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valtih1978/AnovaVsStudentTest.sc

Created February 6, 2015 19:13
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Comparison of ANOVA F-Test with Student's T-Test
Raw
AnovaVsStudentTest.sc
// Rumor says that they must match. They do indeed (I believe less than 1% mistmach is because
// tables are not 100% complete rather than invalid input data)
import math.pow
object student_vs_anova {
def log(msg: String) {
//println(msg)
} //> log: (msg: String)Unit
def fTest(alpha: Double, var1: Double, freedoms1: Int, var2: Double, freedoms2: Int) = {
val (observedF, hiFreedoms, loFreedoms) = if (var1 > var2) (var1/var2, freedoms1, freedoms2) else (var2/var1, freedoms2, freedoms1)
def report(tails: Int): Any = {
val a2 = alpha * tails / 2
val alternative = (if (tails == 1) "one of the variances is larger" else "variances differ")
try {
val criticalF = fisherTable(a2, hiFreedoms, loFreedoms)
val result = Math.abs(observedF) < criticalF
log("at confidence (1-alpha)=" + (1-alpha) + f", $tails-tailed (alternative H1 = $alternative)" + ", observed:critical F=" + f"$observedF:$criticalF, "
+ (if (result) "observed < critical: difference is insignificant" else "observed > critical, difference is significant")
)
!result
} catch {
case e: Exception => println(tails + f"-tailed F-Test (alpha = $a2) is not available.") ; return null
}
}
(1 to 2) map report
} //> fTest: (alpha: Double, var1: Double, freedoms1: Int, var2: Double, freedoms
//| 2: Int)scala.collection.immutable.IndexedSeq[Any]
def fisherTable(singleSideAlpha: Double, largerVarianceFreedom: Int, lowerVarianceFreedom: Int) = {
// Here are two-sided critical values (vairances are just different). For single-sided
// alphas must be halved.
// first line contains freedoms of larger variance, first column denotes freedoms of smaller variance
// q stands for infinity (Int.MaxValue)
val tables = List(0.1 -> """1 2 3 4 5 7 10 15 20 30 60 120 500 1000
1 39.864 49.500 53.593 55.833 57.240 58.906 60.195 61.220 61.740 62.265 62.794 63.061 63.264 63.296
2 8.5264 8.9999 9.1618 9.2434 9.2926 9.3491 9.3915 9.4248 9.4413 9.4580 9.4745 9.4829 9.4893 9.4902
3 5.5384 5.4624 5.3907 5.3426 5.3092 5.2661 5.2304 5.2003 5.1845 5.1681 5.1513 5.1425 5.1358 5.1347
4 4.5448 4.3245 4.1909 4.1073 4.0505 3.9790 3.9198 3.8704 3.8443 3.8175 3.7896 3.7753 3.7643 3.7625
5 4.0605 3.7798 3.6194 3.5202 3.4530 3.3679 3.2974 3.2379 3.2067 3.1740 3.1402 3.1228 3.1094 3.1071
7 3.5895 3.2575 3.0740 2.9605 2.8833 2.7850 2.7025 2.6322 2.5947 2.5555 2.5142 2.4927 2.4761 2.4735
10 3.2850 2.9244 2.7277 2.6054 2.5216 2.4139 2.3226 2.2434 2.2007 2.1554 2.1071 2.0818 2.0618 2.0587
15 3.0731 2.6951 2.4898 2.3615 2.2729 2.1582 2.0593 1.9722 1.9243 1.8727 1.8168 1.7867 1.7629 1.7590
20 2.9746 2.5893 2.3801 2.2490 2.1582 2.0397 1.9368 1.8450 1.7939 1.7383 1.6768 1.6432 1.6163 1.6118
30 2.8808 2.4887 2.2761 2.1423 2.0493 1.9269 1.8195 1.7222 1.6674 1.6064 1.5376 1.4990 1.4669 1.4617
60 2.7911 2.3932 2.1774 2.0409 1.9457 1.8194 1.7070 1.6034 1.5435 1.4756 1.3953 1.3476 1.3060 1.2989
