| // Package thresholds implements the thresholds for hypothesis testing. |
| // |
| // The "low threshold" is the traditional significance threshold. If the p-value is |
| // below the "low threshold", we say the two samples come from different |
| // distributions (reject the null hypothesis). |
| // |
| // We also define a "high threshold". If the p-value is above the "high threshold", |
| // we say the two samples come from the same distribution (reject the alternative |
| // hypothesis). The high thresholds listed in this script are hard coded. They |
| // are generated via [thresholds_functional.py] and [thresholds_performance.py] |
| // |
| // If the p-value is in between the two thresholds, we fail to reject either |
| // hypothesis. This means we need more information to make a decision. As the |
| // sample sizes increase, the high threshold decreases until it crosses the |
| // low threshold. This way, there's a limit on the number of repeats. |
| // Thresholds are used in bisection to reduce the number of computing |
| // resources needed to run bisection. The high threshold scales depending |
| // on the normalized magnitude. |
| // |
| // The normalized magnitude is the size of the difference normalized by the |
| // larger interquartile range of the two samples. |
| // The greater the perceived difference, the fewer iterations are necessary |
| // for concluding that two samples come from the same population. |
| // This [document] gives more context for the high thresholds. |
| // |
| // On the other hand, the low threshold is statically |
| // defined, since the burden of significance is the same regardless |
| // of sample size and normalized magnitude. |
| // |
| // [thresholds_functional.py]: https://chromium.googlesource.com/catapult.git/+/f25d23e77a963e88af9199c7c3a0638268e44538/dashboard/dashboard/pinpoint/models/compare/thresholds_functional.py |
| // [thresholds_performance.py]: https://chromium.googlesource.com/catapult.git/+/f25d23e77a963e88af9199c7c3a0638268e44538/dashboard/dashboard/pinpoint/models/compare/thresholds_performance.py |
| // [document]: https://docs.google.com/document/d/19gig8pv8ei2y45mVDp5awZGj39bZoFjNDn65uOfyUUY/edit#bookmark=id.8k02cmyj7ral |
| |
| package thresholds |
| |
| // The low threshold used in hypothesis testing. |
| // Note that this implies we could be rejecting the null hypothesis if the |
| // p-value is less than this value. It can happen that because we're generating |
| // the table of "high" thresholds with randomised permutations, that this value |
| // is actually higher than the "high" thresholds. |
| const LowThreshold = 0.05 |
| |
| type thresholds [][]float64 |
| |
| // HighThresholdPerformance returns the high threshold for performance hypothesis |
| // testing given the normalized_magnitude and the sample_size. |
| // |
| // The normalized magnitude is an estimate of the size of differences to look for, |
| // normalized by the interquartile range (IQR). We need more values to find |
