执行 2 个样本 t 检验 [英] Perform 2 sample t-test

问题描述

我有样本 1 和样本 2 的均值、标准差和 n - 样本取自样本总体，但由不同实验室测量.

I have a the mean, std dev and n of sample 1 and sample 2 - samples are taken from the sample population, but measured by different labs.

样本 1 和样本 2 的 n 不同.我想做一个加权(考虑 n)双尾 t 检验.

n is different for sample 1 and sample 2. I want to do a weighted (take n into account) two-tailed t-test.

我尝试使用 scipy.stat 模块通过使用 np.random.normal 创建我的数字，因为它只需要数据而不是像 mean 和 std dev 这样的统计值(有没有办法直接使用这些值).但它不起作用，因为数据数组必须具有相同的大小.

I tried using the scipy.stat module by creating my numbers with np.random.normal, since it only takes data and not stat values like mean and std dev (is there any way to use these values directly). But it didn't work since the data arrays has to be of equal size.

任何有关如何获得 p 值的帮助将不胜感激.

Any help on how to get the p-value would be highly appreciated.

推荐答案

如果你有原始数据作为数组 a 和 b，你可以使用 scipy.stats.ttest_ind 带有参数 equal_var=False:

If you have the original data as arrays a and b, you can use scipy.stats.ttest_ind with the argument equal_var=False:

t, p = ttest_ind(a, b, equal_var=False)

如果你只有两个数据集的汇总统计，你可以使用scipy.stats.ttest_ind_from_stats(在 0.16 版中添加到 scipy)或来自公式(http://en.wikipedia.org/wiki/Welch%27s_t_test).

If you have only the summary statistics of the two data sets, you can calculate the t value using scipy.stats.ttest_ind_from_stats (added to scipy in version 0.16) or from the formula (http://en.wikipedia.org/wiki/Welch%27s_t_test).

以下脚本显示了可能性.

The following script shows the possibilities.

from __future__ import print_function

import numpy as np
from scipy.stats import ttest_ind, ttest_ind_from_stats
from scipy.special import stdtr

np.random.seed(1)

# Create sample data.
a = np.random.randn(40)
b = 4*np.random.randn(50)

# Use scipy.stats.ttest_ind.
t, p = ttest_ind(a, b, equal_var=False)
print("ttest_ind:            t = %g  p = %g" % (t, p))

# Compute the descriptive statistics of a and b.
abar = a.mean()
avar = a.var(ddof=1)
na = a.size
adof = na - 1

bbar = b.mean()
bvar = b.var(ddof=1)
nb = b.size
bdof = nb - 1

# Use scipy.stats.ttest_ind_from_stats.
t2, p2 = ttest_ind_from_stats(abar, np.sqrt(avar), na,
                              bbar, np.sqrt(bvar), nb,
                              equal_var=False)
print("ttest_ind_from_stats: t = %g  p = %g" % (t2, p2))

# Use the formulas directly.
tf = (abar - bbar) / np.sqrt(avar/na + bvar/nb)
dof = (avar/na + bvar/nb)**2 / (avar**2/(na**2*adof) + bvar**2/(nb**2*bdof))
pf = 2*stdtr(dof, -np.abs(tf))

print("formula:              t = %g  p = %g" % (tf, pf))

输出:

ttest_ind:            t = -1.5827  p = 0.118873
ttest_ind_from_stats: t = -1.5827  p = 0.118873
formula:              t = -1.5827  p = 0.118873

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