Rank sum ratio (RSR) index calculation

One 、 application

  rsr (RSR) It means that the analysis method can be used to evaluate the comprehensive level of multiple indicators , Its essential principle is to use RSR Value information for various mathematical calculations ,RSR The value is between 0~1 Between and continuous , Usually , The higher the value, the better the evaluation ‘ optimal ’.

  rsr (RSR) Analytical method is widely used in multi - index comprehensive evaluation in the field of medical and health care , Easy to use . For example, use RSR Method comprehensive evaluation 10 The medical level of hospitals and ranking and grading of medical level , Or use RSR Method comprehensive evaluation 10 The academic ability of doctors and ranking and grading .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘WRSR rsr ’ Button . Here's the picture

SPSSAU The dashboard

（2） Drag and drop the data and click start analysis

3、 ... and 、SPSSAU Analysis steps

Four 、 Case study

At present, there is a certain province and a certain year 10 The antenatal check-up rate of maternal health care in four regions X1(%), Maternal mortality X2(%), Perinatal mortality X3(%), At present, we hope to combine this 3 Indicators , in the light of 10 Conduct a comprehensive evaluation of four regions , Evaluate this 10 The level of maternal health care in the regions , In the end 10 The levels of health care work in the four regions are ranked and graded . The data are shown in the table below

region	Antenatal examination rate X1_ couns	Maternal mortality X2_ Low excellent	Perinatal mortality X3_ Low excellent
A	99.54	60.27	16.15
B	96.52	59.67	20.1
C	99.36	43.91	15.6
D	92.83	58.99	17.04
E	91.71	35.4	15.01
F	95.35	44.71	13.93
G	96.09	49.81	17.43
H	99.27	31.69	13.89
I	94.76	22.91	19.87
J	84.8	81.49	23.63

5、 ... and 、 Data processing

  RSR The analytical method is calculating RSR When rank , There are two ways , They are the integral method and the non integral method ; The difference between the two lies in the different formulas when calculating the rank , The same numbers rank the same in the whole time method ( The higher the number of high-quality indicators, the more ‘ optimal ’, The smaller the number of low and excellent indicators, the more ‘ optimal ’); The rank method of the non integral method is as follows

（1） For high-quality indicators ：

（2） For low and excellent indexes ：

6、 ... and 、 result

SPSSAU The resulting analysis results are as follows ：

1.RSR Value calculation table

（1）RSR value

  In style ,i Yes 、j Is listed 、m、n Are the total number of rows 、 The total number of columns （ In this case m=10, n=3）,R_{i j} For the first time i Xing di j Rank of column element .（10+2+6）/3×10=0.6;

（2）RSR ranking

according to RSR Values are arranged from large to small .

2. RSR Distribution table

（1） Cumulative frequency Σ f

Frequency accumulation ; example ：5+2=7;

（2）Probit value

Probit Is the percentage P Corresponding standard normal deviation u（pi quantile ） Add 5 .

  for example ： Percentage P=0.0250 Corresponding standard normal deviation u=-1.28（ Look-up table is ）, Its corresponding probability unit Probit by 5-1.28 =3.72; Percentage P=0.9 Corresponding standard normal deviation u about 1.28（ Look-up table is ）, Its corresponding probability unit Probit by 5+1.28 =6.28.

3. Regression model table

PS: The purpose of this step is to get each RSR Value of the model fit , The fitting effect of the model is of little significance ;

4. Grading sort

  The last step is to get Probit The value of , Take it as an argument X, take RSR The distribution value is used as the dependent variable Y; Carry out regression model fitting , The model formula is ：RSR Distribution values =-0.609+0.222*Probit value . Combined with this regression model formula, the results of each region are obtained RSR The fitting value of , Used for final grading and sorting .

PS: The purpose of this step is to get each RSR Value of the model fit , The fitting effect of the model is of little significance ;

7、 ... and 、 summary

The table above lists 10 The three regions are RSR value ,RSR ranking , as well as RSR Fit value , And combined with the critical value table of grading sorting , Get the final 10 The grading of regions Level（ Be careful ：Level The greater the number , The better the representative grade ）.

It can be seen from the above table that ： take 10 The regions are divided into 3 Level , among C,H The optimal ;B,D,A,E,G,I,F common 6 Regions followed ;J The region is the worst . And it can also be directly applied to 10 Regions are ranked ,H Best ranked , The second is C;J The worst .