function (level) { return level * 100 + '%'; } ).join(', ') + ' confidence intervals.');
return NaN;
}
- if (numberOfSamples - 2 < 0)
- return NaN;
+ if (numberOfSamples < 2)
+ return Number.POSITIVE_INFINITY;
var cdfForProbability = tDistributionInverseCDF[probability];
var degreesOfFreedom = numberOfSamples - 1;
- if (degreesOfFreedom > cdfForProbability.length) {
- console.warn('We only support up to ' + cdfForProbability.length + ' degrees of freedom');
- return NaN;
- }
// tDistributionQuantile(degreesOfFreedom, confidenceLevel) * sampleStandardDeviation / sqrt(numberOfSamples) * S/sqrt(numberOfSamples)
- var quantile = cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom.
+ if (degreesOfFreedom <= 100)
+ var quantile = cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom.
+ else if (degreesOfFreedom <= 300)
+ var quantile = cdfForProbability[Math.round(degreesOfFreedom / 10) + 100 - 10 - 1];
+ else if (degreesOfFreedom <= 1300)
+ var quantile = cdfForProbability[Math.round(degreesOfFreedom / 100) + 120 - 3 - 1];
+ else
+ var quantile = cdfForProbability[cdfForProbability.length - 1];
return quantile * this.sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.sqrt(numberOfSamples);
}
// See http://en.wikipedia.org/wiki/Student's_t-distribution#Table_of_selected_values
// This table contains one sided (a.k.a. tail) values.
+ // Use TINV((1 - probability) * 2, df) in your favorite spreadsheet software to compute these.
+ // The spacing of the values with df greater than 100 maintains error less than 0.8%.
var tDistributionInverseCDF = {
0.9: [
+ // 1 - 100 step 1
3.077684, 1.885618, 1.637744, 1.533206, 1.475884, 1.439756, 1.414924, 1.396815, 1.383029, 1.372184,
1.363430, 1.356217, 1.350171, 1.345030, 1.340606, 1.336757, 1.333379, 1.330391, 1.327728, 1.325341,
1.323188, 1.321237, 1.319460, 1.317836, 1.316345, 1.314972, 1.313703, 1.312527, 1.311434, 1.310415,
1.309464, 1.308573, 1.307737, 1.306952, 1.306212, 1.305514, 1.304854, 1.304230, 1.303639, 1.303077,
1.302543, 1.302035, 1.301552, 1.301090, 1.300649, 1.300228, 1.299825, 1.299439, 1.299069, 1.298714,
-
1.298373, 1.298045, 1.297730, 1.297426, 1.297134, 1.296853, 1.296581, 1.296319, 1.296066, 1.295821,
1.295585, 1.295356, 1.295134, 1.294920, 1.294712, 1.294511, 1.294315, 1.294126, 1.293942, 1.293763,
1.293589, 1.293421, 1.293256, 1.293097, 1.292941, 1.292790, 1.292643, 1.292500, 1.292360, 1.292224,
1.292091, 1.291961, 1.291835, 1.291711, 1.291591, 1.291473, 1.291358, 1.291246, 1.291136, 1.291029,
- 1.290924, 1.290821, 1.290721, 1.290623, 1.290527, 1.290432, 1.290340, 1.290250, 1.290161, 1.290075],
+ 1.290924, 1.290821, 1.290721, 1.290623, 1.290527, 1.290432, 1.290340, 1.290250, 1.290161, 1.290075,
+ // 110 - 300 step 10
+ 1.289295, 1.288646, 1.288098, 1.287628, 1.287221, 1.286865, 1.286551, 1.286272, 1.286023, 1.285799,
+ 1.285596, 1.285411, 1.285243, 1.285089, 1.284947, 1.284816, 1.284695, 1.284582, 1.284478, 1.284380,
+ // 400 - 1300 step 100
+ 1.283672, 1.283247, 1.282964, 1.282762, 1.282611, 1.282493, 1.282399, 1.282322, 1.282257, 1.282203,
+ // Infinity
+ 1.281548],
0.95: [
+ // 1 - 100 step 1
6.313752, 2.919986, 2.353363, 2.131847, 2.015048, 1.943180, 1.894579, 1.859548, 1.833113, 1.812461,
1.795885, 1.782288, 1.770933, 1.761310, 1.753050, 1.745884, 1.739607, 1.734064, 1.729133, 1.724718,
1.720743, 1.717144, 1.713872, 1.710882, 1.708141, 1.705618, 1.703288, 1.701131, 1.699127, 1.697261,
1.695519, 1.693889, 1.692360, 1.690924, 1.689572, 1.688298, 1.687094, 1.685954, 1.684875, 1.683851,
1.682878, 1.681952, 1.681071, 1.680230, 1.679427, 1.678660, 1.677927, 1.677224, 1.676551, 1.675905,
-
1.675285, 1.674689, 1.674116, 1.673565, 1.673034, 1.672522, 1.672029, 1.671553, 1.671093, 1.670649,
1.670219, 1.669804, 1.669402, 1.669013, 1.668636, 1.668271, 1.667916, 1.667572, 1.667239, 1.666914,