120 2.7478 2.3473 2.1300 1.9924 1.8959 1.7675 1.6523 1.5450 1.4821 1.4094 1.3203 1.2646 1.2123 1.2026
500 2.7157 2.3132 2.0947 1.9561 1.8588 1.7288 1.6115 1.5009 1.4354 1.3583 1.2600 1.1937 1.1215 1.1057
1000 2.7106 2.3080 2.0892 1.9505 1.8530 1.7228 1.6051 1.4941 1.4281 1.3501 1.2500 1.1813 1.1031 1.0844
""",
0.05 -> """1 2 3 4 5 6 8 12 24 inf
1 161.4 199.5 215.7 224.6 230.2 234.0 238.9 243.9 249.0 254.3
2 18.51 19.00 19.16 19.25 19.30 19.33 19.37 19.41 19.45 19.50
3 10.13 9.55 9.28 9.12 9.01 8.94 8.84 8.74 8.64 8.53
4 7.71 6.94 6.59 6.39 6.26 6.16 6.04 5.91 5.77 5.63
5 6.61 5.79 5.41 5.19 5.05 4.95 4.82 4.68 4.53 4.36
6 5.99 5.14 4.76 4.53 4.39 4.28 4.15 4.00 3.84 3.67
7 5.59 4.74 4.35 4.12 3.97 3.87 3.73 3.57 3.41 3.23
8 5.32 4.46 4.07 3.84 3.69 3.58 3.44 3.28 3.12 2.93
9 5.12 4.26 3.86 3.63 3.48 3.37 3.23 3.07 2.90 2.71
10 4.96 4.10 3.71 3.48 3.33 3.22 3.07 2.91 2.74 2.54
11 4.84 3.98 3.59 3.36 3.20 3.09 2.95 2.79 2.61 2.40
12 4.75 3.88 3.49 3.26 3.11 3.00 2.85 2.69 2.50 2.30
13 4.67 3.80 3.41 3.18 3.02 2.92 2.77 2.60 2.42 2.21
14 4.60 3.74 3.34 3.11 2.96 2.85 2.70 2.53 2.35 2.13
15 4.54 3.68 3.29 3.06 2.90 2.79 2.64 2.48 2.29 2.07
16 4.49 3.63 3.24 3.01 2.85 2.74 2.59 2.42 2.24 2.01
17 4.45 3.59 3.20 2.96 2.81 2.70 2.55 2.38 2.19 1.96
18 4.41 3.55 3.16 2.93 2.77 2.66 2.51 2.34 2.15 1.92
19 4.38 3.52 3.13 2.90 2.74 2.63 2.48 2.31 2.11 1.88
20 4.35 3.49 3.10 2.87 2.71 2.60 2.45 2.28 2.08 1.84
21 4.32 3.47 3.07 2.84 2.68 2.57 2.42 2.25 2.05 1.81
22 4.30 3.44 3.05 2.82 2.66 2.55 2.40 2.23 2.03 1.78
23 4.28 3.42 3.03 2.80 2.64 2.53 2.38 2.20 2.00 1.76
24 4.26 3.40 3.01 2.78 2.62 2.51 2.36 2.18 1.98 1.73
25 4.24 3.38 2.99 2.76 2.60 2.49 2.34 2.16 1.96 1.71
26 4.22 3.37 2.98 2.74 2.59 2.47 2.32 2.15 1.95 1.69
27 4.21 3.35 2.96 2.73 2.57 2.46 2.30 2.13 1.93 1.67
28 4.20 3.34 2.95 2.71 2.56 2.44 2.29 2.12 1.91 1.65
29 4.18 3.33 2.93 2.70 2.54 2.43 2.28 2.10 1.90 1.64
30 4.17 3.32 2.92 2.69 2.53 2.42 2.27 2.09 1.89 1.62
40 4.08 3.23 2.84 2.61 2.45 2.34 2.18 2.00 1.79 1.51
60 4.00 3.15 2.76 2.52 2.37 2.25 2.10 1.92 1.70 1.39
120 3.92 3.07 2.68 2.45 2.29 2.17 2.02 1.83 1.61 1.25
inf 3.84 2.99 2.60 2.37 2.21 2.09 1.94 1.75 1.52 1.00
""",
0.01 -> """1 2 3 4 5 7 10 15 20 30 60 120 500 1000
1 4052.2 4999.5 5403.4 5624.6 5763.6 5928.4 6055.8 6157.3 6208.7 6260.6 6313.0 6339.4 6359.5 6362.7
2 98.503 99.000 99.166 99.249 99.299 99.356 99.399 99.433 99.449 99.466 99.482 99.491 99.497 99.498
3 34.116 30.817 29.457 28.710 28.237 27.672 27.229 26.872 26.690 26.504 26.316 26.221 26.148 26.137
4 21.198 18.000 16.694 15.977 15.522 14.976 14.546 14.198 14.020 13.838 13.652 13.558 13.486 13.474
5 16.258 13.274 12.060 11.392 10.967 10.455 10.051 9.7222 9.5526 9.3793 9.2020 9.1118 9.0424 9.0314
7 12.246 9.5467 8.4513 7.8466 7.4605 6.9929 6.6201 6.3143 6.1554 5.9920 5.8236 5.7373 5.6707 5.6601
10 10.044 7.5594 6.5523 5.9944 5.6363 5.2001 4.8492 4.5582 4.4055 4.2469 4.0818 3.9964 3.9303 3.9195
15 8.6831 6.3588 5.4169 4.8932 4.5557 4.1416 3.8049 3.5223 3.3719 3.2141 3.0471 2.9594 2.8906 2.8796
