Spark (Python) 中的 Kolmogorov Smirnov 测试不起作用? [英] Kolmogorov Smirnov Test in Spark (Python) not working?

问题描述

我在 Python spark-ml 中进行了正态性测试，发现我认为是一个错误.

这是设置，我有一个标准化的数据集(范围 -1，到 1).

当我做直方图时，我可以清楚地看到数据不正常:

<预><代码>>>>price_norm.histogram(10)([-1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0],[226, 269, 119, 95, 52, 26, 8, 2, 2, 5])

当我运行 Kolmgorov-Smirnov 测试时，我得到以下结果:

<预><代码>>>>testResults = Statistics.kolmogorovSmirnovTest(prices_norm, "norm")>>>打印测试结果Kolmogorov-Smirnov 测试总结:自由度 = 0统计数据 = 0.46231145770077375pValue = 1.742039845709087E-11反对零假设的非常强的假设:样本遵循理论分布.

Kolmgorov-Smirnov 检验将零假设 (H0) 定义为:数据遵循指定的分布(http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm).

在这种情况下，p 值非常低，因此我们应该拒绝原假设.这是有道理的，因为这显然不正常.

那为什么会说:

样本遵循理论分布

这不是错了吗?难道不应该说样本不遵循理论分布吗?我错过了什么吗?

解决方案

把我逼疯了，直接去看源码:

git://git.apache.org/spark.gitspark/mllib/src/main/scala/org/apache/spark/mllib/stat/test/KolmogorovSmirnovTest.scala

代码正确，零假设设置为:

object NullHypothesis extends Enumeration {输入 NullHypothesis = 值val OneSampleTwoSided = Value("样本服从理论分布")}

字符串消息的措辞只是重申零假设:

非常强的反对零假设的假设:样本遵循理论分布.________________________________________H0

可以说这个措辞令人困惑，因为它可以双向解释.但这确实是正确的.

I was doing a normality test in Python spark-ml and saw what I think is an bug.

Here is the setup, i have a data-set that is normalized (range -1, to 1).

When I do a histogram, i can clearly see that the data is NOT normal:

>>> prices_norm.histogram(10)

([-1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0],
 [226, 269, 119, 95, 52, 26, 8, 2, 2, 5])

When I run the Kolmgorov-Smirnov test I get the following results:

>>> testResults = Statistics.kolmogorovSmirnovTest(prices_norm, "norm")
>>> print testResults

Kolmogorov-Smirnov test summary:
degrees of freedom = 0 
statistic = 0.46231145770077375 
pValue = 1.742039845709087E-11 
Very strong presumption against null hypothesis: Sample follows theoretical distribution.

The Kolmgorov-Smirnov test defines the null hypothesis (H0) as: the data follows a specified distribution (http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm).

In this case the p-value is very low, so we should reject the null hypothesis. This makes sense, as it is clearly not normal.

So why then, does it say:

Sample follows theoretical distribution

Isn't this wrong? Shouldn't it say that the sample does NOT follow a theoretical distribution? Am I missing something?

解决方案

This was driving me crazy, so I went to look at the source code directly:

git://git.apache.org/spark.git
spark/mllib/src/main/scala/org/apache/spark/mllib/stat/test/KolmogorovSmirnovTest.scala

The code is correct, the null Hypothesis is set as:

object NullHypothesis extends Enumeration {
  type NullHypothesis = Value
  val OneSampleTwoSided = Value("Sample follows theoretical distribution")
}

The verbiage of the string message is just restating the null hypothesis:

Very strong presumption against null hypothesis: Sample follows theoretical distribution.
                                                 ________________________________________
                                                                    H0

Arguably the verbiage is confusing as it could be interpreted both ways. But it is indeed correct.

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