| // smaller differences. |
| func HighThresholdPerformance(normalized_magnitude float64, sample_size int) (float64, error) { |
| magnitude_index := int(normalized_magnitude*10) - 3 |
| return getHighThreshold(highThresholdsPerformance, magnitude_index, sample_size), nil |
| } |
| |
| // HighThresholdFunctional returns the high threshold for functional hypothesis |
| // testing given the normalized_magnitude and the sample_size. |
| // |
| // The normalized magnitude is an estimate of failure rate between 0 and 1. |
| // We need more values to find smaller differences. |
| func HighThresholdFunctional(normalized_magnitude float64, sample_size int) (float64, error) { |
| magnitude_index := int(normalized_magnitude*10) - 1 |
| return getHighThreshold(highThresholdsFunctional, magnitude_index, sample_size), nil |
| } |
| |
| func getHighThreshold(high_thresholds thresholds, magnitude_index int, sample_size int) float64 { |
| magnitude_index = max(magnitude_index, 0) |
| magnitude_index = min(magnitude_index, len(high_thresholds)-1) |
| sample_size_index := min(sample_size, len(high_thresholds[magnitude_index])) - 1 |
| return high_thresholds[magnitude_index][sample_size_index] |
| } |
| |
| // highThresholdsFunctional is the set of high thresholds |
| // used in functional analysis by normalized_magnitude. |
| // Run [thresholds_functional.py] to generate these numbers. |
| // The magnitudes are expressed in difference in failure rate. |
| // The sample sizes start at 1. |
| // |
| // [thresholds_functional.py]: https://chromium.googlesource.com/catapult.git/+/f25d23e77a963e88af9199c7c3a0638268e44538/dashboard/dashboard/pinpoint/models/compare/thresholds_functional.py |
| var highThresholdsFunctional = thresholds{ |
| // normalized magnitude: 0.1 |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, 1.000, .3285, .3282, .3280, .3278, .3275, .3273, .3271, |
| .3269, .3268, .3266, .3264, .3262, .3261, .3259, .3258, .3256, .3255, |
| .3254, .3252, .3251, .1590, .1589, .1589, .1589, .1589, .1589, .1588, |
| .1588, .1588, .1588, .1587, .1587, .1587, .1587, .1587, .1587, .1586, |
| .0827, .0827, .0827, .0827, .0827, .0827, .0827, .0827, .0827, .0827, |
| .0827, .0827, .0827, .0828, .0828, .0828, .0444, .0444, .0444, .0445, |
| .0445, .0445, .0445, .0445, .0445, .0445, .0445, .0445, .0445, .0446, |
| .0446, .0446, .0244, .0244, .0244, .0244, .0244, .0244, .0244, .0244, |
| .0244, .0244, .0244, .0245, .0245, .0245, .0135, .0135, .0135, .0135, |
| .0136, .0136, .0136, .0136, .0136, .0136, .0136, .0136, .0136, .0136, |
| .0136, .0076, |
| }, |
| // normalized magnitude: 0.2 |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| .3410, .3399, .3389, .3379, .3371, .3363, .3356, .3350, .3343, .3338, |
| .1607, .1606, .1605, .1604, .1603, .1602, .1601, .1601, .0819, .0819, |
| .0820, .0820, .0820, .0821, .0821, .0821, .0432, .0433, .0433, .0433, |
| .0434, .0434, .0435, .0435, .0233, .0233, .0233, .0234, .0234, .0234, |
