False positive rate to false negative rate profile for Welch and two sample t-tests when different normally distributed data is passed to them.

fpr_fnr_t_tests.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import poisson, norm, t
from hypothtst.alpha_beta_sim import AlphaBetaSim
from hypothtst.sim_utils.mean.normal import NormDist
# pip install hypothtst to get this library.

def same_var_diff_var_t_test(ax, n_prms0=(10, 15, 26), n_prms1=(13, 5, 6)):
    g0 = NormDist(*n_prms0)
    g1 = NormDist(*n_prms1)
    t_tst_obj0 = ttst.TTest_diffvar(alternative='two-sided')
    tst_0 = t_tst_obj0.tst
    t_tst_obj1 = ttst.TTest_equalvar(alternative='two-sided')
    tst_1 = t_tst_obj1.tst
    ab = AlphaBetaSim()
    alphas1, betas1 = ab.alpha_beta_tracer(g0, g1, tst_0, n_sim=10000)
    alphas2, betas2 = ab.alpha_beta_tracer(g0, g1, tst_1, n_sim=10000)
    ax.plot(alphas1, betas1, label="Different variance test")
    ax.plot(alphas2, betas2, label="Equal variance test")
    ax.legend()


def plot_grid():
    ns = np.array([0.3, 1.0, 5.0])
    sigs = np.array([0.3, 1.0, 3.0])
    fig, axs = plt.subplots(len(ns),len(sigs))
    i=-1
    for n_ratio in ns:
        i+=1
        n1 = int(30)
        n2 = int(n1*n_ratio)
        j=-1
        for sig_ratio in sigs:
            j+=1
            sig1 = 10
            sig2 = sig1*sig_ratio
            prms0 = (10, sig1, n1)
            prms1 = (13, sig2, n2)
            ax = axs[i,j]
            ax.set_title('n1='+str(n1)+' n2=' + str(n2)+' sig1='+str(sig1)+' sig2='+str(sig2))
            same_var_diff_var_t_test(ax, prms0, prms1)
            print("Plotted: " + str((i,j)))
    plt.show()