and the incomplete Beta function appear frequently in statistics the table may be used in a number of problems:

Cite this paper

@article{clark1953percentage,
  title = {{Percentage Points of the Incomplete Beta Function}},
  author = {Clark, Robert E.},
  journal = {Journal of the American Statistical Association},
  volume = {48},
  number = {264},
  pages = {831--843},
  year = {1953},
  doi = {10.1080/01621459.1953.10501205}
}

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