| .0235, .0127, .0127, .0127, .0128, .0128, .0128, .0128, .0070, |
| }, |
| // normalized magnitude: 0.3 |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, |
| 1.000, 1.000, .3560, .3532, .3507, .3486, .3467, .3450, .3435, .1625, |
| .1623, .1620, .1618, .1616, .0810, .0811, .0812, .0813, .0814, .0418, |
| .0419, .0421, .0422, .0423, .0220, .0221, .0222, .0223, .0224, .0118, |
| .0118, .0119, .0120, .0063, |
| }, |
| // normalized magnitude: 0.4, |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, .3682, |
| .3634, .3594, .3560, .1647, .1642, .1638, .1634, .0800, .0802, .0804, |
| .0806, .0404, .0406, .0409, .0207, .0209, .0210, .0212, .0108, .0109, |
| .0110, .0057, |
| }, |
| // normalized magnitude: 0.5, |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, 1.000, .3914, .3816, .3741, .3682, |
| .1666, .1659, .1652, .0789, .0793, .0796, .0388, .0392, .0192, .0195, |
| .0198, .0098, |
| }, |
| // normalized magnitude: 0.6, |
| { |
| 1.000, 1.000, 1.000, 1.000, 1.000, .4047, .3914, .1700, .1686, .1675, |
| .0775, .0781, .0366, .0373, .0175, .0180, .0185, .0088, |
| }, |
| // normalized magnitude: 0.7, |
| { |
| 1.000, 1.000, 1.000, .4533, .4238, .4047, .1717, .1700, .0758, .0768, |
| .0348, .0156, .0163, .0074, |
| }, |
| // normalized magnitude: 0.8, |
| { |
| 1.000, 1.000, .5050, .4533, .1771, .1740, .0730, .0746, .0322, .0137, |
| .0147, .0064, |
| }, |
| // normalized magnitude: 0.9, |
| { |
| 1.000, .6171, .5050, .1814, .0668, .0706, .0279, .0110, .0043, |
| }, |
| // normalized magnitude: 1.0, |
| { |
| 1.000, .1940, .0469, .0132, .0040, |
| }, |
| } |
| |
| // highThresholdsPerformance is the set of high thresholds |
| // used in functional analysis by normalized magnitude. |
| // Run [thresholds_performance.py] to generate these numbers. |
| // The normalized magnitudes are expressed in multiples of the |
| // interquartile range (IQR). |
| // The sample sizes start at 1. |
| // |
| // [thresholds_performance.py]: https://chromium.googlesource.com/catapult.git/+/f25d23e77a963e88af9199c7c3a0638268e44538/dashboard/dashboard/pinpoint/models/compare/thresholds_performance.py |
| var highThresholdsPerformance = thresholds{ |
| // normalized magnitude 0.3 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| 1.000, |
| .9699, |
| 1.000, |
| .9770, |
| 1.000, |
| .9817, |
| 1.000, |
| .9850, |
| 1.000, |
| .9874, |
| .9768, |
| .9893, |
| .9800, |
| .9907, |
| .9825, |
| .9754, |
| .9846, |
| .9781, |
| .9724, |
| .9804, |
| .9752, |
| .9706, |
| .9776, |
| .9733, |
| .9694, |
| .9756, |
| .9626, |
| .9686, |
| .9656, |
| .9628, |
| .9602, |
| .9578, |
| .9557, |
| .9537, |
| .9518, |
| .9435, |
| .9486, |
| .9409, |
| .9338, |
| .9446, |
| .9378, |
| .9314, |
| .9307, |
| .9249, |
| .9145, |
| .9144, |
| .9144, |
| .9097, |
| .9143, |
| .9012, |
| .9015, |
| .8936, |
| .8860, |
| .8828, |
| .8760, |
| .8807, |
| .8853, |
| .8861, |
| .8833, |
| .8670, |
| .8615, |
| .8529, |
| .8512, |
| .8433, |
| .8266, |
| .8315, |
| .8275, |
