Data standardization processing

1. Why should data standardization be carried out

In the multi index evaluation system , Due to the different nature of each evaluation index , It usually has different dimensions and orders of magnitude . When the level of each index varies greatly , If the original index value is directly used for analysis , It will highlight the role of indicators with higher values in comprehensive analysis , Relatively weaken the role of indicators with low numerical level . therefore , In order to ensure the reliability of the results , It is necessary to standardize the original index data .

2. What is data standardization

Scale the data , To fall into a small, specific area . It is often used in the processing of some comparison and evaluation indicators , Remove the unit limit of data , Convert it to dimensionless pure values , It is convenient to compare and weight indexes of different units or scales .

3. Data standardization methods

Common methods are ：min-max Standardization （Min-max normalization）,log Function conversion ,atan Function conversion ,z-score Standardization （zero-mena normalization, This method is most commonly used ）, Fuzzy quantification . This article only introduces min-max Law （ Standardized methods ）,z-score Law （ Normalization method ）, Normalization method .

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Method 1 ： Standardized methods （min-max Law ）

min-max Standardization (Min-maxnormalization) Also called dispersion standardization , It's a linear transformation of the original data , Make the result fall to [0,1] Section , The conversion function is as follows : among max Is the maximum value of the sample data ,min Is the minimum value of sample data . One drawback of this approach is that when new data is added , May lead to max and min The change of , Need to redefine .

characteristic ： It's a linear transformation of the original data , The result falls into [0,1]  Section

Method 2 ： Normalization method （z-score Law ）

The most common way to standardize is Z Standardization , It's also SPSS The most commonly used standardization method in :z-score Standardization (zero-meannormalization) It's also called standard deviation standardization , The processed data conform to the standard normal distribution , That is, the mean value is 0, The standard deviation is 1, The transformation function is : among μ Is the mean of all sample data ,σ Is the standard deviation of all sample data .

• This method is based on the mean value of the original data （mean） And standard deviation （standard deviation） Standardize data . take A Original value x Use z-score Standardize to x’.
• z-score Standardized methods apply to properties A When the maximum and minimum values of are unknown , Or there are outliers beyond the value range .
• spss The default standardization method is z-score Standardization .
• use Excel Conduct z-score Standardized methods ： stay Excel There are no ready-made functions in , Step by step calculation is required , In fact, the standardized formula is very simple .

Steps are as follows ：
1. Find out the variables （ indicators ） The arithmetic mean of （ Mathematical expectation ）xi And standard deviation si ;
2. Standardized treatment ：
zij=（xij－xi）/si
among ：zij Is the normalized variable value ;xij Is the actual variable value .
3. Reverse the sign in front of the indicator .
The standardized variable values revolve around 0 Up and down , Greater than 0 Above average , Less than 0 It means below average .

Method 3 ： Normalization method