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How to calculate the D value and W value of statistics in normality test?

2022-06-25 08:16:00 【spssau】

Catalog

One 、 Application background

Two 、SPSSAU operation

3、 ... and 、 Analysis and summary

1、 Calculation formula

2. summary

Four 、 Expand

1. inductive

2.SPSSAU Analysis and suggestion

5、 ... and 、 operation

6、 ... and 、 reference

One 、 Application background

Normality test is used to analyze whether the data show normality characteristics .

Two 、SPSSAU operation

3、 ... and 、 Analysis and summary

Put data into analysis box ,SPSSAU The system automatically generates analysis results after calculating statistics , as follows ：

1、 Calculation formula

（1） skewness

Skewness is a characteristic number that describes the degree to which the distribution deviates from symmetry . Its formula is as follows ：

In style , among m_3 It's a sample 3 Step center distance ,s That's the standard deviation of our sample , $\bar{x}$ Is the mean value of the sample .

（2） kurtosis

Kurtosis is a characteristic number that describes the steepness of the distribution and the thickness of the tail . Its formula is as follows :

In style , $\bar{x}$ Is the mean value of the sample .

（3）Kolmogorov-Smirnov test

Kolmogorov-Smirnov The basic idea of inspection is ： According to the difference between the cumulative distribution of the empirical distribution function and the expected distribution function , You can construct a subject Kolmogorov Statistics of distribution , And then test .

For the cumulative distribution function of a sample set Fn(x) And a hypothetical theoretical distribution F(x),Kolmogorov–Smirnov statistic D Defined as ：

In style , $F_{n}(x)$ Is the cumulative distribution function , $F_{n}(x)=\frac{1}{n} \sum_{i=1}^{n} I_{[-\infty, x]}\left(X_{i}\right)$ ; among $I_{[-\infty, x]}$ For indicating function , ;

（4）Shapro-Wilk test

Its statistics （W） The formula is ：

2. summary

Conduct normality test for annual rainfall , As can be seen from the table above ： The sample size of the research data is all less than or equal to 50, Thus using S-W test . The specific term , The annual rainfall is not significant (p>0.05), It means accepting the original hypothesis ( The null hypothesis ： The data is normally distributed ), The annual rainfall is all normal .
Summing up ： The annual rainfall is all normal .