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Table 2 Shape parameters [ a,b] of beta distribution given mode m and variance τ 2

From: Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian procedure

m/ τ 2 0.001 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08
0.01 [1.33,33.99] [1.12,12.73] [1.07,8.18] [1.05,6.21] [1.04,5.05] [1.03,4.26] [1.03,3.67] [1.02,3.21] [1.02,2.84] [1.02,2.53] [1.01,2.26] [1.01,2.03] [1.01,1.82] [1.01,1.63] [1.01,1.45] [1,1.28] [1,1.12]
0.05 [3.89,55.92] [1.77,15.55] [1.43,9.21] [1.3,6.74] [1.23,5.36] [1.18,4.45] [1.15,3.79] [1.12,3.29] [1.1,2.89] [1.08,2.56] [1.07,2.28] [1.05,2.03] [1.04,1.82] [1.03,1.62] [1.02,1.44] [1.02,1.28] [1.01,1.11]
0.1 [10.36,85.26] [3.05,19.4] [2.07,10.59] [1.72,7.44] [1.53,5.76] [1.41,4.7] [1.33,3.95] [1.27,3.39] [1.22,2.95] [1.18,2.59] [1.14,2.3] [1.12,2.04] [1.09,1.82] [1.07,1.62] [1.05,1.44] [1.03,1.27] [1.01,1.11]
0.15 [20.24,110] [4.88,23.01] [2.93,11.91] [2.25,8.1] [1.91,6.14] [1.69,4.92] [1.55,4.09] [1.44,3.48] [1.35,3] [1.29,2.62] [1.23,2.31] [1.18,2.04] [1.14,1.81] [1.11,1.61] [1.08,1.43] [1.05,1.26] [1.02,1.1]
0.2 [32.84,128.38] [7.22,25.89] [4,13] [2.91,8.65] [2.36,6.45] [2.03,5.11] [1.8,4.2] [1.64,3.54] [1.51,3.04] [1.41,2.64] [1.33,2.31] [1.26,2.04] [1.2,1.8] [1.15,1.6] [1.1,1.41] [1.06,1.25] [1.02,1.1]
0.25 [47.46,140.37] [9.95,27.84] [5.25,13.75] [3.68,9.03] [2.89,6.66] [2.41,5.23] [2.09,4.27] [1.86,3.57] [1.68,3.05] [1.55,2.63] [1.43,2.3] [1.34,2.02] [1.26,1.78] [1.19,1.58] [1.13,1.4] [1.08,1.24] [1.03,1.09]
0.3 [63.33,146.43] [12.92,28.82] [6.62,14.11] [4.52,9.21] [3.46,6.75] [2.83,5.27] [2.4,4.28] [2.1,3.57] [1.87,3.03] [1.69,2.61] [1.55,2.27] [1.43,1.99] [1.33,1.76] [1.24,1.56] [1.16,1.38] [1.1,1.23] [1.04,1.09]
0.35 [79.71,147.18] [16.01,28.88] [8.05,14.09] [5.39,9.16] [4.06,6.69] [3.27,5.21] [2.73,4.22] [2.35,3.51] [2.07,2.98] [1.84,2.56] [1.66,2.23] [1.52,1.96] [1.39,1.73] [1.29,1.53] [1.2,1.36] [1.12,1.21] [1.04,1.08]
0.4 [95.87,143.3] [19.07,28.1] [9.47,13.7] [6.27,8.9] [4.67,6.5] [3.71,5.06] [3.06,4.1] [2.61,3.41] [2.26,2.89] [2,2.49] [1.78,2.17] [1.61,1.91] [1.46,1.69] [1.33,1.5] [1.23,1.34] [1.13,1.2] [1.05,1.08]
0.45 [111.04,135.5] [21.94,26.6] [10.81,12.99] [7.09,8.45] [5.24,6.18] [4.12,4.82] [3.38,3.91] [2.85,3.26] [2.45,2.77] [2.14,2.4] [1.89,2.09] [1.69,1.85] [1.52,1.64] [1.38,1.46] [1.26,1.31] [1.15,1.18] [1.06,1.07]
