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bmgr_download_speeds["Download Speed (Mbps)"].describe()
pm_download_speeds["Download Speed (Mbps)"].describe()
# Test assuption of normality with the full dataset
W_bmgr, p_bmgr = stats.shapiro(bmgr_download_speeds["Download Speed (Mbps)"])
W_pm, p_pm = stats.shapiro(pm_download_speeds["Download Speed (Mbps)"])
print("BMGR-E W normality: ",W_bmgr,", p-test: ", p_bmgr)
print("PM W normality: ",W_pm,", p-test: ", p_pm)
BMGR-E W normality: 0.8805059790611267 , p-test: 0.0020480433013290167
PM W normality: 0.9654922485351562 , p-test: 0.06662767380475998
def welch_ttest(x, y):
## Welch-Satterthwaite Degrees of Freedom ##
dof = (x.var()/x.size + y.var()/y.size)**2 / ((x.var()/x.size)**2 / (x.size-1) + (y.var()/y.size)**2 / (y.size-1))
t, p = stats.ttest_ind(x, y, equal_var = False)
print("\n",
f"Welch's t-test= {t:.6f}", "\n",
f"p-value = {p:.6f}", "\n",
f"Welch-Satterthwaite Degrees of Freedom= {dof:.6f}")
welch_ttest(bmgr_download_speeds["Download Speed (Mbps)"],pm_download_speeds["Download Speed (Mbps)"])
welch_ttest(bmgr_download_speeds["Log10_transformation"],pm_download_speeds["Log10_transformation"])
Welch's t-test= 4.874664
p-value = 0.000027
Welch-Satterthwaite Degrees of Freedom= 32.759408
Welch's t-test= 4.600267
p-value = 0.000039
Welch-Satterthwaite Degrees of Freedom= 41.658817