/* Purpose: Relaxed chi square test for differences in frequencies between observed and
expected frequencies. This version keeps going, even if expected frequencies (E) are < 5 in
more than 20% of the categories. This also excludes skips categories that
have E = 0, reducing degrees of freedom accordingly.
Parameters: *observed = array of ints with event counts for each category
in the sample
*expected = array of ints with event counts for each category
as expected from the known population
k = number of categories
df = degrees of freedom (e.g. k-1)
Returns: Probability of making an error when rejecting the NULL hypothesis
-1 if data does not support Chi^2 test
*/
double gstats_rtest_XF (int *observed, int *expected, int k, int df) {
double chi;
int i;
long sum, sum2;
if ( df < 1 ) {
gstats_error ("Chi^2 test: need at least one category with expected frequency > 0.");
return (-1);
}
if ( k < 2 ) {
gstats_error ("Chi^2 test: number of categories must be > 1.");
return (-1);
}
/* check if parameters given make sense */
sum = 0;
sum2 = 0;
for (i = 0; i < k; i++) {
sum = sum + observed [i];
sum2 = sum2 + expected [i];
}
if ( sum < 2 ) {
gstats_error ("Chi^2 test: sum of observed frequencies over all categories must be > 2.");
return (-1);
}
if ( sum2 < 2 ) {
gstats_error ("Chi^2 test: sum of expected frequencies over all categories must be > 2.");
return (-1);
}
/* finally, calculate Chi! */
chi = 0;
for (i = 0; i < k; i++) {
if (expected[i] > 0) {
chi = chi + ( ((float) ((observed[i]-expected[i])*(observed[i]-expected[i])) / expected[i]) );
}
else {
df --;
if ( df < 1 ) {
gstats_error ("Chi^2 test: need at least one category with expected frequency > 0.");
return (-1);
}
}
}
return (gsl_ran_chisq_pdf (chi, (double) df));
}
double
chisq (double x, void *p)
{
double * c = (double *)p;
return gsl_ran_chisq_pdf (x, c[0]);
}
double
test_chisq_pdf (double x)
{
return gsl_ran_chisq_pdf (x, 13.0);
}
static double one_chisq(double in, void *df){ return log(gsl_ran_chisq_pdf(in, *(double*)df)); }
/* Purpose: chi square test for differences in frequencies between sample and
population
Parameters: *observed = array of ints with event counts for each category
in the sample
*expected = array of ints with event counts for each category
as expected from the known population
k = number of categories
df = degrees of freedom (e.g. k-1)
Returns: Probability of making an error when rejecting the NULL hypothesis
-1 if data does not support Chi^2 test
*/
double gstats_test_XF (int *observed, int *expected, int k, int df) {
double chi;
int i;
long sum, sum2;
double checksum;
int lessThanFive;
if ( df < 1 ) {
gstats_error ("Chi^2 test: need at least one category with expected frequency > 0.");
return (-1);
}
if ( k < 2 ) {
gstats_error ("Chi^2 test: number of categories must be > 1.");
return (-1);
}
lessThanFive = 0; /* keeps count of categories with < 1 expected frequency */
/* check if parameters given make sense */
sum = 0;
sum2 = 0;
for (i = 0; i < k; i++) {
sum = sum + observed [i];
sum2 = sum2 + expected [i];
}
if ( sum < 2 ) {
gstats_error ("Chi^2 test: sum of observed frequencies over all categories must be > 2.");
return (-1);
}
if ( sum2 < 2 ) {
gstats_error ("Chi^2 test: sum of expected frequencies over all categories must be > 2.");
return (-1);
}
/* finally, calculate Chi! */
chi = 0;
for (i = 0; i < k; i++) {
if (expected[i] > 0) {
chi = chi + ( ((float) ((observed[i]-expected[i])*(observed[i]-expected[i])) / expected[i]) );
if (expected[i] < 5) {
lessThanFive ++;
}
}
else {
gstats_error ("Chi^2 test: expected frequency for category < 1.");
return (-1);
}
}
/* check if more than 20% of categories have less than 5 observations */
checksum = lessThanFive / ((double) (k)/100.0);
if (checksum > 20) {
gstats_error ("Chi^2 test: more than 20% of categories have an expected frequency < 5.");
return (-1);
}
return (gsl_ran_chisq_pdf (chi, (double) df));
}
