db_t_tests

/** Do a t-test entirely inside the database.
  Returns only the two-tailed p-value.
*/
double apop_db_t_test(char * tab1, char *col1, char *tab2, char *col2){
    gsl_matrix *result1, *result2;
    result1 = apop_query_to_matrix("select avg(%s), var(%s), count(*) from %s", col1, col1, tab1);
    result2 = apop_query_to_matrix("select avg(%s), var(%s), count(*) from %s", col2, col2, tab2);
    double a_avg = gsl_matrix_get(result1, 0, 0),
           a_var   = gsl_matrix_get(result1, 0, 1),
           a_count = gsl_matrix_get(result1, 0, 2),
           b_avg   = gsl_matrix_get(result2, 0, 0),
           b_var   = gsl_matrix_get(result2, 0, 1),
           b_count = gsl_matrix_get(result2, 0, 2),
           stat    = (a_avg - b_avg)/ sqrt(b_var/(b_count-1) + a_var/(a_count-1));
    return fabs(1 - (1 - gsl_cdf_tdist_P(stat, a_count+b_count-2))*2); //two-tailify a one-tailed stat
}

/** Do a paired t-test entirely inside the database.
  Returns only the two-tailed p-value.
*/
double apop_db_paired_t_test(char * tab1, char *col1, char *col2){
    gsl_matrix *result=
            apop_query_to_matrix("select avg(%s - %s), var(%s - %s), count(*) from %s tab1",
                                            col1,col2,   col1, col2,             tab1);
    double avg  = gsl_matrix_get(result, 0, 0),
           var   = gsl_matrix_get(result, 0, 1),
           count = gsl_matrix_get(result, 0, 2),
           stat  = avg/ sqrt(var/(count-1));
    return 2*GSL_MIN(gsl_cdf_tdist_P(stat, count-1),gsl_cdf_tdist_Q(stat, count-1));
}