20 8.0960 5.8489 4.9382 4.4306 4.1027 3.6987 3.3682 3.0880 2.9377 2.7785 2.6078 2.5167 2.4446 2.4330
30 7.5624 5.3903 4.5098 4.0179 3.6990 3.3046 2.9791 2.7002 2.5486 2.3859 2.2078 2.1108 2.0321 2.0192
60 7.0771 4.9774 4.1259 3.6491 3.3388 2.9530 2.6318 2.3522 2.1978 2.0284 1.8362 1.7264 1.6328 1.6169
120 6.8509 4.7865 3.9490 3.4795 3.1736 2.7918 2.4720 2.1914 2.0345 1.8600 1.6557 1.5330 1.4215 1.4015
500 6.6858 4.6479 3.8210 3.3569 3.0539 2.6751 2.3564 2.0746 1.9152 1.7353 1.5175 1.3774 1.2317 1.2007
1000 6.6603 4.6264 3.8012 3.3379 3.0356 2.6571 2.3387 2.0564 1.8967 1.7158 1.4953 1.3513 1.1947 1.1586"""
).toMap
val lines = tables(singleSideAlpha).stripMargin.split('\n'). map{_.replace("inf", Int.MaxValue.toString).split('\t')}
//println ("freedoms (larger, smaller) = " + f"($largerVarianceFreedom, $lowerVarianceFreedom)")
//println("k1 = " + lines(0).mkString(","))
val closestCol = lines(0).takeWhile{_.toDouble < largerVarianceFreedom}.length
var closestLine = lines.takeWhile(_(0).toDouble < lowerVarianceFreedom).length
val k1 = lines(0)(closestCol) ; val k2 = lines(closestLine)(0) ;
val fCritical = lines(closestLine)(Math.min(lines(closestLine).length-1, closestCol+1))
//println("k1/k2 = " + f"$k1/$k2, F_crit = " + fCritical)
log(f"Fisher table ($singleSideAlpha, $largerVarianceFreedom, $lowerVarianceFreedom) = "
+ f"Fisher table ($singleSideAlpha, $k1, $k2) = " + fCritical)
fCritical.toDouble // observed > critical: difference is significant
} //> fisherTable: (singleSideAlpha: Double, largerVarianceFreedom: Int, lowerVar
//| ianceFreedom: Int)Double
def ANOVA3(alpha: Double, pairs: List[(Int, Int, Int)]) = {
val l2 = pairs.map {pair => List(pair._1, pair._2, pair._3).map(_.toDouble)}
ANOVA(alpha, l2)
} //> ANOVA3: (alpha: Double, pairs: List[(Int, Int, Int)])scala.collection.immut
//| able.IndexedSeq[Any]
def ANOVAList(alpha: Double, pairs: List[List[Int]]) = {
ANOVA(alpha, pairs.map {_.map(_.toDouble)})
} //> ANOVAList: (alpha: Double, pairs: List[List[Int]])scala.collection.immutabl
//| e.IndexedSeq[Any]
def ANOVA(alpha: Double, rows: List[List[Double]]) = {
val cols: Int = rows(0).length
def accumulate(rowReduce: List[Double] => Double) = {
rows.foldLeft(0.0) { _ + rowReduce(_)}
}
val avg = accumulate(_.sum)/cols / rows.length
val S_total = accumulate{_.map(e => pow(e - avg,2)).sum }
val groupAvg = (1 to cols) map {group => accumulate(row => row.apply(group-1))/rows.length }
val S_between = (1 to cols).map {group =>
val groupAvg = accumulate(row => row.apply(group-1))/rows.length
rows.length * pow(avg - groupAvg, 2)
}.sum
val S_within = S_total - S_between
val betweenFreedoms = cols-1 ; val withinFreedoms = cols*(rows.length-1)
val between = S_between/betweenFreedoms ; val within = S_within/withinFreedoms
log("avg = " + avg + ", sgen = " + S_total + ", group averages = " + groupAvg
+ ", S_beteen " + S_between + ", S_within = " + S_within
+", normalized square: beteen " + between + ", within = " + within
)
fTest(alpha, between, betweenFreedoms, within, withinFreedoms)
} //> ANOVA: (alpha: Double, rows: List[List[Double]])scala.collection.immutable.
