4 /* This program is implemented with ideas from this web page:
6 * http://www.langsrud.com/fisher.htm
10 static double lbinom(int n, int k)
12 if (k == 0 || n == k) return 0;
13 return lgamma(n+1) - lgamma(k+1) - lgamma(n-k+1);
21 // hypergeometric distribution
22 static double hypergeo(int n11, int n1_, int n_1, int n)
24 return exp(lbinom(n1_, n11) + lbinom(n-n1_, n_1-n11) - lbinom(n, n_1));
32 // incremental version of hypergenometric distribution
33 static double hypergeo_acc(int n11, int n1_, int n_1, int n, hgacc_t *aux)
35 if (n1_ || n_1 || n) {
36 aux->n11 = n11; aux->n1_ = n1_; aux->n_1 = n_1; aux->n = n;
37 } else { // then only n11 changed; the rest fixed
38 if (n11%11 && n11 + aux->n - aux->n1_ - aux->n_1) {
39 if (n11 == aux->n11 + 1) { // incremental
40 aux->p *= (double)(aux->n1_ - aux->n11) / n11
41 * (aux->n_1 - aux->n11) / (n11 + aux->n - aux->n1_ - aux->n_1);
45 if (n11 == aux->n11 - 1) { // incremental
46 aux->p *= (double)aux->n11 / (aux->n1_ - n11)
47 * (aux->n11 + aux->n - aux->n1_ - aux->n_1) / (aux->n_1 - n11);
54 aux->p = hypergeo(aux->n11, aux->n1_, aux->n_1, aux->n);
58 double kt_fisher_exact(int n11, int n12, int n21, int n22, double *_left, double *_right, double *two)
61 double p, q, left, right;
65 n1_ = n11 + n12; n_1 = n11 + n21; n = n11 + n12 + n21 + n22; // calculate n1_, n_1 and n
66 max = (n_1 < n1_) ? n_1 : n1_; // max n11, for right tail
67 min = (n1_ + n_1 - n < 0) ? 0 : (n1_ + n_1 - n < 0); // min n11, for left tail
68 *two = *_left = *_right = 1.;
69 if (min == max) return 1.; // no need to do test
70 q = hypergeo_acc(n11, n1_, n_1, n, &aux); // the probability of the current table
72 p = hypergeo_acc(min, 0, 0, 0, &aux);
73 for (left = 0., i = min + 1; p < 0.99999999 * q; ++i) // loop until underflow
74 left += p, p = hypergeo_acc(i, 0, 0, 0, &aux);
76 if (p < 1.00000001 * q) left += p;
79 p = hypergeo_acc(max, 0, 0, 0, &aux);
80 for (right = 0., j = max - 1; p < 0.99999999 * q; --j) // loop until underflow
81 right += p, p = hypergeo_acc(j, 0, 0, 0, &aux);
82 if (p < 1.00000001 * q) right += p;
86 if (*two > 1.) *two = 1.;
87 // adjust left and right
88 if (abs(i - n11) < abs(j - n11)) right = 1. - left + q;
89 else left = 1.0 - right + q;
90 *_left = left; *_right = right;
97 int main(int argc, char *argv[])
100 int n11, n12, n21, n22;
101 double left, right, twotail, prob;
103 while (scanf("%s%d%d%d%d", id, &n11, &n12, &n21, &n22) == 5) {
104 prob = kt_fisher_exact(n11, n12, n21, n22, &left, &right, &twotail);
105 printf("%s\t%d\t%d\t%d\t%d\t%.6g\t%.6g\t%.6g\t%.6g\n", id, n11, n12, n21, n22,
106 prob, left, right, twotail);