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ttest_ind_from_stats(mean1, std1, nobs1, mean2, std2, nobs2, equal_var=True, alternative='two-sided')

This is a test for the null hypothesis that two independent samples have identical average (expected) values.

Notes

The statistic is calculated as (mean1 - mean2)/se, where se is the standard error. Therefore, the statistic will be positive when mean1 is greater than mean2 and negative when mean1 is less than mean2.

Parameters

mean1 : array_like

The mean(s) of sample 1.

std1 : array_like

The corrected sample standard deviation of sample 1 (i.e. ddof=1).

nobs1 : array_like

The number(s) of observations of sample 1.

mean2 : array_like

The mean(s) of sample 2.

std2 : array_like

The corrected sample standard deviation of sample 2 (i.e. ddof=1).

nobs2 : array_like

The number(s) of observations of sample 2.

equal_var : bool, optional

If True (default), 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 .

alternative : {'two-sided', 'less', 'greater'}, optional

Defines the alternative hypothesis. The following options are available (default is 'two-sided'):

'two-sided': the means of the distributions are unequal.
'less': the mean of the first distribution is less than the mean of the second distribution.
'greater': the mean of the first distribution is greater than the mean of the second distribution.

Returns

statistic : float or array: The calculated t-statistics.
pvalue : float or array: The two-tailed p-value.

T-test for means of two independent samples from descriptive statistics.

Examples

Suppose we have the summary data for two samples, as follows (with the Sample Variance being the corrected sample variance)::

Sample Sample Size Mean Variance Sample 1 13 15.0 87.5 Sample 2 11 12.0 39.0

Apply the t-test to this data (with the assumption that the population variances are equal):

import numpy as np
from scipy.stats import ttest_ind_from_stats
ttest_ind_from_stats(mean1=15.0, std1=np.sqrt(87.5), nobs1=13,
                     mean2=12.0, std2=np.sqrt(39.0), nobs2=11)

For comparison, here is the data from which those summary statistics were taken. With this data, we can compute the same result using `scipy.stats.ttest_ind`:

a = np.array([1, 3, 4, 6, 11, 13, 15, 19, 22, 24, 25, 26, 26])
b = np.array([2, 4, 6, 9, 11, 13, 14, 15, 18, 19, 21])
from scipy.stats import ttest_ind
ttest_ind(a, b)

Suppose we instead have binary data and would like to apply a t-test to compare the proportion of 1s in two independent groups::

Number of Sample Sample Size ones Mean Variance Sample 1 150 30 0.2 0.161073 Sample 2 200 45 0.225 0.175251

The sample mean :math:`\hat{p}` is the proportion of ones in the sample and the variance for a binary observation is estimated by :math:`\hat{p}(1-\hat{p})`.

ttest_ind_from_stats(mean1=0.2, std1=np.sqrt(0.161073), nobs1=150,
                     mean2=0.225, std2=np.sqrt(0.175251), nobs2=200)

For comparison, we could compute the t statistic and p-value using arrays of 0s and 1s and `scipy.stat.ttest_ind`, as above.

group1 = np.array([1]*30 + [0]*(150-30))
group2 = np.array([1]*45 + [0]*(200-45))
ttest_ind(group1, group2)

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

GitHub : /scipy/stats/_stats_py.py#6368
type: <class 'function'>
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Notes

Parameters

Returns

See Also

Examples

Local connectivity graph