//| IndexedSeq[Any]
def ANOVA2(alpha: Double, sample1: List[Double], sample2: List[Double]) = {
ANOVA(alpha, sample1.zip(sample2) map {pair => List(pair._1, pair._2)})
} //> ANOVA2: (alpha: Double, sample1: List[Double], sample2: List[Double])scala.
//| collection.immutable.IndexedSeq[Any]
def variance(samples: List[Double]): Double = {
var avg = samples.sum / samples.length
samples.foldLeft(0.0) {(acc, x) => acc + pow(x-avg,2)} / (samples.length-1)
} //> variance: (samples: List[Double])Double
def tTest(alpha: Double, averages: List[Double], variances: List[Double], df: Tuple2[Int, Int]) = df match { case(n,m) =>
val df = n+m-2
val tObserved = (averages(0)-averages(1)) * pow(n*m*df/ (variances(0)*(n-1) + variances(1)*(m-1))/(n+m),1.0/2)
log("at confidence (1-alpha)=" + (1-alpha) + ", T observed = " + tObserved)
//println("t-test: averages = " + f"$averages, variances = " + f"$variances, df=$df, fObserved=$tObserved")
var table = List(
// source: https://www.easycalculation.com/statistics/t-distribution-critical-value-table.php
// this is a double-tailed list. For single-tail, use halved alpha
0.1 -> List(Double.NaN, 6.3138,2.9200,2.3534,2.1319,2.0150,1.9432,1.8946,1.8595,1.8331,1.8124,1.7959,1.7823,1.7709,1.7613,1.7530,1.7459,1.7396,1.7341,1.7291,1.7247,1.7207,1.7172,1.7139,1.7109,1.7081,1.7056,1.7033,1.7011,1.6991,1.6973,1.6955,1.6939,1.6924,1.6909,1.6896,1.6883,1.6871,1.6859,1.6849,1.6839,1.6829,1.6820,1.6811,1.6802,1.6794,1.6787,1.6779,1.6772,1.6766,1.6759,1.6753,1.6747,1.6741,1.6736,1.6730,1.6725,1.6720,1.6715,1.6711,1.6706,1.6702,1.6698,1.6694,1.6690,1.6686,1.6683,1.6679,1.6676,1.6673,1.6669,1.6666,1.6663,1.6660,1.6657,1.6654,1.6652,1.6649,1.6646,1.6644,1.6641,1.6639,1.6636,1.6634,1.6632,1.6630,1.6628,1.6626,1.6623,1.6622,1.6620,1.6618,1.6616,1.6614,1.6612,1.6610,1.6609,1.6607,1.6606,1.6604,1.6602,1.6601,1.6599,1.6598,1.6596,1.6595,1.6593,1.6592,1.6591,1.6589,1.6588,1.6587,1.6586,1.6585,1.6583,1.6582,1.6581,1.6580,1.6579,1.6578,1.6577,1.6575,1.6574,1.6573,1.6572,1.6571,1.6570,1.6570,1.6568,1.6568,1.6567,1.6566,1.6565,1.6564,1.6563,1.6562,1.6561,1.6561,1.6560,1.6559,1.6558,1.6557,1.6557,1.6556,1.6555,1.6554,1.6554,1.6553,1.6552,1.6551,1.6551,1.6550,1.6549,1.6549,1.6548,1.6547,1.6547,1.6546,1.6546,1.6545,1.6544,1.6544,1.6543,1.6543,1.6542,1.6542,1.6541,1.6540,1.6540,1.6539,1.6539,1.6538,1.6537,1.6537,1.6537,1.6536,1.6536,1.6535,1.6535,1.6534,1.6534,1.6533,1.6533,1.6532,1.6532,1.6531,1.6531,1.6531,1.6530,1.6529,1.6529,1.6529,1.6528,1.6528,1.6528,1.6527,1.6527,1.6526,1.6526,1.6525,1.6525),
