P-value correction: Difference between revisions
→{{header|D}}
Line 883:
Same as Kotlin (Version 2) output.
</pre>
=={{header|C#}}==
{{trans|Java}}
<lang csharp>using System;
using System.Collections.Generic;
using System.Linq;
namespace PValueCorrection {
class Program {
static List<int> SeqLen(int start, int end) {
var result = new List<int>();
if (start == end) {
for (int i = 0; i < end + 1; ++i) {
result.Add(i + 1);
}
} else if (start < end) {
for (int i = 0; i < end - start + 1; ++i) {
result.Add(start + i);
}
} else {
for (int i = 0; i < start - end + 1; ++i) {
result.Add(start - i);
}
}
return result;
}
static List<int> Order(List<double> array, bool decreasing) {
List<int> idx = new List<int>();
for (int i = 0; i < array.Count; ++i) {
idx.Add(i);
}
IComparer<int> cmp;
if (decreasing) {
cmp = Comparer<int>.Create((a, b) => array[a] < array[b] ? 1 : array[b] < array[a] ? -1 : 0);
} else {
cmp = Comparer<int>.Create((a, b) => array[b] < array[a] ? 1 : array[a] < array[b] ? -1 : 0);
}
idx.Sort(cmp);
return idx;
}
static List<double> Cummin(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummin requires at least one element");
var output = new List<double>();
double cumulativeMin = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] < cumulativeMin) cumulativeMin = array[i];
output.Add(cumulativeMin);
}
return output;
}
static List<double> Cummax(List<double> array) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("cummax requires at least one element");
var output = new List<double>();
double cumulativeMax = array[0];
for (int i = 0; i < array.Count; ++i) {
if (array[i] > cumulativeMax) cumulativeMax = array[i];
output.Add(cumulativeMax);
}
return output;
}
static List<double> Pminx(List<double> array, double x) {
if (array.Count < 1) throw new ArgumentOutOfRangeException("pmin requires at least one element");
var result = new List<double>();
for (int i = 0; i < array.Count; ++i) {
if (array[i] < x) {
result.Add(array[i]);
} else {
result.Add(x);
}
}
return result;
}
static void Say(List<double> array) {
Console.Write("[ 1] {0:E}", array[0]);
for (int i = 1; i < array.Count; ++i) {
Console.Write(" {0:E}", array[i]);
if ((i + 1) % 5 == 0) Console.Write("\n[{0,2}]", i + 1);
}
Console.WriteLine();
}
static List<double> PAdjust(List<double> pvalues, string str) {
var size = pvalues.Count;
if (size < 1) throw new ArgumentOutOfRangeException("pAdjust requires at least one element");
int type;
switch (str.ToLower()) {
case "bh":
case "fdr":
type = 0;
break;
case "by":
type = 1;
break;
case "bonferroni":
type = 2;
break;
case "hochberg":
type = 3;
break;
case "holm":
type = 4;
break;
case "hommel":
type = 5;
break;
default:
throw new ArgumentException(str + " doesn't match any accepted FDR types");
}
if (2 == type) { // Bonferroni method
var result2 = new List<double>();
for (int i = 0; i < size; ++i) {
double b = pvalues[i] * size;
if (b >= 1) {
result2.Add(1);
} else if (0 <= b && b < 1) {
result2.Add(b);
} else {
throw new Exception(b + " is outside [0, 1)");
}
}
return result2;
} else if (4 == type) { // Holm method
var o4 = Order(pvalues, false);
var o4d = o4.ConvertAll(x => (double)x);
var cummaxInput = new List<double>();
for (int i = 0; i < size; ++i) {
cummaxInput.Add((size - i) * pvalues[o4[i]]);
}
var ro4 = Order(o4d, false);
var cummaxOutput = Cummax(cummaxInput);
var pmin4 = Pminx(cummaxOutput, 1.0);
var hr = new List<double>();
for (int i = 0; i < size; ++i) {
hr.Add(pmin4[ro4[i]]);
}
return hr;
} else if (5 == type) { // Hommel method
var indices = SeqLen(size, size);
var o5 = Order(pvalues, false);
var p = new List<double>();
for (int i = 0; i < size; ++i) {
p.Add(pvalues[o5[i]]);
}
var o5d = o5.ConvertAll(x => (double)x);
var ro5 = Order(o5d, false);
var q = new List<double>();
var pa = new List<double>();
var npi = new List<double>();
for (int i = 0; i < size; ++i) {
npi.Add(p[i] * size / indices[i]);
}
double min = npi.Min();
q.AddRange(Enumerable.Repeat(min, size));
pa.AddRange(Enumerable.Repeat(min, size));
for (int j = size; j >= 2; --j) {
var ij = SeqLen(1, size - j + 1);
for (int i = 0; i < size - j + 1; ++i) {
ij[i]--;
}
int i2Length = j - 1;
var i2 = new List<int>();
for (int i = 0; i < i2Length; ++i) {
i2.Add(size - j + 2 + i - 1);