| .8322, |
| .8228, |
| .8247, |
| .8077, |
| .8152, |
| .8095, |
| .8014, |
| .7837, |
| .7838, |
| .7720, |
| .7653, |
| .7497, |
| .7126, |
| .7010, |
| .6794, |
| .6730, |
| .6790, |
| .6729, |
| .6651, |
| .6576, |
| .6598, |
| .6307, |
| .6225, |
| .6164, |
| .6122, |
| .5931, |
| .5846, |
| .5764, |
| .5530, |
| .5564, |
| .5643, |
| .5541, |
| .5457, |
| .5377, |
| .5203, |
| .5077, |
| .4930, |
| .5007, |
| .5031, |
| .4842, |
| .4843, |
| .4678, |
| .4623, |
| .4639, |
| .4409, |
| .4297, |
| .4149, |
| .4108, |
| .4150, |
| .3982, |
| .3889, |
| .3941, |
| .3805, |
| .3856, |
| .3718, |
| .3673, |
| .3595, |
| .3528, |
| .3504, |
| .3562, |
| .3467, |
| .3461, |
| .3281, |
| .3219, |
| .3159, |
| .3165, |
| .3156, |
| .3066, |
| .3154, |
| .3120, |
| .3028, |
| .2883, |
| .2824, |
| .2792, |
| .2719, |
| .2735, |
| .2682, |
| .2710, |
| .2648, |
| .2562, |
| .2553, |
| .2426, |
| .2384, |
| .2324, |
| .2380, |
| .2317, |
| .2266, |
| .2142, |
| .2126, |
| .1999, |
| .1961, |
| .1902, |
| .1883, |
| .1831, |
| .1871, |
| .1861, |
| .1776, |
| .1723, |
| .1675, |
| .1613, |
| .1641, |
| .1606, |
| .1548, |
| .1540, |
| .1500, |
| .1486, |
| .1460, |
| .1405, |
| .1352, |
| .1324, |
| .1278, |
| .1307, |
| .1298, |
| .1208, |
| .1223, |
| .1200, |
| .1167, |
| .1192, |
| .1156, |
| .1151, |
| .1145, |
| .1121, |
| .1100, |
| .1025, |
| .1039, |
| .1016, |
| .0998, |
| .1003, |
| .0994, |
| .0920, |
| .0930, |
| .0900, |
| .0872, |
| .0845, |
| .0806, |
| .0813, |
| .0769, |
| .0792, |
| .0766, |
| .0700, |
| .0689, |
| .0693, |
| .0657, |
| .0658, |
| .0655, |
| .0652, |
| .0643, |
| .0629, |
| .0611, |
| .0570, |
| .0572, |
| .0558, |
| .0544, |
| .0533, |
| .0520, |
| .0521, |
| .0499, |
| .0481, |
| .0473, |
| .0477, |
| .0452, |
| .0454, |
| .0453, |
| .0418, |
| .0417, |
| .0417, |
| .0404, |
| .0403, |
| .0375, |
| .0383, |
| .0375, |
| .0381, |
| .0377, |
| .0349, |
| .0349, |
| .0324, |
| .0330, |
| .0310, |
| .0312, |
| .0308, |
| .0310, |
| .0307, |
| .0295, |
| .0286, |
| .0280, |
| .0286, |
| .0272, |
| .0275, |
| .0270, |
| .0255, |
| .0259, |
| .0252, |
| .0236, |
| .0239, |
| .0242, |
| .0231, |
| .0238, |
| .0235, |
| .0232, |
| .0216, |
| .0213, |
| .0212, |
| .0213, |
| .0205, |
| .0201, |
| .0201, |
| .0191, |
| .0197, |
| .0184, |
| .0186, |
| .0186, |
| .0171, |
| .0162, |
| .0165, |
| .0159, |
| .0149, |
| .0146, |
| .0139, |
| .0132, |
| .0131, |
| .0124, |
| .0121, |
| .0120, |
| .0121, |
| .0112, |
| .0114, |
| .0114, |
| .0104, |
| .0105, |
| .0106, |
| .0104, |
| .0102, |
| .0104, |
| .0102, |
| .0102, |
| .0102, |
| .0094, |
| .0092, |
| .0089, |
| .0082, |
| .0081, |
| .0076, |
| .0074, |
| .0074, |
| .0071, |
| .0066, |
| .0067, |
| .0065, |
| .0065, |
| .0059, |
| .0057, |
| .0057, |
| .0054, |
| .0055, |
| .0053, |
| .0050, |
| .0049, |
| .0048, |
| .0047, |
| .0047, |
| .0048, |
| .0045, |
| .0043, |
| .0042, |
| .0042, |
| .0041, |
| .0039, |
| .0040, |
| .0038, |
| .0036, |
| .0036, |
| .0036, |