0.05 -> List(Double.NaN, 12.7065,4.3026,3.1824,2.7764,2.5706,2.4469,2.3646,2.3060,2.2621,2.2282,2.2010,2.1788,2.1604,2.1448,2.1314,2.1199,2.1098,2.1009,2.0930,2.0860,2.0796,2.0739,2.0686,2.0639,2.0596,2.0555,2.0518,2.0484,2.0452,2.0423,2.0395,2.0369,2.0345,2.0322,2.0301,2.0281,2.0262,2.0244,2.0227,2.0211,2.0196,2.0181,2.0167,2.0154,2.0141,2.0129,2.0117,2.0106,2.0096,2.0086,2.0076,2.0066,2.0057,2.0049,2.0041,2.0032,2.0025,2.0017,2.0010,2.0003,1.9996,1.9990,1.9983,1.9977,1.9971,1.9966,1.9960,1.9955,1.9950,1.9944,1.9939,1.9935,1.9930,1.9925,1.9921,1.9917,1.9913,1.9909,1.9904,1.9901,1.9897,1.9893,1.9889,1.9886,1.9883,1.9879,1.9876,1.9873,1.9870,1.9867,1.9864,1.9861,1.9858,1.9855,1.9852,1.9850,1.9847,1.9845,1.9842,1.9840,1.9837,1.9835,1.9833,1.9830,1.9828,1.9826,1.9824,1.9822,1.9820,1.9818,1.9816,1.9814,1.9812,1.9810,1.9808,1.9806,1.9805,1.9803,1.9801,1.9799,1.9798,1.9796,1.9794,1.9793,1.9791,1.9790,1.9788,1.9787,1.9785,1.9784,1.9782,1.9781,1.9779,1.9778,1.9777,1.9776,1.9774,1.9773,1.9772,1.9771,1.9769,1.9768,1.9767,1.9766,1.9765,1.9764,1.9762,1.9761,1.9760,1.9759,1.9758,1.9757,1.9756,1.9755,1.9754,1.9753,1.9752,1.9751,1.9750,1.9749,1.9748,1.9747,1.9746,1.9745,1.9744,1.9744,1.9743,1.9742,1.9741,1.9740,1.9739,1.9739,1.9738,1.9737,1.9736,1.9735,1.9735,1.9734,1.9733,1.9732,1.9731,1.9731,1.9730,1.9729,1.9729,1.9728,1.9727,1.9727,1.9726,1.9725,1.9725,1.9724,1.9723,1.9723,1.9722,1.9721,1.9721,1.9720,1.9720,1.9719),
0.02 -> List(Double.NaN, 31.819,6.9646,4.5407,3.7470,3.3650,3.1426,2.9980,2.8965,2.8214,2.7638,2.7181,2.6810,2.6503,2.6245,2.6025,2.5835,2.5669,2.5524,2.5395,2.5280,2.5176,2.5083,2.4998,2.4922,2.4851,2.4786,2.4727,2.4671,2.4620,2.4572,2.4528,2.4487,2.4448,2.4411,2.4377,2.4345,2.4315,2.4286,2.4258,2.4233,2.4208,2.4185,2.4162,2.4142,2.4121,2.4102,2.4083,2.4066,2.4049,2.4033,2.4017,2.4002,2.3988,2.3974,2.3961,2.3948,2.3936,2.3924,2.3912,2.3901,2.3890,2.3880,2.3870,2.3860,2.3851,2.3842,2.3833,2.3824,2.3816,2.3808,2.3800,2.3793,2.3785,2.3778,2.3771,2.3764,2.3758,2.3751,2.3745,2.3739,2.3733,2.3727,2.3721,2.3716,2.3710,2.3705,2.3700,2.3695,2.3690,2.3685,2.3680,2.3676,2.3671,2.3667,2.3662,2.3658,2.3654,2.3650,2.3646,2.3642,2.3638,2.3635,2.3631,2.3627,2.3624,2.3620,2.3617,2.3614,2.3611,2.3607,2.3604,2.3601,2.3598,2.3595,2.3592,2.3589,2.3586,2.3583,2.3581,2.3578,2.3576,2.3573,2.3571,2.3568,2.3565,2.3563,2.3561,2.3559,2.3556,2.3554,2.3552,2.3549,2.3547,2.3545,2.3543,2.3541,2.3539,2.3537,2.3535,2.3533,2.3531,2.3529,2.3527,2.3525,2.3523,2.3522,2.3520,2.3518,2.3516,2.3515,2.3513,2.3511,2.3510,2.3508,2.3507,2.3505,2.3503,2.3502,2.3500,2.3499,2.3497,2.3496,2.3495,2.3493,2.3492,2.3490,2.3489,2.3487,2.3486,2.3485,2.3484,2.3482,2.3481,2.3480,2.3478,2.3477,2.3476,2.3475,2.3474,2.3472,2.3471,2.3470,2.3469,2.3468,2.3467,2.3466,2.3465,2.3463,2.3463,2.3461,2.3460,2.3459,2.3458,2.3457,2.3456,2.3455,2.3454,2.3453,2.3452,2.3451),
0.01 -> List(Double.NaN, 63.655,9.9247,5.8408,4.6041,4.0322,3.7074,3.4995,3.3554,3.2498,3.1693,3.1058,3.0545,3.0123,2.9768,2.9467,2.9208,2.8983,2.8784,2.8609,2.8454,2.8314,2.8188,2.8073,2.7970,2.7874,2.7787,2.7707,2.7633,2.7564,2.7500,2.7440,2.7385,2.7333,2.7284,2.7238,2.7195,2.7154,2.7115,2.7079,2.7045,2.7012,2.6981,2.6951,2.6923,2.6896,2.6870,2.6846,2.6822,2.6800,2.6778,2.6757,2.6737,2.6718,2.6700,2.6682,2.6665,2.6649,2.6633,2.6618,2.6603,2.6589,2.6575,2.6561,2.6549,2.6536,2.6524,2.6512,2.6501,2.6490,2.6479,2.6468