0.5 [124.5,124.5] [24.5,24.5] [12,12] [7.83,7.83] [5.75,5.75] [4.5,4.5] [3.67,3.67] [3.07,3.07] [2.63,2.63] [2.28,2.28] [2,2] [1.77,1.77] [1.58,1.58] [1.42,1.42] [1.29,1.29] [1.17,1.17] [1.06,1.06]
0.55 [135.5,111.04] [26.6,21.94] [12.99,10.81] [8.45,7.09] [6.18,5.24] [4.82,4.12] [3.91,3.38] [3.26,2.85] [2.77,2.45] [2.4,2.14] [2.09,1.89] [1.85,1.69] [1.64,1.52] [1.46,1.38] [1.31,1.26] [1.18,1.15] [1.07,1.06]
0.6 [143.3,95.87] [28.1,19.07] [13.7,9.47] [8.9,6.27] [6.5,4.67] [5.06,3.71] [4.1,3.06] [3.41,2.61] [2.89,2.26] [2.49,2] [2.17,1.78] [1.91,1.61] [1.69,1.46] [1.5,1.33] [1.34,1.23] [1.2,1.13] [1.08,1.05]
0.65 [147.18,79.71] [28.88,16.01] [14.09,8.05] [9.16,5.39] [6.69,4.06] [5.21,3.27] [4.22,2.73] [3.51,2.35] [2.98,2.07] [2.56,1.84] [2.23,1.66] [1.96,1.52] [1.73,1.39] [1.53,1.29] [1.36,1.2] [1.21,1.12] [1.08,1.04]
0.7 [146.43,63.33] [28.82,12.92] [14.11,6.62] [9.21,4.52] [6.75,3.46] [5.27,2.83] [4.28,2.4] [3.57,2.1] [3.03,1.87] [2.61,1.69] [2.27,1.55] [1.99,1.43] [1.76,1.33] [1.56,1.24] [1.38,1.16] [1.23,1.1] [1.09,1.04]
0.75 [140.37,47.46] [27.84,9.95] [13.75,5.25] [9.03,3.68] [6.66,2.89] [5.23,2.41] [4.27,2.09] [3.57,1.86] [3.05,1.68] [2.63,1.55] [2.3,1.43] [2.02,1.34] [1.78,1.26] [1.58,1.19] [1.4,1.13] [1.24,1.08] [1.09,1.03]
0.8 [128.38,32.84] [25.89,7.22] [13,4] [8.65,2.91] [6.45,2.36] [5.11,2.03] [4.2,1.8] [3.54,1.64] [3.04,1.51] [2.64,1.41] [2.31,1.33] [2.04,1.26] [1.8,1.2] [1.6,1.15] [1.41,1.1] [1.25,1.06] [1.1,1.02]
0.85 [110,20.24] [23.01,4.88] [11.91,2.93] [8.1,2.25] [6.14,1.91] [4.92,1.69] [4.09,1.55] [3.48,1.44] [3,1.35] [2.62,1.29] [2.31,1.23] [2.04,1.18] [1.81,1.14] [1.61,1.11] [1.43,1.08] [1.26,1.05] [1.1,1.02]
0.9 [85.26,10.36] [19.4,3.05] [10.59,2.07] [7.44,1.72] [5.76,1.53] [4.7,1.41] [3.95,1.33] [3.39,1.27] [2.95,1.22] [2.59,1.18] [2.3,1.14] [2.04,1.12] [1.82,1.09] [1.62,1.07] [1.44,1.05] [1.27,1.03] [1.11,1.01]
0.95 [55.93,3.89] [15.55,1.77] [9.21,1.43] [6.74,1.3] [5.36,1.23] [4.45,1.18] [3.79,1.15] [3.29,1.12] [2.89,1.1] [2.56,1.08] [2.28,1.07] [2.03,1.05] [1.82,1.04] [1.62,1.03] [1.44,1.02] [1.28,1.02] [1.11,1.01]
0.99 [33.99,1.33] [12.73,1.12] [8.18,1.07] [6.21,1.05] [5.05,1.04] [4.26,1.03] [3.67,1.03] [3.21,1.02] [2.84,1.02] [2.53,1.02] [2.26,1.01] [2.03,1.01] [1.82,1.01] [1.63,1.01] [1.45,1.01] [1.28,1.003] [1.12,1.001]