def test_betai_symmetry():
"""
Checks relation Ix(a, b) = 1 - Ix-1(b, a)
"""
a, b, x = 1, 10, 0.15
calculated_value = nr.betai(a, b, x) + nr.betai(b, a, 1 - x)
expected_value = 1
assert_almost_equal(calculated_value, expected_value)
def test_betai_recurrence():
"""
Checks relation Ix(a, b) = xIx(a−1, b) + (1−x)Ix(a, b−1)
"""
a, b, x = 1, 10, 0.15
calculated_value = nr.betai(a, b, x) - x * nr.betai(a - 1, b, x) - \
(1 - x) * nr.betai(a, b - 1, x)
expected_value = 0
assert_almost_equal(calculated_value, expected_value)
def tptest(data1, data2):
# Given the arrays "data1" and "data2" of length "n", returns
# the Student's "t" for paired data and its significance as "prob".
# Small values of "prob" indicates that the arrays have different
# means.
n1 = len(data1)
n2 = len(data2)
if (n1 != n2):
print("Data arrays must have the same size")
else:
n = n1
ave1, var1 = nr.avevar(data1)
ave2, var2 = nr.avevar(data2)
cov = 0.0
for i in range(n):
cov = cov + (data1[i] - ave1) * (data2[i] - ave2)
df = n - 1.0
cov = cov / df
# Student's t
t = (ave1 - ave2) / np.sqrt((var1 + var2 - 2.0 * cov) / n)
# significance
prob = nr.betai(0.5 * df, 0.5, df / (df + t**2))
return t, prob
def ttest(data1, data2):
# Given the arrays "data1" and "data2", returns the
# Student's "t" and its significance as "prob".
# Data are assumed to be drawn from populations with
# the same true variance.
# Small values of "prob" indicates that the arrays
# have different means.
n1 = len(data1)
n2 = len(data2)
ave1, var1 = nr.avevar(data1)
ave2, var2 = nr.avevar(data2)
# print(ave1, ave2)
# print(var1, var2)
# degrees of freedom
df = n1 + n2 - 2.
# pooled variance
var = ((n1 - 1.) * var1 + (n2 - 1) * var2) / df
# Student's t
t = (ave1 - ave2) / np.sqrt(var * (1 / n1 + 1 / n2))
# significance
prob = nr.betai(0.5 * df, 0.5, df / (df + t**2))
return t, prob
def tutest(data1, data2):
# Given the arrays "data1" and "data2", returns the
# Student's "t" and its significance as "prob".
# Data are assumed to be drawn from populations with
# the same true variance.
# Small values of "prob" indicates that the arrays
# have different means.
n1 = len(data1)
n2 = len(data2)
ave1, var1 = nr.avevar(data1)
ave2, var2 = nr.avevar(data2)
# print(ave1, ave2)
# print(var1, var2)
# Student's t
t = (ave1 - ave2) / np.sqrt(var1/n1 + var2/n2)
df = (var1/n1 + var2/n2)**2 / ((var1/n1)**2 / (n1 - 1) + (var2/n2)**2 / (n2 - 1))
# significance
prob = nr.betai(0.5 * df, 0.5, df/(df + t**2))
return t, prob
def test_betai_x1():
"""
Checks betai output for x = 1
"""
a, b, x = 0.5, 0.5, 1
calculated_value = nr.betai(a, b, x)
expected_value = 1
assert_almost_equal(calculated_value, expected_value)
def biwt_tutest(n1, ave1, var1, n2, ave2, var2):
t = (ave1-ave2)/sqrt(var1/n1+var2/n2)
df = (var1/n1+var2/n2)**2/((var1/n1)**2/(n1-1)+(var2/n2)**2/(n2-1))
df = 0.7 * df
prob = nr.betai(0.5*df,0.5,df/(df+t**2))
return t, prob
def biwt_ttest(n1, ave1, var1, n2, ave2, var2):
df = 0.7 * (n1+n2-2)
svar = ((n1-1)*var1+(n2-1)*var2)/df
t = (ave1-ave2)/sqrt(svar*(1.0/n1+1.0/n2))
prob = nr.betai(0.5*df,0.5,df/(df+t**2))
return t, prob
def prob(df, t):
return (1 - nr.betai(0.5*df,0.5,df/(df+t**2))/2)