Class 8 common non-parametric test in SPSS 4: Single Sample K-S Test

I. Definition

Definition: a single sample K-S test is named by two former Soviet mathematicians Kolmogorov and Smirnov, and is also a non-parametric test method for goodness of fit. The single sample K-S test is a method to infer whether the population is subject to a certain theoretical distribution by using the sample data, which is suitable for exploring the distribution pattern of continuous random variables.

The actual frequency distribution of a variable can be compared with the Normal, Uniform, Poisson, and Exponential distribution of a single sample K-S test. Its zero hypothesis H0 indicates that the population from the sample is not significantly different from the specified theoretical distribution.

The process of K-S test is as follows:

(1) construct a theoretical distribution based on the sample data and user-specified data, and obtain the corresponding theoretical cumulative probability distribution function F0 (X) from the distribution table)

(2) Calculate the cumulative probability of individual sample data points using sample data to obtain the cumulative probability distribution function S0 (X)

(3) Calculate the difference D (X) between F0 (X) and S0 (x) at the corresponding variable value point x to obtain the difference sequence D. The K-S test of single sample mainly studied the difference sequence.

SPSS will calculate the Z-statistic of K-S in statistics, and give the corresponding accompanied probability value according to the K-S distribution table (Small Sample) or normal distribution table (large sample. If the accompanied probability is less than or equal to the user's significance level α, the null hypothesis H0 should be rejected, and the population from the sample has a significant difference with the specified distribution; if the accompanied probability value is greater than the significance level, therefore, it is not allowed to reject the null hypothesis H0, and there is no significant difference between the population and the specified distribution.

 

Ii. Instances

As shown in table 10-4, the height data of 144 children aged in a certain region shows normal distribution of height frequencies of Children Aged in this region?

Height Interval	Number of students
64-	2
68-	4
69-	7
70-	16
71-	20
72-	25
73-	24
74-	22
76-	16
78-	2
79-	6
83-	1

 

Test procedure:

 

Single Sample K-S test: http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test

 

1. Chi-square test: http://www.cnblogs.com/downmoon/archive/2012/03/06/2382042.html

2. Two-item distribution test: http://www.cnblogs.com/downmoon/archive/2012/03/26/2417668.html

3, travel inspection: http://www.cnblogs.com/downmoon/archive/2012/03/26/2417882.html

4. Single Sample K-S test: http://www.cnblogs.com/downmoon/archive/2012/03/26/2418003.html