我正在寻找关于我在 python 中创建的模型的一些统计数据。我想对其进行 t 检验,但想知道是否有一种简单的方法可以使用 numpy/scipy 来执行此操作。周围有什么好的解释吗?
例如,我有三个相关的数据集,如下所示:
[55.0, 55.0, 47.0, 47.0, 55.0, 55.0, 55.0, 63.0]
现在,我想对它们进行学生 t 检验。
我正在寻找关于我在 python 中创建的模型的一些统计数据。我想对其进行 t 检验,但想知道是否有一种简单的方法可以使用 numpy/scipy 来执行此操作。周围有什么好的解释吗?
例如,我有三个相关的数据集,如下所示:
[55.0, 55.0, 47.0, 47.0, 55.0, 55.0, 55.0, 63.0]
现在,我想对它们进行学生 t 检验。
在scipy.stats包中,函数很少ttest_...
。请参阅此处的示例:
>>> print 't-statistic = %6.3f pvalue = %6.4f' % stats.ttest_1samp(x, m)
t-statistic = 0.391 pvalue = 0.6955
van 使用 scipy 的回答是完全正确的,使用scipy.stats.ttest_*
函数非常方便。
但是我来到这个页面寻找一个纯numpy的解决方案,如标题中所述,以避免对 scipy 的依赖。为此,让我指出这里给出的示例:https ://docs.scipy.org/doc/numpy/reference/generated/numpy.random.standard_t.html
主要问题是,numpy 没有累积分布函数,因此我的结论是你应该真正使用 scipy。无论如何,只使用 numpy 是可能的:
从最初的问题我猜你想比较你的数据集并用 t 检验判断是否存在显着偏差?此外,样本是配对的吗?(请参阅https://en.wikipedia.org/wiki/Student%27s_t-test#Unpaired_and_paired_two-sample_t-tests)在这种情况下,您可以像这样计算 t 值和 p 值:
import numpy as np
sample1 = np.array([55.0, 55.0, 47.0, 47.0, 55.0, 55.0, 55.0, 63.0])
sample2 = np.array([54.0, 56.0, 48.0, 46.0, 56.0, 56.0, 55.0, 62.0])
# paired sample -> the difference has mean 0
difference = sample1 - sample2
# the t-value is easily computed with numpy
t = (np.mean(difference))/(difference.std(ddof=1)/np.sqrt(len(difference)))
# unfortunately, numpy does not have a build in CDF
# here is a ridiculous work-around integrating by sampling
s = np.random.standard_t(len(difference), size=100000)
p = np.sum(s<t) / float(len(s))
# using a two-sided test
print("There is a {} % probability that the paired samples stem from distributions with the same means.".format(2 * min(p, 1 - p) * 100))
这将打印There is a 73.028 % probability that the paired samples stem from distributions with the same means.
由于这远高于任何合理的置信区间(例如 5%),因此您不应针对具体案例得出任何结论。
一旦你得到你的 t 值,你可能想知道如何将它解释为概率——我做到了。这是我写的一个函数来帮助解决这个问题。
它基于我从http://www.vassarstats.net/rsig.html和http://en.wikipedia.org/wiki/Student%27s_t_distribution收集的信息。
# Given (possibly random) variables, X and Y, and a correlation direction,
# returns:
# (r, p),
# where r is the Pearson correlation coefficient, and p is the probability
# of getting the observed values if there is actually no correlation in the given
# direction.
#
# direction:
# if positive, p is the probability of getting the observed result when there is no
# positive correlation in the normally distributed full populations sampled by X
# and Y
# if negative, p is the probability of getting the observed result, when there is no
# negative correlation
# if 0, p is the probability of getting your result, if your hypothesis is true that
# there is no correlation in either direction
def probabilityOfResult(X, Y, direction=0):
x = len(X)
if x != len(Y):
raise ValueError("variables not same len: " + str(x) + ", and " + \
str(len(Y)))
if x < 6:
raise ValueError("must have at least 6 samples, but have " + str(x))
(corr, prb_2_tail) = stats.pearsonr(X, Y)
if not direction:
return (corr, prb_2_tail)
prb_1_tail = prb_2_tail / 2
if corr * direction > 0:
return (corr, prb_1_tail)
return (corr, 1 - prb_1_tail)