1, concept definition

Suppose it is necessary to compare whether the two test papers of candidates A and B are the same, and the indicators for answering the same questions are defined as follows:

Always choose the same number: Volume A and Volume B have the same number of questions;

Total selection rate: the ratio of the number of questions with the same options in volume A and volume B to the total number of questions;

Same number: the same number of questions selected in Volume A and Volume B;

The same number of mistakes: the same number of questions selected in Volume A and Volume B;

Proportion of A questions with the same rate: both A and B answers correctly and the options are the same, accounting for the number of correct questions in A;

Error-identical rate A: the ratio of the same question selected in Volume A and Volume B to the number of questions with wrong answers in Volume A;

Coincidence rate b: the ratio of the number of questions with the same option in Volume B to the number of correctly answered questions;

Error rate b: the ratio of the number of questions with the same option in volume A and volume B to the number of wrong questions in volume B;

2. Research methods

Taking the 200 1 National English Entrance Examination for Medical Doctors and the 200 1 Physician Qualification Examination as the research objects, various research samples are selected according to the research purpose, and the answers of candidates in the sample groups are paired and compared, that is, two different candidates are selected from each group for comparison at a time. The frequency formula of paired comparison is:

n(n- 1)/2

3. Conclusion

The results show that under the condition of 1, there is no cheating in the normal examination room, and the error rate is relatively stable in different scores, close to the random selection rate of options. 2. The error rate and stability are not affected by the sample of candidates, the sample of test questions and the size of the examination room. 3. The upper limit of the average error rate of four-choice multiple-choice questions is 0.27, and the upper limit of the error rate is 0.70; The upper limit of the average error rate of five-choice multiple-choice questions is 0.24, and the upper limit of the error rate is 0.54. This study suggests that when the two-way error rate of two candidates is statistically significantly higher than the average level of the normal examination room, and there are objective conditions for cheating, the examination institution can consider them cheating. The research results have reference and application value for judging cheating in multiple-choice questions without direct evidence.