正态性检验

通过学习MINITAB的帮助文件，对正态性检验的方法以及结果的判断有了一定的了解。

结果如下，其中很多只是意译，可能不到位。

【原文】
Anderson-Darling normality test

The Anderson-Darling normality test can help you determine whether the data follow a normal distribution. The A statistic that the test provides is not very informative by itself, but it is used to determine the p-value. The p-value ranges from 0 to 1, and indicates how likely it is that your data follow a normal distribution.
First, you need to decide how low p must be for you to conclude that the data are not normal. (A commonly chosen value is 0.1.) Then, if the p-value you is lower than your criterion, you must conclude that the data do not follow a normal distribution. Otherwise, you can continue to assume the data are normal.

The value of A for the precipitation data is 0.987, and the associated p-value is 0.008. Assuming you chose 0.1 as your criterion, you must conclude that the data do not follow a normal distribution, because 0.008 is lower than 0.1.

Skewness

Skewness refers to a lack of symmetry. A distribution is skewed if one tail extends farther than the other. A skewness statistic is provided with the graphical summary:

· A value close to 0 indicates symmetric data

· Negative values imply negative/left skew

· Positive values indicate positive/right skew

The skewness value for the precipitation data is 2.11078 indicating that the distribution is right-skewed. This is due to the outlier shown a the far right of the histogram.

Kurtosis

Kurtosis refers to how sharply peaked a distribution is. A kurtosis statistic is provided with the graphical summary:

· Values close to 0 indicate normally peaked data

· Negative values indicate a distribution that is flatter than normal

· Positive values indicate a distribution with a sharper than normal peak

The kurtosis value for the precipitation data is 5.61936 indicating that the distribution is more sharply peaked than normal. This is illustrated in the histogram which shows that the peak of the data rises well above the normal curve (red).

? All Rights Reserved. 2000 Minitab, Inc.

【译文】
Anderson-Darling 正态测试

Anderson-Darling正态测试可以帮助你检验数据是否符合正态分布。这种统计方法不会直接告诉你结果，但是我们通常通过P值来判断。P值的范围从0到1，来表明你的数据有多少程度满足正态分布。（译注：数值越大说明越满足正态分布，用EXCEL生成的随机数列的P值是0！）
首先，你需要设定P值小于多少时可以认为数据不是正态分布（通常选定0.1）。然后，如果P值小于你的基准（译注：P设定值0.1），你可以判断数据不符合正态分布。否则，你可以认为数据是正态分布的。

这里（例子中）的A值是0.987，对应的P值是0.008。假如你选定0.1作为你判断的基准，你会认为这个数据不满足正态分布，因为0.008小于0.1。

Skewness

Skewness表明数据的不对称性。分布歪斜是指分布的一侧比另一侧伸展得远。Skewness统计法以图形的方式给出了总结：
－数值接近0表明是对称数据
－负数表示负倾斜、左倾斜
－正数表示正倾斜、右倾斜
例子中的Skewness值是2.11078，说明数据是右倾斜。在柱状图上表现为右侧有数据偏得很远。

Kurtosis

Kurtosis表明分布的尖峰程度。Kurtosis统计法以图形的方式给出了总结：
－数值接近0表明是正态分布的尖峰
－负数表示分布比较平坦
－正数表示分布比较尖锐
例子中的Kurtosis值是5.61936，表明数据比较尖锐。柱状图中显示数据高出红色的正态分布曲线。