1.666600, 1.666294, 1.665996, 1.665707, 1.665425, 1.665151, 1.664885, 1.664625, 1.664371, 1.664125,
1.663884, 1.663649, 1.663420, 1.663197, 1.662978, 1.662765, 1.662557, 1.662354, 1.662155, 1.661961,
- 1.661771, 1.661585, 1.661404, 1.661226, 1.661052, 1.660881, 1.660715, 1.660551, 1.660391, 1.660234],
+ 1.661771, 1.661585, 1.661404, 1.661226, 1.661052, 1.660881, 1.660715, 1.660551, 1.660391, 1.660234,
+ // 110 - 300 step 10
+ 1.658824, 1.657651, 1.656659, 1.655811, 1.655076, 1.654433, 1.653866, 1.653363, 1.652913, 1.652508,
+ 1.652142, 1.651809, 1.651506, 1.651227, 1.650971, 1.650735, 1.650517, 1.650314, 1.650125, 1.649949,
+ // 400 - 1300 step 100
+ 1.648672, 1.647907, 1.647397, 1.647033, 1.646761, 1.646548, 1.646379, 1.646240, 1.646124, 1.646027,
+ // Infinity
+ 1.644847],
0.975: [
+ // 1 - 100 step 1
12.706205, 4.302653, 3.182446, 2.776445, 2.570582, 2.446912, 2.364624, 2.306004, 2.262157, 2.228139,
2.200985, 2.178813, 2.160369, 2.144787, 2.131450, 2.119905, 2.109816, 2.100922, 2.093024, 2.085963,
2.079614, 2.073873, 2.068658, 2.063899, 2.059539, 2.055529, 2.051831, 2.048407, 2.045230, 2.042272,
2.039513, 2.036933, 2.034515, 2.032245, 2.030108, 2.028094, 2.026192, 2.024394, 2.022691, 2.021075,
2.019541, 2.018082, 2.016692, 2.015368, 2.014103, 2.012896, 2.011741, 2.010635, 2.009575, 2.008559,
-
2.007584, 2.006647, 2.005746, 2.004879, 2.004045, 2.003241, 2.002465, 2.001717, 2.000995, 2.000298,
1.999624, 1.998972, 1.998341, 1.997730, 1.997138, 1.996564, 1.996008, 1.995469, 1.994945, 1.994437,
1.993943, 1.993464, 1.992997, 1.992543, 1.992102, 1.991673, 1.991254, 1.990847, 1.990450, 1.990063,
1.989686, 1.989319, 1.988960, 1.988610, 1.988268, 1.987934, 1.987608, 1.987290, 1.986979, 1.986675,
- 1.986377, 1.986086, 1.985802, 1.985523, 1.985251, 1.984984, 1.984723, 1.984467, 1.984217, 1.983972],
+ 1.986377, 1.986086, 1.985802, 1.985523, 1.985251, 1.984984, 1.984723, 1.984467, 1.984217, 1.983972,
+ // 110 - 300 step 10
+ 1.981765, 1.979930, 1.978380, 1.977054, 1.975905, 1.974902, 1.974017, 1.973231, 1.972528, 1.971896,
+ 1.971325, 1.970806, 1.970332, 1.969898, 1.969498, 1.969130, 1.968789, 1.968472, 1.968178, 1.967903,
+ // 400 - 1300 step 100
+ 1.965912, 1.964720, 1.963926, 1.963359, 1.962934, 1.962603, 1.962339, 1.962123, 1.961943, 1.961790,
+ // Infinity
+ 1.959964],
0.99: [
+ // 1 - 100 step 1
31.820516, 6.964557, 4.540703, 3.746947, 3.364930, 3.142668, 2.997952, 2.896459, 2.821438, 2.763769,
2.718079, 2.680998, 2.650309, 2.624494, 2.602480, 2.583487, 2.566934, 2.552380, 2.539483, 2.527977,
2.517648, 2.508325, 2.499867, 2.492159, 2.485107, 2.478630, 2.472660, 2.467140, 2.462021, 2.457262,
2.452824, 2.448678, 2.444794, 2.441150, 2.437723, 2.434494, 2.431447, 2.428568, 2.425841, 2.423257,
2.420803, 2.418470, 2.416250, 2.414134, 2.412116, 2.410188, 2.408345, 2.406581, 2.404892, 2.403272,
-
2.401718, 2.400225, 2.398790, 2.397410, 2.396081, 2.394801, 2.393568, 2.392377, 2.391229, 2.390119,
2.389047, 2.388011, 2.387008, 2.386037, 2.385097, 2.384186, 2.383302, 2.382446, 2.381615, 2.380807,
2.380024, 2.379262, 2.378522, 2.377802, 2.377102, 2.376420, 2.375757, 2.375111, 2.374482, 2.373868,
2.373270, 2.372687, 2.372119, 2.371564, 2.371022, 2.370493, 2.369977, 2.369472, 2.368979, 2.368497,
- 2.368026, 2.367566, 2.367115, 2.366674, 2.366243, 2.365821, 2.365407, 2.365002, 2.364606, 2.364217]
+ 2.368026, 2.367566, 2.367115, 2.366674, 2.366243, 2.365821, 2.365407, 2.365002, 2.364606, 2.364217,
+ // 110 - 300 step 10
+ 2.360726, 2.357825, 2.355375, 2.353278, 2.351465, 2.349880, 2.348483, 2.347243, 2.346134, 2.345137,
+ 2.344236, 2.343417, 2.342670, 2.341985, 2.341356, 2.340775, 2.340238, 2.339739, 2.339275, 2.338842,
+ // 400 - 1300 step 100
+ 2.335706, 2.333829, 2.332579, 2.331687, 2.331018, 2.330498, 2.330083, 2.329743, 2.329459, 2.329220,
+ // Infinity
+ 2.326348],
};
})();
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