| .0035, |
| .0035, |
| .0033, |
| .0033, |
| .0033, |
| .0035, |
| .0035, |
| .0033, |
| .0033, |
| .0032, |
| .0030, |
| .0032, |
| .0030, |
| }, |
| // 0.4 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| 1.000, |
| .9699, |
| 1.000, |
| .9770, |
| 1.000, |
| .9817, |
| 1.000, |
| .9850, |
| .9726, |
| .9874, |
| .9768, |
| .9677, |
| .9599, |
| .9720, |
| .9650, |
| .9589, |
| .9536, |
| .9344, |
| .9311, |
| .9282, |
| .9257, |
| .9235, |
| .9104, |
| .9198, |
| .9082, |
| .9170, |
| .8972, |
| .8792, |
| .8627, |
| .8476, |
| .8338, |
| .8286, |
| .8167, |
| .7988, |
| .7757, |
| .7607, |
| .7408, |
| .7283, |
| .7167, |
| .7278, |
| .7171, |
| .6970, |
| .6733, |
| .6561, |
| .6492, |
| .6340, |
| .6283, |
| .6025, |
| .5826, |
| .5715, |
| .5503, |
| .5444, |
| .5356, |
| .5306, |
| .5133, |
| .5062, |
| .4763, |
| .4541, |
| .4336, |
| .4220, |
| .4284, |
| .4176, |
| .3984, |
| .3849, |
| .3702, |
| .3584, |
| .3572, |
| .3427, |
| .3117, |
| .3167, |
| .3083, |
| .3004, |
| .2838, |
| .2786, |
| .2694, |
| .2622, |
| .2554, |
| .2366, |
| .2310, |
| .2234, |
| .2174, |
| .2087, |
| .1956, |
| .1976, |
| .1856, |
| .1833, |
| .1726, |
| .1691, |
| .1658, |
| .1626, |
| .1582, |
| .1519, |
| .1427, |
| .1324, |
| .1305, |
| .1202, |
| .1193, |
| .1158, |
| .1134, |
| .1157, |
| .1101, |
| .1058, |
| .1049, |
| .0960, |
| .0981, |
| .0962, |
| .0913, |
| .0854, |
| .0815, |
| .0770, |
| .0749, |
| .0772, |
| .0758, |
| .0710, |
| .0684, |
| .0660, |
| .0666, |
| .0611, |
| .0591, |
| .0577, |
| .0570, |
| .0530, |
| .0504, |
| .0520, |
| .0500, |
| .0502, |
| .0471, |
| .0481, |
| .0450, |
| .0448, |
| .0410, |
| .0397, |
| .0386, |
| .0357, |
| .0339, |
| .0330, |
| .0315, |
| .0310, |
| .0300, |
| .0293, |
| .0275, |
| .0273, |
| .0257, |
| .0251, |
| .0240, |
| .0228, |
| .0212, |
| .0198, |
| .0194, |
| .0194, |
| .0188, |
| .0176, |
| .0171, |
| .0164, |
| .0153, |
| .0150, |
| .0131, |
| .0130, |
| .0117, |
| .0122, |
| .0117, |
| .0115, |
| .0108, |
| .0098, |
| .0098, |
| .0092, |
| .0087, |
| .0082, |
| .0082, |
| .0079, |
| .0073, |
| .0073, |
| .0067, |
| .0065, |
| .0063, |
| .0063, |
| .0057, |
| .0053, |
| .0052, |
| .0052, |
| .0050, |
| .0049, |
| .0046, |
| .0043, |
| .0041, |
| .0038, |
| .0037, |
| .0038, |
| .0035, |
| .0034, |
| .0033, |
| .0032, |
| .0032, |
| .0029, |
| .0028, |
| .0026, |
| .0025, |
| .0026, |
| .0024, |
| .0025, |
| .0023, |
| .0022, |
| .0023, |
| .0022, |
| .0021, |
| .0020, |
| .0018, |
| .0018, |
| .0017, |
| .0016, |
| .0015, |
| .0015, |
| .0014, |
| .0014, |
| .0013, |
| .0012, |
| .0011, |
| .0012, |
| .0011, |
| .0011, |
| .0010, |
| .0010, |
| .0009, |
| .0009, |
| .0009, |
| .0009, |
| .0008, |
| .0008, |
| .0008, |
| .0007, |
| .0007, |
| .0006, |
| }, |
| // 0.5 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| 1.000, |
| .9699, |
| 1.000, |
| .9770, |
| 1.000, |
| .9817, |
| .9670, |
| .9550, |
| .9451, |
| .9370, |
| .9535, |
| .9246, |
| .9199, |
| .9159, |
| .8952, |