,2.6459,2.6449,2.6439,2.6430,2.6421,2.6412,2.6404,2.6395,2.6387,2.6379,2.6371,2.6364,2.6356,2.6349,2.6342,2.6335,2.6328,2.6322,2.6316,2.6309,2.6303,2.6297,2.6292,2.6286,2.6280,2.6275,2.6269,2.6264,2.6259,2.6254,2.6249,2.6244,2.6240,2.6235,2.6230,2.6225,2.6221,2.6217,2.6212,2.6208,2.6204,2.6200,2.6196,2.6192,2.6189,2.6185,2.6181,2.6178,2.6174,2.6171,2.6168,2.6164,2.6161,2.6158,2.6154,2.6151,2.6148,2.6145,2.6142,2.6139,2.6136,2.6133,2.6130,2.6127,2.6125,2.6122,2.6119,2.6117,2.6114,2.6112,2.6109,2.6106,2.6104,2.6102,2.6099,2.6097,2.6094,2.6092,2.6090,2.6088,2.6085,2.6083,2.6081,2.6079,2.6077,2.6075,2.6073,2.6071,2.6069,2.6067,2.6065,2.6063,2.6062,2.6060,2.6058,2.6056,2.6054,2.6052,2.6051,2.6049,2.6047,2.6046,2.6044,2.6042,2.6041,2.6039,2.6037,2.6036,2.6034,2.6033,2.6031,2.6030,2.6028,2.6027,2.6025,2.6024,2.6022,2.6021,2.6019,2.6018,2.6017,2.6015,2.6014,2.6013,2.6012,2.6010,2.6009,2.6008,2.6007),
0.005 -> List(Double.NaN, 127.34,14.088,7.4534,5.5976,4.7734,4.3168,4.0294,3.8325,3.6896,3.5814,3.4966,3.4284,3.3725,3.3257,3.2860,3.2520,3.2224,3.1966,3.1737,3.1534,3.1352,3.1188,3.1040,3.0905,3.0782,3.0669,3.0565,3.0469,3.0380,3.0298,3.0221,3.0150,3.0082,3.0019,2.9961,2.9905,2.9853,2.9803,2.9756,2.9712,2.9670,2.9630,2.9591,2.9555,2.9521,2.9488,2.9456,2.9426,2.9397,2.9370,2.9343,2.9318,2.9293,2.9270,2.9247,2.9225,2.9204,2.9184,2.9164,2.9146,2.9127,2.9110,2.9092,2.9076,2.9060,2.9045,2.9030,2.9015,2.9001,2.8987,2.8974,2.8961,2.8948,2.8936,2.8925,2.8913,2.8902,2.8891,2.8880,2.8870,2.8859,2.8850,2.8840,2.8831,2.8821,2.8813,2.8804,2.8795,2.8787,2.8779,2.8771,2.8763,2.8755,2.8748,2.8741,2.8734,2.8727,2.8720,2.8713,2.8706,2.8700,2.8694,2.8687,2.8682,2.8675,2.8670,2.8664,2.8658,2.8653,2.8647,2.8642,2.8637,2.8632,2.8627,2.8622,2.8617,2.8612,2.8608,2.8603,2.8599,2.8594,2.8590,2.8585,2.8582,2.8577,2.8573,2.8569,2.8565,2.8561,2.8557,2.8554,2.8550,2.8546,2.8542,2.8539,2.8536,2.8532,2.8529,2.8525,2.8522,2.8519,2.8516,2.8512,2.8510,2.8506,2.8503,2.8500,2.8497,2.8494,2.8491,2.8489,2.8486,2.8483,2.8481,2.8478,2.8475,2.8472,2.8470,2.8467,2.8465,2.8463,2.8460,2.8458,2.8455,2.8452,2.8450,2.8448,2.8446,2.8443,2.8441,2.8439,2.8437,2.8435,2.8433,2.8430,2.8429,2.8427,2.8424,2.8423,2.8420,2.8419,2.8416,2.8415,2.8413,2.8411,2.8409,2.8407,2.8406,2.8403,2.8402,2.8400,2.8398,2.8397,2.8395,2.8393,2.8392,2.8390,2.8388,2.8387,2.8385),
0.002 -> List(Double.NaN, 318.49,22.327,10.214,7.1732,5.8934,5.2076,4.7852,4.5008,4.2969,4.1437,4.0247,3.9296,3.8520,3.7874,3.7328,3.6861,3.6458,3.6105,3.5794,3.5518,3.5272,3.5050,3.4850,3.4668,3.4502,3.4350,3.4211,3.4082,3.3962,3.3852,3.3749,3.3653,3.3563,3.3479,3.3400,3.3326,3.3256,3.3190,3.3128,3.3069,3.3013,3.2959,3.2909,3.2861,3.2815,3.2771,3.2729,3.2689,3.2651,3.2614,3.2579,3.2545,3.2513,3.2482,3.2451,3.2423,3.2394,3.2368,3.2342,3.2317,3.2293,3.2269,3.2247,3.2225,3.2204,3.2184,3.2164,3.2144,3.2126,3.2108,3.2090,3.2073,3.2056,3.2040,3.2025,3.2010,3.1995,3.1980,3.1966,3.1953,3.1939,3.1926,3.1913,3.1901,3.1889,3