}
double q1 = j * p[i2[0]] / 2.0;
for (int i = 1; i < i2Length; ++i) {
double temp_q1 = p[i2[i]] * j / (2.0 + i);
if (temp_q1 < q1) q1 = temp_q1;
}
for (int i = 0; i < size - j + 1; ++i) {
q[ij[i]] = Math.Min(p[ij[i]] * j, q1);
}
for (int i = 0; i < i2Length; ++i) {
q[i2[i]] = q[size - j];
}
for (int i = 0; i < size; ++i) {
if (pa[i] < q[i]) {
pa[i] = q[i];
}
}
}
for (int i = 0; i < size; ++i) {
q[i] = pa[ro5[i]];
}
return q;
}
var ni = new List<double>();
var o = Order(pvalues, true);
var od = o.ConvertAll(x => (double)x);
for (int i = 0; i < size; ++i) {
if (pvalues[i] < 0 || pvalues[i] > 1) {
throw new Exception("array[" + i + "] = " + pvalues[i] + " is outside [0, 1]");
}
ni.Add((double)size / (size - i));
}
var ro = Order(od, false);
var cumminInput = new List<double>();
if (0 == type) { // BH method
for (int i = 0; i < size; ++i) {
cumminInput.Add(ni[i] * pvalues[o[i]]);
}
} else if (1 == type) { // BY method
double q = 0;
for (int i = 1; i < size + 1; ++i) {
q += 1.0 / i;
}
for (int i = 0; i < size; ++i) {
cumminInput.Add(q * ni[i] * pvalues[o[i]]);
}
} else if (3 == type) { // Hochberg method
for (int i = 0; i < size; ++i) {
cumminInput.Add((i + 1) * pvalues[o[i]]);
}
}
var cumminArray = Cummin(cumminInput);
var pmin = Pminx(cumminArray, 1.0);
var result = new List<double>();
for (int i = 0; i < size; ++i) {
result.Add(pmin[ro[i]]);
}
return result;
}
static void Main(string[] args) {
var pvalues = new List<double> {
4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01,
8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01,
4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01,
8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02,
3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01,
1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02,
4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04,
3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04,
1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04,
2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03
};
var correctAnswers = new List<List<double>> {
new List<double> { // Benjamini-Hochberg
6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01,
9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01,
6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01,
9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01,
4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01,
2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01,
1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03,
2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03,
4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03,
2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02
},
new List<double> { // Benjamini & Yekutieli
1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01,
7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02,
1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02,
2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02,
1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02
},
new List<double> { // Bonferroni
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00,
2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02,
1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02,
9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02,
1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01
},
new List<double> { // Hochberg
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01,
1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Holm
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00,
1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00,
1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02,
1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02,
8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02,
1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01
},
new List<double> { // Hommel
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01,
9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01,
9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01,
1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02,
1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02,
8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02,
