1. Case introduction
A doctor studied the curative effect of physical therapy, drug therapy and topical plaster on peripheral facial paralysis. Through the overall Chi-square test, it was found that the difference in the effectiveness of the three treatments was statistically significant (χ2=21.0377, p=0.000) conclusion. Now I want to know further, which specific difference between the two treatments is statistically significant. The data is as shown in Figure 1:
figure 1
2. Problem Analysis
In this case, we already know that the difference in the effective rate (%) of the three treatments is statistically significant. Next, we want to know which two treatments have the difference. You can use the multiple comparison of the chi-square test to perform pairwise category combinations and repeat the card. Party inspection. In SPSSAU, directly using the RxC chi-square test for analysis will automatically output multiple comparison results.
3. Software operation and result interpretation
(1) Upload data
First organize the data into the correct format of the RxC chi-square test, study the relationship between therapy and treatment effect, the therapy is divided into 3 categories, and the treatment effect is divided into 2 categories, so there are 3*2=6 combinations, and the combination of each type The number of samples is identified in a separate column as the weight value, and finally the data of this case is organized into the format shown in Figure 2 below:
figure 2
Upload the sorted data to the SPSSAU system, click the upload data button in the upper right corner, and upload the data according to the prompts. The operation is as shown in Figure 3:
image 3
After uploading the data, the chi-square test for multiple comparison analysis was started next.
(2) Software operation
In the SPSSAU medical/experimental research module, select [Chi-square test], drag "therapy" to the X (classification) analysis box on the right, and drag "treatment effect" to the Y (classification) analysis box on the right , drag "number of people" to the right "weighted item" analysis box, and then click "start analysis", the operation is as shown in Figure 4:
Figure 4
(3) Interpretation of results
1. Chi-square test analysis results
SPSSAU first outputs the overall chi-square test analysis results as shown in Figure 5:
Figure 5
The known conclusion is that the difference in the treatment effect of the three treatments is statistically significant (χ2=21.0377, p=0.000), and then multiple comparisons are made to compare any two treatments.
2. Multiple comparisons of treatment effect*treatment
The multiple comparison results of the SPSSAU output chi-square test are shown in Figure 6:
Figure 6
It can be seen from the above table that multiple comparisons are made between the three treatments: whether there is any difference in the treatment effect between the external plaster and physical therapy for the first time, the chi-square value is 21.3228, and the corresponding p value is 0.000<0.0167, indicating that external use The difference in the therapeutic effects of plaster and physical therapy was statistically significant. In the same way, there is no statistically significant difference in the therapeutic effect between external plaster and drug therapy (chi-square value is 4.591, p=0.0321>0.0167); the difference in the therapeutic effect of physical therapy and drug therapy is statistically significant Significance (chi-square value 6.756, p=0.0093<0.0167).
Special reminder: In multiple comparisons, increasing the number of tests will increase the probability of a type of error. It is recommended to use the corrected significance level (Bonferroni correction) ; if the significance level in this case is 0.05, and the number of pairwise comparisons is 3, then Bonferroni correction The significance level is 0.05/3 times = 0.0167, i.e. the p-value needs to be compared to 0.0167, not 0.05.
4. Conclusion
In this case, the chi-square test was used to compare the differences in the treatment effects between the three treatments. The results showed that, according to the adjusted significance level of 0.0167, the difference between external plaster and physical therapy, physical therapy and drug treatment The difference of treatment effect was statistically significant; but the difference of treatment effect of external plaster and drug treatment was not statistically significant. Combined with the analysis of the effective rate in Figure 1, it can be considered that the effective rate of physical therapy is higher than that of the other two therapies, but it cannot be considered that there is a difference in the effective rate of external ointment and drug treatment.
5. Knowledge Tips
Chi-square test for multiple comparisons refers to repeated chi-square tests for any combination of two categories. SPSSAU is only performed for the first Y, and multiple comparisons of other items can be realized by replacing the unknown of Y. Pearson chi-square test was provided for multiple comparisons.
The number of multiple comparisons = C (number of X categories) * (number of Y categories)
For example, if the X category is 3 and the number of Y categories is 5, then C(3,2)*C(5,2)=30 times. In this case, X is of 3 types and Y is of 2 types, so the number of multiple comparisons=3*1=3 times.
references:
[1] Sun Zhenqiu, Xu Yongyong. Medical Statistics. 4th Edition [M]. People's Health Publishing House, 2014