As an example, let's look at differences between groups. The example I use in _Think Stats_ is first babies compared with others. The `first` module provides code to read the data into three pandas Dataframes.
The apparent effect we're interested in is the difference in the means. Other examples might include a correlation between variables or a coefficient in a linear regression. The number that quantifies the size of the effect, whatever it is, is the "test statistic".
For the first example, I extract the pregnancy length for first babies and others. The results are pandas Series objects.
对于第一个例子，我提取了第一个婴儿和其他人的怀孕时间。结果是 pandas `Series`对象。
```py
group1=firsts.prglngth
group2=others.prglngth
```
The actual difference in the means is 0.078 weeks, which is only 13 hours.
平均值的实际差异为 0.078 周，仅为13小时。
```py
actual=TestStatistic((group1,group2))
...
...
@@ -874,14 +872,14 @@ actual
# 0.078037266777549519
```
The null hypothesis is that there is no difference between the groups. We can model that by forming a pooled sample that includes first babies and others.
零假设是组之间没有差异。我们可以通过形成包括第一个婴儿和其他婴儿的合并样本来对其进行建模。
```py
n,m=len(group1),len(group2)
pool=numpy.hstack((group1,group2))
```
Then we can simulate the null hypothesis by shuffling the pool and dividing it into two groups, using the same sizes as the actual sample.
然后我们可以通过打乱池子，并将其分成两组来模拟零假设，使用与实际样本相同的大小。
```py
defRunModel():
...
...
@@ -890,7 +888,7 @@ def RunModel():
returndata
```
The result of running the model is two NumPy arrays with the shuffled pregnancy lengths:
Here's the sampling distribution of the test statistic under the null hypothesis, with the actual difference in means indicated by a gray line.
这是零假设下的检验统计量的抽样分布，其中均值的实际差异用灰线表示。
```py
defVertLine(x):
...
...
@@ -931,8 +929,7 @@ None
The p-value is the probability that the test statistic under the null hypothesis exceeds the actual value.
p 值是零假设下的检验统计量超过实际值的概率。
```py
pvalue=sum(test_stats>=actual)/len(test_stats)
...
...
@@ -941,14 +938,13 @@ pvalue
# 0.14999999999999999
```
In this case the result is about 15%, which means that even if there is no difference between the groups, it is plausible that we could see a sample difference as big as 0.078 weeks.
We conclude that the apparent effect might be due to chance, so we are not confident that it would appear in the general population, or in another sample from the same population.
我们的结论是，表观效应可能是偶然的，所以我们不相信它会出现在一般总体或同一总体的另一个样本中。
Part Two
========
### 第二部分
We can take the pieces from the previous section and organize them in a class that represents the structure of a hypothesis test.
我们可以从上一节中获取部分，并将它们组织在一个表示假设检验结构的类中。
```py
classHypothesisTest(object):
...
...
@@ -1015,7 +1011,7 @@ class HypothesisTest(object):
```
`HypothesisTest` is an abstract parent class that encodes the template. Child classes fill in the missing methods. For example, here's the test from the previous section.
@@ -1047,7 +1043,7 @@ class DiffMeansPermute(HypothesisTest):
returndata
```
Now we can run the test by instantiating a DiffMeansPermute object:
现在我们可以通过实例化`DiffMeansPermute`对象来运行测试：
```py
data=(firsts.prglngth,others.prglngth)
...
...
@@ -1065,7 +1061,7 @@ means permute pregnancy length
ts max = 0.173695697482
And we can plot the sampling distribution of the test statistic under the null hypothesis.
我们可以在零假设下绘制检验统计量的抽样分布。
```py
ht.PlotHist()
...
...
@@ -1074,7 +1070,7 @@ ht.PlotHist()
As an exercise, write a class named `DiffStdPermute` that extends `DiffMeansPermute` and overrides `TestStatistic` to compute the difference in standard deviations. Is the difference in standard deviations statistically significant?
In this case, after 1000 attempts, we never see a sample difference as big as the observed difference, so we conclude that the apparent effect is unlikely under the null hypothesis. Under normal circumstances, we can also make the inference that the apparent effect is unlikely to be caused by random sampling.
One final note: in this case I would report that the p-value is less than 1/1000 or 0.001. I would not report that p=0, because the apparent effect is not impossible under the null hypothesis; just unlikely.
This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://github.com/donnemartin/data-science-ipython-notebooks).