9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01
}
};
string[] types = { "bh", "by", "bonferroni", "hochberg", "holm", "hommel" };
for (int type = 0; type < types.Length; ++type) {
var q = PAdjust(pvalues, types[type]);
double error = 0.0;
for (int i = 0; i < pvalues.Count; ++i) {
error += Math.Abs(q[i] - correctAnswers[type][i]);
}
Say(q);
Console.WriteLine("type {0} = '{1}' has a cumulative error of {2:E}", type, types[type], error);
Console.WriteLine();
}
}
}
}</lang>
{{out}}
<pre>[ 1] 6.126681E-001 8.521710E-001 1.987205E-001 1.891595E-001 3.217789E-001
[ 5] 9.301450E-001 4.870370E-001 9.301450E-001 6.049731E-001 6.826753E-001
[10] 6.482629E-001 7.253723E-001 5.280973E-001 8.769926E-001 4.705703E-001
[15] 9.241867E-001 6.049731E-001 7.856107E-001 4.887526E-001 1.136717E-001
[20] 4.991891E-001 8.769926E-001 9.991834E-001 3.217789E-001 9.301450E-001
[25] 2.304958E-001 5.832475E-001 3.899547E-002 8.521710E-001 1.476843E-001
[30] 1.683638E-002 2.562902E-003 3.516084E-002 6.250189E-002 3.636589E-003
[35] 2.562902E-003 2.946883E-002 6.166064E-003 3.899547E-002 2.688991E-003
[40] 4.502863E-004 1.252228E-005 7.881555E-002 3.142613E-002 4.846527E-003
[45] 2.562902E-003 4.846527E-003 1.101708E-003 7.252033E-002 2.205958E-002
[50]
type 0 = 'bh' has a cumulative error of 8.030529E-007
[ 1] 1.000000E+000 1.000000E+000 8.940844E-001 8.510676E-001 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 5.114323E-001
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 1.754486E-001 1.000000E+000 6.644618E-001
[30] 7.575031E-002 1.153102E-002 1.581959E-001 2.812089E-001 1.636176E-002
[35] 1.153102E-002 1.325863E-001 2.774239E-002 1.754486E-001 1.209832E-002
[40] 2.025930E-003 5.634031E-005 3.546073E-001 1.413926E-001 2.180552E-002
[45] 1.153102E-002 2.180552E-002 4.956812E-003 3.262838E-001 9.925057E-002
[50]
type 1 = 'by' has a cumulative error of 3.640716E-007
[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 7.019185E-001 1.000000E+000 1.000000E+000
[30] 2.020365E-001 1.516675E-002 5.625735E-001 1.000000E+000 2.909271E-002
[35] 1.537741E-002 4.125636E-001 6.782670E-002 6.803480E-001 1.882294E-002
[40] 9.005725E-004 1.252228E-005 1.000000E+000 4.713920E-001 4.395577E-002
[45] 1.088916E-002 4.846527E-002 3.305125E-003 1.000000E+000 2.867745E-001
[50]
type 2 = 'bonferroni' has a cumulative error of 6.500000E-008
[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.632662E-001 9.991834E-001 9.991834E-001
[30] 1.575885E-001 1.383967E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.383967E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 3 = 'hochberg' has a cumulative error of 2.737500E-007
[ 1] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[ 5] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[10] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[15] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[20] 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000 1.000000E+000
[25] 1.000000E+000 1.000000E+000 4.632662E-001 1.000000E+000 1.000000E+000
[30] 1.575885E-001 1.395341E-002 3.938015E-001 7.600230E-001 2.501973E-002
[35] 1.395341E-002 3.052971E-001 5.426136E-002 4.626366E-001 1.656419E-002
[40] 8.825611E-004 1.252228E-005 9.930759E-001 3.394022E-001 3.692284E-002
[45] 1.023581E-002 3.974152E-002 3.172920E-003 8.992520E-001 2.179486E-001
[50]
type 4 = 'holm' has a cumulative error of 2.809500E-007
[ 1] 9.991834E-001 9.991834E-001 9.991834E-001 9.987624E-001 9.991834E-001
[ 5] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[10] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[15] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.595180E-001
[20] 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001 9.991834E-001
[25] 9.991834E-001 9.991834E-001 4.351895E-001 9.991834E-001 9.766523E-001
[30] 1.414256E-001 1.304340E-002 3.530937E-001 6.887709E-001 2.385602E-002
[35] 1.322457E-002 2.722920E-001 5.426136E-002 4.218158E-001 1.581127E-002
[40] 8.825611E-004 1.252228E-005 8.743649E-001 3.016908E-001 3.516461E-002
[45] 9.582456E-003 3.877222E-002 3.172920E-003 8.122276E-001 1.950067E-001
[50]
type 5 = 'hommel' has a cumulative error of 4.353024E-007</pre>
=={{header|D}}==
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