One of the eight common non-parameter tests in SPSS: Chi-square

After a batch of sample data is obtained, people often want to see whether the overall distribution of the sample is fit with a specific distribution. This can be done by plotting
Sample Data histogram Method for rough judgment. If you need to make a more accurate judgment, you need to use the non-parameter test method. The Chi-square test of the overall distribution (also recorded as the Chi-2 test) is a ratio.
Better method.

I. Definition

The Chi-square test of the population distribution is applicable to the regression test. It is used to infer whether the population distribution is significantly different from the expected or theoretical distribution based on the actual frequency of the sample data. Its zero hypothesis H0: there is no significant difference between the overall distribution of samples and the expected distribution or a certain theoretical distribution.

The principle of the card side test of the overall distribution is: if several observation samples are randomly selected from a random variable, the observed frequencies of these observed samples in k subsets of X are subject to a multiclass distribution. When k tends to be infinite, it is almost subject to the overall distribution of X.

Therefore, assume that the population is subject to the actual observed frequencies of a certain expected or theoretical distribution set, and obtain the actual observed frequencies of each subset of the sample data. Then, calculate the statistic Q based on the formula below.

Where Oi indicates the observed frequency, and Ei indicates the expected or theoretical frequency.

The larger the Q value, the less close the observed frequency and the theoretical frequency. The smaller the Q value, the closer the observed frequency and the theoretical frequency. SPSS will automatically calculate the Q statistic, because the Q statistic is subject to the X-square distribution of degrees of freedom of K-1, so SPSS will give the accompanied probability value corresponding to the Q statistic according to the X-square distribution table.

If the accompanied probability is less than or equal to the user's significance level, the null hypothesis H0 should be rejected, and the overall distribution form of the sample comes from a significant difference with the expected distribution or theoretical distribution; if the accompanied probability value is greater than the significance level, the null hypothesis HO cannot be rejected, and there is no significant difference between the overall distribution of samples and the expected or theoretical distribution.

Therefore, the chi-square test of the overall distribution isKissTest, applicableOne factorOfMulticlass classificationData analysis. The card side of the overall distribution tests the sample data actually collected, rather than the frequency data.

Ii. Instances

The following table lists the number of people with depression in each day of a week in a specified place. Check whether the number of people with melancholy in each day of a week meets the requirements of 1: 1: 2: 2: 1: 1: 1.

Sunday	Patient count
1	31
2	38
3	70
4	80
5	29
6	24
7	31

Implementation steps:

1. Open PAWS Statistics 18 (SPSS 18) and import data.

2. Data-weighted case, as shown in

3. Analysis-non-parameter test-chi-square test

 

Chi-square test: http://baike.baidu.com/view/852140.htm