def ttest_ind(a, b, axis=0, equal_var=True):
"""
Calculates the T-test for the means of two independent samples of scores.
Parameters
----------
a, b : array_like
The arrays must have the same shape, except in the dimension
corresponding to `axis` (the first, by default).
axis : int or None, optional
Axis along which to compute test. If None, compute over the whole
arrays, `a`, and `b`.
equal_var : bool, optional
If True, perform a standard independent 2 sample test that assumes equal
population variances.
If False, perform Welch's t-test, which does not assume equal population
variance.
.. versionadded:: 0.17.0
Returns
-------
statistic : float or array
The calculated t-statistic.
pvalue : float or array
The two-tailed p-value.
Notes
-----
For more details on `ttest_ind`, see `stats.ttest_ind`.
"""
a, b, axis = _chk2_asarray(a, b, axis)
if a.size == 0 or b.size == 0:
return 'One of the vector is empty'
(mean1, mean2) = (a.mean(axis), b.mean(axis))
(var1, var2) = (a.var(axis=axis, ddof=1), b.var(axis=axis, ddof=1))
(n1, n2) = (a.count(axis), b.count(axis))
if equal_var:
# force df to be an array for masked division not to throw a warning
df = ma.asanyarray(n1 + n2 - 2.0)
svar = ((n1 - 1) * var1 + (n2 - 1) * var2) / df
denom = ma.sqrt(svar * (1.0 / n1 + 1.0 / n2)) # n-D computation here!
else:
vn1 = var1 / n1
vn2 = var2 / n2
with np.errstate(divide='ignore', invalid='ignore'):
df = (vn1 + vn2) ** 2 / (vn1 ** 2 / (n1 - 1) + vn2 ** 2 / (n2 - 1))
# If df is undefined, variances are zero.
# It doesn't matter what df is as long as it is not NaN.
df = np.where(np.isnan(df), 1, df)
denom = ma.sqrt(vn1 + vn2)
with np.errstate(divide='ignore', invalid='ignore'):
t = (mean1 - mean2) / denom
probs = special.betainc(0.5 * df, 0.5, df / (df + t * t)).reshape(t.shape)
return Ttest_ind(t, probs.squeeze())
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