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)
# Degrees of freedom
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)
# 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 test_avevar_22():
"""
Checks variance (sample) values of an input dataset
"""
data = [1, 3, 5, 7, 9]
calculated_value = nr.avevar(data)[1]
expected_value = 10.0
assert_almost_equal(calculated_value, expected_value, 4)
def test_avevar_21():
"""
Checks variance (sample) values of an input dataset
"""
data = [1, 2, 3, 4, 5]
calculated_value = nr.avevar(data)[1]
expected_value = 2.5
assert_almost_equal(calculated_value, expected_value, 4)
def test_avevar_12():
"""
Checks average values of an input dataset
"""
data = [1, 2, 3, 4, 5]
calculated_value = nr.avevar(data)[0]
expected_value = 3
assert_almost_equal(calculated_value, expected_value, 4)
def test_avevar_11():
"""
Checks average values of an input dataset
"""
data = [-2, -1, 0, 1, 2]
calculated_value = nr.avevar(data)[0]
expected_value = 0.0
assert_almost_equal(calculated_value, expected_value, 4)
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)
# 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