def calc_double_sided_student_t_probability(t, n):
"Calculate the p-value using a double sided student t distribution"
# integrate a finite area from the origin to t
p_aux = simpson_rule_integrate(f_student_t_distribution(n), 0, t)
# return the area of the two tails of the distribution (symmetrical)
return (0.5 - p_aux) * 2
def calc_student_t_probability(x, n):
"Integrate t distribution from -infinity to x with n degrees of freedom"
inf = float("infinity")
p = simpson_rule_integrate(f_student_t_distribution(n), -inf, x)
return p
