问题描述
如何进行 F 检验以检查 Python 中两个向量的方差是否相等?
How do I do an F-test to check if the variance is equivalent in two vectors in Python?
例如如果我有
a = [1,2,1,2,1,2,1,2,1,2]
b = [1,3,-1,2,1,5,-1,6,-1,2]
有没有类似的东西
scipy.stats.ttest_ind(a, b)
我找到了
sp.stats.f(a, b)
但它似乎与 F-test 不同
But it appears to be something different to an F-test
推荐答案
等方差的检验统计量 F 检验很简单:
The test statistic F test for equal variances is simply:
F = Var(X) / Var(Y)
其中 F 分布为 df1 = len(X) - 1, df2 = len(Y) - 1
scipy.stats.f 您在问题中提到的具有 CDF 方法.这意味着您可以为给定的统计量生成 p 值并测试该 p 值是否大于您选择的 alpha 水平.
scipy.stats.f which you mentioned in your question has a CDF method. This means you can generate a p-value for the given statistic and test whether that p-value is greater than your chosen alpha level.
因此:
alpha = 0.05 #Or whatever you want your alpha to be.
p_value = scipy.stats.f.cdf(F, df1, df2)
if p_value > alpha:
# Reject the null hypothesis that Var(X) == Var(Y)
请注意，F 检验对 X 和 Y 的非正态性极为敏感，因此您最好进行更可靠的测试，例如 Levene's test 或 Bartlett's test 除非您有理由确信 X和 Y 正态分布.这些测试可以在 scipy api 中找到:
Note that the F-test is extremely sensitive to non-normality of X and Y, so you're probably better off doing a more robust test such as Levene's test or Bartlett's test unless you're reasonably sure that X and Y are distributed normally. These tests can be found in the scipy api:
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