.1877,3.1866,3.1854,3.1844,3.1833,3.1822,3.1812,3.1802,3.1792,3.1782,3.1773,3.1764,3.1755,3.1746,3.1738,3.1729,3.1720,3.1712,3.1704,3.1697,3.1689,3.1681,3.1674,3.1667,3.1660,3.1653,3.1646,3.1640,3.1633,3.1626,3.1620,3.1614,3.1607,3.1601,3.1595,3.1589,3.1584,3.1578,3.1573,3.1567,3.1562,3.1556,3.1551,3.1546,3.1541,3.1536,3.1531,3.1526,3.1522,3.1517,3.1512,3.1508,3.1503,3.1499,3.1495,3.1491,3.1486,3.1482,3.1478,3.1474,3.1470,3.1466,3.1462,3.1458,3.1455,3.1451,3.1447,3.1443,3.1440,3.1436,3.1433,3.1430,3.1426,3.1423,3.1419,3.1417,3.1413,3.1410,3.1407,3.1403,3.1400,3.1398,3.1394,3.1392,3.1388,3.1386,3.1383,3.1380,3.1377,3.1375,3.1372,3.1369,3.1366,3.1364,3.1361,3.1358,3.1356,3.1354,3.1351,3.1349,3.1346,3.1344,3.1341,3.1339,3.1337,3.1334,3.1332,3.1330,3.1328,3.1326,3.1323,3.1321,3.1319,3.1317,3.1315),
0.001 -> List(Double.NaN, 636.04,31.598,12.924,8.6103,6.8688,5.9589,5.4079,5.0414,4.7809,4.5869,4.4369,4.3178,4.2208,4.1404,4.0728,4.0150,3.9651,3.9216,3.8834,3.8495,3.8193,3.7921,3.7676,3.7454,3.7251,3.7067,3.6896,3.6739,3.6594,3.6459,3.6334,3.6218,3.6109,3.6008,3.5912,3.5822,3.5737,3.5657,3.5581,3.5510,3.5442,3.5378,3.5316,3.5258,3.5202,3.5149,3.5099,3.5051,3.5004,3.4960,3.4917,3.4877,3.4838,3.4800,3.4764,3.4730,3.4696,3.4663,3.4632,3.4602,3.4573,3.4545,3.4518,3.4491,3.4466,3.4441,3.4417,3.4395,3.4372,3.4350,3.4329,3.4308,3.4288,3.4269,3.4250,3.4232,3.4214,3.4197,3.4180,3.4164,3.4147,3.4132,3.4117,3.4101,3.4087,3.4073,3.4059,3.4046,3.4032,3.4020,3.4006,3.3995,3.3982,3.3970,3.3959,3.3947,3.3936,3.3926,3.3915,3.3905,3.3894,3.3885,3.3875,3.3866,3.3856,3.3847,3.3838,3.3829,3.3820,3.3812,3.3803,3.3795,3.3787,3.3779,3.3771,3.3764,3.3756,3.3749,3.3741,3.3735,3.3727,3.3721,3.3714,3.3707,3.3700,3.3694,3.3688,3.3682,3.3676,3.3669,3.3663,3.3658,3.3652,3.3646,3.3641,3.3635,3.3630,3.3624,3.3619,3.3614,3.3609,3.3604,3.3599,3.3594,3.3589,3.3584,3.3579,3.3575,3.3570,3.3565,3.3561,3.3557,3.3552,3.3548,3.3544,3.3540,3.3536,3.3531,3.3528,3.3523,3.3520,3.3516,3.3512,3.3508,3.3505,3.3501,3.3497,3.3494,3.3490,3.3487,3.3483,3.3480,3.3477,3.3473,3.3470,3.3466,3.3464,3.3460,3.3457,3.3454,3.3451,3.3448,3.3445,3.3442,3.3439,3.3436,3.3433,3.3430,3.3428,3.3425,3.3422,3.3419,3.3417,3.3414,3.3411,3.3409,3.3406,3.3403,3.3401,3.3398)
) toMap
def report(tails: Int): Any = {
val a2 = alpha * tails / 2
if (!table.contains(a2)) {println(tails + "-tailed T-Test is not available"); return null}
val tCrit = table(a2)(df)
val alternative = if (tails == 1) "larger mean is larger" else "a_mean != b_mean"
val result = Math.abs(tObserved) < tCrit
log(f"$tails-tailed (alternative H1 = $alternative), "
+ (if (result) f"observed < critical $tCrit : difference is insignificant" else f"observed > critical $tCrit : difference is significant")
)
return !result
}
(1 to 2) map report
} //> tTest: (alpha: Double, averages: List[Double], variances: List[Double], df
//| : (Int, Int))scala.collection.immutable.IndexedSeq[Any]
//tTest(0.1, List(31.2, 29.2), List(0.84, 0.40), (12, 18))