| .8771, |
| .8614, |
| .8477, |
| .8356, |
| .7869, |
| .8035, |
| .7619, |
| .7461, |
| .7524, |
| .7196, |
| .6812, |
| .6469, |
| .6084, |
| .5741, |
| .5643, |
| .5555, |
| .5223, |
| .4810, |
| .4882, |
| .4629, |
| .4452, |
| .4197, |
| .4101, |
| .3846, |
| .3694, |
| .3557, |
| .3260, |
| .3220, |
| .2938, |
| .2828, |
| .2674, |
| .2536, |
| .2481, |
| .2274, |
| .2193, |
| .2003, |
| .1904, |
| .1815, |
| .1686, |
| .1735, |
| .1722, |
| .1570, |
| .1511, |
| .1420, |
| .1372, |
| .1296, |
| .1236, |
| .1163, |
| .1096, |
| .1044, |
| .0919, |
| .0880, |
| .0850, |
| .0791, |
| .0732, |
| .0664, |
| .0642, |
| .0594, |
| .0584, |
| .0519, |
| .0494, |
| .0486, |
| .0441, |
| .0419, |
| .0394, |
| .0355, |
| .0342, |
| .0334, |
| .0316, |
| .0306, |
| .0293, |
| .0297, |
| .0272, |
| .0260, |
| .0235, |
| .0218, |
| .0211, |
| .0187, |
| .0186, |
| .0173, |
| .0165, |
| .0158, |
| .0142, |
| .0124, |
| .0118, |
| .0106, |
| .0102, |
| .0096, |
| .0091, |
| .0087, |
| .0091, |
| .0083, |
| .0078, |
| .0073, |
| .0066, |
| .0063, |
| .0061, |
| }, |
| // 0.6 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| 1.000, |
| .9699, |
| 1.000, |
| .9770, |
| .9592, |
| .9086, |
| .9339, |
| .8951, |
| .8905, |
| .8619, |
| .8610, |
| .7972, |
| .8014, |
| .7693, |
| .7418, |
| .6877, |
| .6555, |
| .6277, |
| .5918, |
| .5719, |
| .5442, |
| .5012, |
| .4556, |
| .4401, |
| .4118, |
| .3739, |
| .3355, |
| .3135, |
| .2894, |
| .2917, |
| .2674, |
| .2542, |
| .2389, |
| .2255, |
| .2012, |
| .1888, |
| .1727, |
| .1587, |
| .1487, |
| .1360, |
| .1232, |
| .1169, |
| .1025, |
| .0955, |
| .0916, |
| .0774, |
| .0759, |
| .0727, |
| .0681, |
| .0601, |
| .0547, |
| .0512, |
| .0453, |
| .0418, |
| .0382, |
| .0338, |
| .0308, |
| .0298, |
| .0286, |
| .0269, |
| .0246, |
| .0207, |
| .0201, |
| .0190, |
| .0179, |
| .0155, |
| .0140, |
| .0122, |
| .0117, |
| .0105, |
| .0098, |
| .0097, |
| .0087, |
| .0081, |
| .0068, |
| .0061, |
| .0058, |
| .0051, |
| .0048, |
| .0046, |
| .0040, |
| .0037, |
| }, |
| // 0.7 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| .9297, |
| .9699, |
| .8956, |
| .8853, |
| .8778, |
| .8362, |
| .8035, |
| .7487, |
| .7048, |
| .6693, |
| .6197, |
| .5793, |
| .5295, |
| .4741, |
| .4163, |
| .4037, |
| .3619, |
| .3367, |
| .2993, |
| .2617, |
| .2373, |
| .2171, |
| .1953, |
| .1730, |
| .1661, |
| .1531, |
| .1421, |
| .1270, |
| .1096, |
| .0997, |
| .0857, |
| .0791, |
| .0706, |
| .0635, |
| .0575, |
| .0494, |
| .0445, |
| .0420, |
| .0356, |
| .0316, |
| .0308, |
| .0272, |
| .0242, |
| .0220, |
| .0191, |
| .0167, |
| .0150, |
| .0136, |
| .0119, |
| .0109, |
| .0097, |
| .0085, |
| .0076, |
| .0066, |
| .0061, |
| .0054, |
| .0046, |
| .0039, |
| .0036, |
| .0030, |
| .0028, |
| .0026, |
| }, |
| // 0.8 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| 1.000, |
| .9582, |
| .9297, |
| .8502, |
| .8439, |
| .7951, |
| .7197, |
| .6295, |
| .6187, |
| .5341, |
| .4910, |
| .4383, |
