def t_test(x, y=None, mu=None):
x = tensor(x)
if y is not None:
y = tensor(y)
if y is None and mu is None:
raise TypeError('Count of arguments must be 2, but only 1')
t = 0
df = 0
if y is not None:
n1 = len(x)
n2 = len(y)
if n1 <= 1 or n2 <= 1:
raise ValueError
mean1 = Tensor.mean(x)
mean2 = Tensor.mean(y)
var1 = Tensor.sum((x - mean1)**2) / (n1 - 1)
var2 = Tensor.sum((y - mean2)**2) / (n2 - 1)
t = (mean1 - mean2) / _math.sqrt(var1 / n1 + var2 / n2)
df = (var1 / n1 + var2 / n2)**2 / (var1**2 / (n1**2 *
(n1 - 1)) + var2**2 /
(n2**2 * (n2 - 1)))
if mu is not None:
n = len(x)
mean = Tensor.mean(x)
sd = (Tensor.sum((x - mean)**2) / (n - 1))**0.5
t = (mean - mu) / (sd / _math.sqrt(n))
df = n - 1
p = betainc(df / (t**2 + df), df / 2, 1 / 2, regularized=True)
return t, df, p
def chi2_uniform2d_distance(table, correct):
row_sums = Tensor.sum(table, axis=1)
col_sums = Tensor.sum(table, axis=0)
all_sums = Tensor.sum(row_sums)
expected = zeros_like(table)
_correct = False
if (table.shape[0] - 1) * (table.shape[1] - 1) == 1:
_correct = True
for i in range(table.shape[0]):
for j in range(table.shape[1]):
expected_ij = row_sums[i] * col_sums[j] / all_sums
expected[i, j] = expected_ij
if expected_ij < 10:
_correct = correct and True
if _correct:
return Tensor.sum((abs(table - expected) - 0.5)**2 / expected)
return Tensor.sum((table - expected)**2 / expected)
def norm(x):
x = tensor(x)
return sqrt((Tensor.sum(square(x))))
def chi2_uniform_distance(table):
expected = Tensor.sum(table) / len(table)
cntrd = table - expected
return Tensor.sum(cntrd**2) / expected