/*Student's test*/
def student(alpha: Double, sample1: List[Double], sample2: List[Double]) = {
val samples = List(sample1, sample2)
def accumulate(sample: List[Double], func: Double => Double) = {
sample.foldLeft(0.0){_ + func(_)}
}
def avg(sample: List[Double]) = accumulate(sample, (x: Double) => x) / sample.length
val averages = samples map avg
def variances = List(0, 1) map {i =>
accumulate(samples(i), (x: Double) => pow(x - averages(i), 2))/ (samples(i).length-1)} // no need to divide because we need to muliply in the factor
val (n,m) = (samples(0).length, samples(1).length)
tTest(alpha, averages, variances, (n,m))
} //> student: (alpha: Double, sample1: List[Double], sample2: List[Double])scal
//| a.collection.immutable.IndexedSeq[Any]
def fTestSamples(alpha: Double, list1: List[Double], list2: List[Double]) = {
//val f = fTest(alpha, variance(list1), list1.length-1, variance(list2), list2.length-1)
val f = ANOVA2(alpha, list1, list2)
val t = student(alpha, list1, list2)
val res = List(f, t) map {_.toList}
res
} //> fTestSamples: (alpha: Double, list1: List[Double], list2: List[Double])Lis
//| t[List[Any]]
//fTest(0.05, 0.84, 13, 2.52, 9)
//student(0.1, List(3.4, 3.4, 3.5, 3.5, 3.5, 3.7, 3.7, 3.7, 3.7, 3.9), List(3.2, 3.2, 3.4, 3.4, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6))
fTestSamples(0.1, List(9.6, 10, 9.8, 10.2, 10.6), List(10.4, 9.7, 10, 10.3))
//> res0: List[List[Any]] = List(List(false, false), List(false, false))
ANOVA3(0.05, List((38,20,21), (36,24,22), (35,26,31), (31,30,34)))
//> 1-tailed F-Test (alpha = 0.025) is not available.
//| res1: scala.collection.immutable.IndexedSeq[Any] = Vector(null, true)
val N = 2000 //> N : Int = 2000
val failures = (1 to N) map {_ =>
def gen() = {
val avg = Math.random() * 100
val list = List.tabulate(50){_ => Math.random()*100 + avg} map {_.toInt}
(avg, list)
}
val s1 = gen() ; val s2 = gen()
val result = fTestSamples(0.1, s1._2 map {_.toDouble}, s2._2 map {_.toDouble})
//(s1._1 + ", " + s2._1 + ": " + result +
//(if (result(0) != result(1)) s1._1 + ", " + s2._1 + ": " + result + s1._2 + ", " + s2._2 else "")} filter(_.length > 0 ) mkString("\n")
result} filter (r => r(0) != r(1))//> failures : scala.collection.immutable.IndexedSeq[List[List[Any]]] = Vecto
//| r(List(List(false, true), List(false, false)), List(List(false, true), Lis
//| t(false, false)), List(List(false, true), List(false, false)), List(List(f
//| alse, true), List(false, false)), List(List(true, true), List(false, true)
//| ), List(List(true, true), List(false, true)), List(List(false, true), List
//| (false, false)), List(List(false, true), List(false, false)), List(List(fa
//| lse, true), List(false, false)))
println ("t-test mismatches f-test with as " + failures.length + " / "+ N + " = " + (failures.length.toDouble/N*100) + '%')
//> t-test mismatches f-test with as 9 / 2000 = 0.44999999999999996%
}
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