| .3655, |
| .3235, |
| .2908, |
| .2649, |
| .2270, |
| .2048, |
| .1745, |
| .1561, |
| .1369, |
| .1139, |
| .0993, |
| .0850, |
| .0761, |
| .0649, |
| .0561, |
| .0505, |
| .0446, |
| .0357, |
| .0324, |
| .0281, |
| .0240, |
| .0197, |
| .0176, |
| .0152, |
| .0126, |
| .0108, |
| .0092, |
| .0079, |
| .0070, |
| .0063, |
| .0052, |
| .0041, |
| }, |
| // 0.9 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| .8984, |
| .8749, |
| .7911, |
| .7338, |
| .6936, |
| .6237, |
| .5384, |
| .4484, |
| .4068, |
| .3366, |
| .2857, |
| .2482, |
| .2094, |
| .1806, |
| .1590, |
| .1301, |
| .1088, |
| .0970, |
| .0743, |
| .0659, |
| .0527, |
| .0448, |
| .0387, |
| .0327, |
| .0252, |
| .0221, |
| .0183, |
| .0150, |
| .0128, |
| .0105, |
| .0084, |
| .0073, |
| .0064, |
| .0049, |
| }, |
| // 1.0 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .9362, |
| .8984, |
| .7929, |
| .6589, |
| .5708, |
| .4702, |
| .4026, |
| .3299, |
| .2803, |
| .2291, |
| .1810, |
| .1579, |
| .1329, |
| .1084, |
| .0859, |
| .0702, |
| .0558, |
| .0456, |
| .0364, |
| .0313, |
| .0239, |
| .0196, |
| .0143, |
| .0123, |
| .0095, |
| .0078, |
| .0063, |
| .0048, |
| .0039, |
| .0032, |
| }, |
| // 1.1 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| 1.000, |
| .8102, |
| .7983, |
| .6366, |
| .5365, |
| .4274, |
| .3247, |
| .2603, |
| .2185, |
| .1611, |
| .1354, |
| .1012, |
| .0790, |
| .0642, |
| .0472, |
| .0386, |
| .0306, |
| .0250, |
| .0188, |
| .0138, |
| .0111, |
| }, |
| // 1.2 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| .8346, |
| .8102, |
| .6093, |
| .4949, |
| .3773, |
| .2731, |
| .2122, |
| .1573, |
| .1119, |
| .0936, |
| .0680, |
| .0523, |
| .0388, |
| .0279, |
| .0211, |
| .0144, |
| .0103, |
| .0078, |
| .0061, |
| .0043, |
| .0030, |
| }, |
| // 1.3 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| .8346, |
| .5752, |
| .4433, |
| .3721, |
| .2510, |
| .1859, |
| .1310, |
| .0999, |
| .0727, |
| .0509, |
| .0422, |
| .0275, |
| .0192, |
| .0131, |
| .0094, |
| .0066, |
| }, |
| // 1.4 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .8853, |
| .6762, |
| .4712, |
| .3067, |
| .2702, |
| .1854, |
| .1213, |
| .0878, |
| .0607, |
| .0403, |
| .0259, |
| .0181, |
| .0122, |
| .0080, |
| .0057, |
| .0039, |
| .0026, |
| }, |
| // 1.5 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .6651, |
| .5309, |
| .3785, |
| .2502, |
| .1563, |
| .1120, |
| .0757, |
| .0489, |
| .0304, |
| .0211, |
| .0140, |
| .0090, |
| }, |
| // 1.6 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .6651, |
| .4034, |
| .2980, |
| .1599, |
| .1036, |
| .0774, |
| .0452, |
| .0303, |
| .0166, |
| .0104, |
| .0072, |
| .0048, |
| }, |
| // 1.7 |
| { |
| 1.000, |
| .6986, |
| 1.000, |
| .6651, |
| .4034, |
| .2298, |
| .1253, |
| .0832, |
| .0423, |
| .0258, |
| .0152, |
| .0102, |
| .0066, |
| .0036, |
| .0022, |
| }, |
| // 1.8 |
| { |
| 1.000, |
| .6986, |
| .6626, |
| .4705, |
| .2963, |
| .1735, |
| .0967, |
| .0521, |
