Welch's t-test

Welch's t-test is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given two lists of data, calculate the p-Value used for null hypothesis testing.

C

Works with: C99

This shows how pvalue can be calculated from any two arrays, using Welch's 2-sided t-test, which doesn't assume equal variance. The high "n" value ensures roughly 17 digits convergence with Simpson's integral approximation. <lang C>#include <stdio.h>

1. include <math.h>

double calculate_pvalue (const double *array1, const size_t array1_size, const double *array2, const size_t array2_size) { double mean1 = 0.0, mean2 = 0.0; // printf("array1:"); for (size_t x = 0; x < array1_size; x++) { mean1 += array1[x]; // printf("\t%.1f",array1[x]); // printf("array[%d] = %lf\n",x,array1[x]); } // printf("\narray2:"); for (size_t x = 0; x < array2_size; x++) { mean2 += array2[x]; // printf("\t%.1f",array2[x]); // printf("array[%d] = %lf\n",x,array2[x]); } mean1 /= array1_size; mean2 /= array2_size; double variance1 = 0.0, variance2 = 0.0; for (size_t x = 0; x < array1_size; x++) { variance1 += (array1[x]-mean1)*(array1[x]-mean1); } for (size_t x = 0; x < array2_size; x++) { variance2 += (array2[x]-mean2)*(array2[x]-mean2); } if ((mean1 == mean2) && (variance1 == variance2)) { return 1701.1864;//not worth calculating } variance1 = variance1/(array1_size-1); variance2 = variance2/(array2_size-1); const double WELCH_T_STATISTIC = (mean1-mean2)/sqrt(variance1/array1_size+variance2/array2_size); const double DEGREES_OF_FREEDOM = pow((variance1/array1_size+variance2/array2_size),2.0)//numerator / ( (variance1*variance1)/(array1_size*array1_size*(array1_size-1))+ (variance2*variance2)/(array2_size*array2_size*(array2_size-1)) ); // printf("Welch's t statistic is %lf, degrees of freedom is %lf\n",WELCH_T_STATISTIC,DEGREES_OF_FREEDOM); //modified implementation of Simpson's rule from http://rosettacode.org/wiki/Numerical_integration#C //this function Simpson-integrates from 0 to x, so there isn't any "from" term const double a = DEGREES_OF_FREEDOM/2, x = DEGREES_OF_FREEDOM/(WELCH_T_STATISTIC*WELCH_T_STATISTIC+DEGREES_OF_FREEDOM); const double n = 11000, h = x/n; double sum1 = 0.0, sum2 = 0.0; for(unsigned int i = 0;i < n; i++) { // printf("a = %.2f, b = %.2f => t = %lf, sum1 = %lf\n",a,b,t,sum1);

     sum1 += (pow(h * i + h / 2.0,a-1))*(pow(1-(h * i + h / 2.0),-0.5));

}

  for(unsigned int i = 1;i < n;i++) {
     sum2 += (pow(h * i,a-1))*(pow(1-h * i,-0.5));

} // printf("Sum1 = %lf; sum2 = %lf\n",sum1,sum2); return ((h / 6.0) * ((pow(x,a-1))*(pow(1-x,-0.5)) + 4.0 * sum1 + 2.0 * sum2))/(tgamma(a)*1.77245385090551610/tgamma(a+0.5));//heavily simplified to speed computation }

int main(void) { //examples of how to use function const double dset1[] = {27.5,21.0,19.0,23.6,17.0,17.9,16.9,20.1,21.9,22.6,23.1,19.6,19.0,21.7,21.4}; const double dset2[] = {27.1,22.0,20.8,23.4,23.4,23.5,25.8,22.0,24.8,20.2,21.9,22.1,22.9,20.5,24.4}; printf("%.17f\n",calculate_pvalue(dset1,sizeof(dset1)/sizeof(*dset1),dset2,sizeof(dset2)/sizeof(*dset2))); const double dset3[] = {17.2,20.9,22.6,18.1,21.7,21.4,23.5,24.2,14.7,21.8}; const double dset4[] = {21.5,22.8,21.0,23.0,21.6,23.6,22.5,20.7,23.4,21.8,20.7,21.7,21.5,22.5,23.6,21.5,22.5,23.5,21.5,21.8}; printf("%.17f\n",calculate_pvalue(dset3,sizeof(dset3)/sizeof(*dset3),dset4,sizeof(dset4)/sizeof(*dset4))); const double dset5[] = {19.8,20.4,19.6,17.8,18.5,18.9,18.3,18.9,19.5,22.0}; const double dset6[] = {28.2,26.6,20.1,23.3,25.2,22.1,17.7,27.6,20.6,13.7,23.2,17.5,20.6,18.0,23.9,21.6,24.3,20.4,24.0,13.2}; printf("%.17f\n",calculate_pvalue(dset5,sizeof(dset5)/sizeof(*dset5),dset6,sizeof(dset6)/sizeof(*dset6))); const double dset7[] = {30.02,29.99,30.11,29.97,30.01,29.99}; const double dset8[] = {29.89,29.93,29.72,29.98,30.02,29.98}; printf("%.17f\n",calculate_pvalue(dset7,sizeof(dset7)/sizeof(*dset7),dset8,sizeof(dset8)/sizeof(*dset8)));/**/ const double x[] = {3.0,4.0,1.0,2.1}; const double y[] = {490.2,340.0,433.9}; printf("%.17f\n",calculate_pvalue(x,sizeof(x)/sizeof(*x),y,sizeof(y)/sizeof(*y))); return 0; } </lang>