def simple_decision(cls, r, n, alphas):
"""Decide whether to accept or reject the null hypothesis.
"""
df = n - 2
t = (r * math.sqrt(df)) / math.sqrt(1 - r**2)
p = StatTool.probability_for_t(t, StatTool.TWO_TAILED_TEST, df)
for alpha in alphas:
ci = StatTool.pearson_r_confidence_interval(r, alpha, n)
conclusion1 = cls.spell_conclusion_by_ci(ci)
conclusion2 = cls.spell_conclusion_by_p(p, alpha)
print("For alpha=%.4f:" % alpha)
print(" - %s" % conclusion1)
print(" - %s" % conclusion2)
print("")
def print_correlation(self, grp0, grp1):
print("%s --> %s correlation" % (grp0.title, grp1.title))
print('-' * 70)
r, _ = StatTool.pearson_r(grp0.members, grp1.members)
"""r, also called Pearson's r, is correlation coefficient, to quantify relationship.
r measures the correlatoin for the sample
cov(x,y)
r = ---------
Sx * Sy
"""
r_squared = r**2
""""r squared (r^2):
r^2 = % of variation in Y explained by variation in x
r^2 = coefficient of determination
"""
df = grp0.n - 2
""""Degree of freedom. We substract one from each sample"""
# Convert r to t
t = (r * math.sqrt(df)) / math.sqrt(1 - r**2)
# Calculate the probability for t
p = pval2 = StatTool.probability_for_t(t, StatTool.TWO_TAILED_TEST, df)
ci = StatTool.pearson_r_confidence_interval(r, self.alpha, grp0.n)
"""
if ρ (rho) is true correlation for population, CI is the confidence interval
for ρ, meaning the range of likely values for the population correlation
coefficient ρ.
"""
conclusion1 = self.spell_conclusion_by_ci(ci)
conclusion2 = self.spell_conclusion_by_p(p, self.alpha)
slope = r * grp1.sd / grp0.sd
"""Slope for linear regression."""
intercept = grp1.mean - slope * grp0.mean
"""The regression line always goes through the mean."""
def calc_se_est(x, y, slope, intercept):
# Calculate standard error of the estimate.
# y = slope * x + intercept
ss = 0.0
n = len(x)
for i in range(n):
ss += (y[i] - (slope * x[i] + intercept))**2
return math.sqrt(ss / float(n - 2))
se_est = calc_se_est(grp0.members, grp1.members, slope, intercept)
"""Standard error of the estimate, measures the accuracy of our regression
line compared to the actual data."""
print("DF : % d" % df)
print("Pearson r : % .3f" % r)
print("r^2 (coef of determ.) : % .3f (%.2f%%)" %
(r_squared, r_squared * 100.0))
print("Confidence interval : % .3f - %.3f" % ci)
print("t-statistic : % .3f" % t)
print("P-value : % .5f" % p)
print("Conclusion : - %s" % conclusion1)
print(" - %s" % conclusion2)
print("Linear regression:")
print("Slope : % .3f" % slope)
print("Intercept : % .3f" % intercept)
print("Standard err. of estimate: % .3f" % se_est)
print("")