| .0341, |
| .0173, |
| .0105, |
| .0061, |
| .0035, |
| .0020, |
| .0011, |
| }, |
| // 1.9 |
| { |
| 1.000, |
| .6986, |
| .6626, |
| .3124, |
| .2101, |
| .1283, |
| .0737, |
| .0406, |
| .0217, |
| .0114, |
| }, |
| // 2.0 |
| { |
| 1.000, |
| .6986, |
| .6626, |
| .3124, |
| .2101, |
| .0927, |
| .0553, |
| .0240, |
| .0135, |
| .0073, |
| }, |
| // 2.1 |
| { |
| 1.000, |
| .6986, |
| .6626, |
| .3124, |
| .1437, |
| .0656, |
| .0410, |
| .0182, |
| .0105, |
| .0046, |
| }, |
| // 2.2 |
| { |
| 1.000, |
| .6986, |
| .3828, |
| .1940, |
| .0947, |
| .0656, |
| .0299, |
| .0136, |
| .0062, |
| .0037, |
| }, |
| // 2.3 |
| { |
| 1.000, |
| .6986, |
| .3828, |
| .1940, |
| .0947, |
| .0454, |
| .0215, |
| .0101, |
| .0048, |
| .0023, |
| }, |
| // 2.4 |
| { |
| 1.000, |
| .6986, |
| .3828, |
| .1940, |
| .0947, |
| .0307, |
| .0152, |
| .0075, |
| .0036, |
| .0018, |
| }, |
| // 2.5 |
| { |
| 1.000, |
| .6986, |
| .3828, |
| .1124, |
| .0602, |
| .0307, |
| .0152, |
| .0075, |
| .0027, |
| .0014, |
| }, |
| // 2.6 |
| { |
| 1.000, |
| .6986, |
| .1905, |
| .1124, |
| .0602, |
| .0203, |
| .0107, |
| .0054, |
| .0020, |
| .0011, |
| }, |
| // 2.7 |
| { |
| 1.000, |
| .6986, |
| .1905, |
| .1124, |
| .0368, |
| .0203, |
| .0107, |
| .0039, |
| .0020, |
| .0008, |
| }, |
| // 2.8 |
| { |
| 1.000, |
| .6986, |
| .1905, |
| .1124, |
| .0368, |
| .0131, |
| .0073, |
| .0039, |
| .0015, |
| .0008, |
| }, |
| // 2.9 |
| { |
| 1.000, |
| .6986, |
| .1905, |
| .0607, |
| .0368, |
| .0131, |
| .0073, |
| .0028, |
| .0015, |
| .0006, |
| }, |
| // 3.0 |
| { |
| 1.000, |
| .2453, |
| .1905, |
| .0607, |
| .0216, |
| .0131, |
| .0050, |
| .0028, |
| .0011, |
| .0005, |
| }, |
| // 3.1 |
| { |
| 1.000, |
| .2453, |
| .1905, |
| .0607, |
| .0216, |
| .0083, |
| .0050, |
| .0020, |
| .0008, |
| .0005, |
| }, |
| // 3.2 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0607, |
| .0216, |
| .0083, |
| .0050, |
| .0020, |
| .0008, |
| .0004, |
| }, |
| // 3.3 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0607, |
| .0216, |
| .0083, |
| .0033, |
| .0020, |
| .0008, |
| .0004, |
| }, |
| // 3.4 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0216, |
| .0083, |
| .0033, |
| .0014, |
| .0006, |
| .0004, |
| }, |
| // 3.5 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0083, |
| .0033, |
| .0014, |
| .0006, |
| .0003, |
| }, |
| // 3.6 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0051, |
| .0033, |
| .0014, |
| .0006, |
| .0003, |
| }, |
| // 3.7 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0051, |
| .0022, |
| .0014, |
| .0006, |
| .0003, |
| }, |
| // 3.8 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0051, |
| .0022, |
| .0010, |
| .0005, |
| .0003, |
| }, |
| // 3.9 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0051, |
| .0022, |
| .0010, |
| .0005, |
| .0002, |
| }, |
| // 4.0 |
| { |
| 1.000, |
| .2453, |
| .0809, |
| .0304, |
| .0122, |
| .0051, |
| .0022, |
| .0010, |
| .0005, |
| .0002, |
| }, |
| } |
