For the new college entrance examination reform in Zhejiang, it is not a novel system to give corresponding scores according to the relative ranking of all candidates' scores in the exam. It is well known that CET-4 and CET-6 give the final score according to the same idea (see: CET-6), and the college entrance examination was graded in this way for a while, but later most provinces and cities canceled this system and changed it back to pure paper to score points directly. In fact, this scoring method is a variant of Z-score in statistics. The conversion formula of standard score is as follows: z=(X-M)/SD, where x stands for original score (volume score), m stands for average value and SD stands for standard deviation. If the score distribution of all the students taking the exam meets the normal distribution, then the relative position of a candidate in the crowd can be directly obtained from the Z score. For example, if the score distribution of all candidates in an exam satisfies normal distribution, the original score of one person is 90, the average score of all candidates is 60, and the standard deviation is 10, then the student's z=(90-60)/ 10=3. According to the normal distribution table, we can know that the student's score is higher than 99.86% of the candidates.

Using standard score has at least several advantages that the original score does not have:

1. The standard score can be added directly, but the original score cannot be added directly in principle. Because standard score uses the same reference point-that is, taking the standard deviation as the "unit" and the average value of the original score as zero-Standard Score can directly add up to represent the sum of someone's achievements in different subjects. But the original score does not have this advantage, because the difficulty of different subjects is different, and the overall distribution may be different. For example, we all know that mathematics is more difficult than biology, so with a total score of 100, A scored 98 points in mathematics, 95 points in biology, 96 points in mathematics and 98 points in biology. Whose learning ability or learning level is higher? If we only look at the total score, B will surpass A by 1, but the difficulty of mathematics may be that A's 98 is the first in the province, while B's 98 may be hundreds in the province. In this case, we can't say that math 98 of A and biology 98 of B have the same weight for us to judge their abilities. If converted according to the standard score, the total score of A may be better than that of B (the mathematical average score is 50, the standard deviation is 5, the biological average score is 80, and the standard deviation 15 is the case).

2. The standard score can directly reflect the relative position of individuals in the group, but the original score is difficult to do this. As mentioned above, under the premise of normality, the standard score may directly calculate the relative position, so the z score is essentially a relative quantity to measure the relative position of individuals in the group. The direct addition of original scores can almost never do this, except in extreme cases such as perfect score or zero score. In addition, in the original original score system, the college entrance examination admission is still based on the relative ranking of individuals in the province, which is why we say that the college entrance examination score is not important, but the provincial ranking is important. Imagine if I got 740 out of 750 in the college entrance examination, but if everyone else got 740+ or even 750, are there any reasons for Peking University and Tsinghua to be admitted? If IQ is the only criterion, then the highest IQ is the criterion for selecting talents, not the IQ higher than 140.

3. The standard score is less influenced by luck and the difficulty of the test paper. The score of a single exam is greatly influenced by luck and the difficulty of the test paper, but the standard score does not consider the original score, but the relative position, so the influence is less than the original score. If the heterogeneity of the group is relatively large, it is even possible that the final score will not change despite bad luck and wrong answers.

Step 4 wait

Considering the above points, standard score or its variants are the most consistent with statistics and measurement, or can be said to be the most scientific. This is probably the reason why standard score is often used in foreign exams. But this does not mean that the use of standard score is foolproof.

Standard score's advantage is based on several assumptions:

1. The sample is representative enough. This is also one of the chief culprits of dissatisfaction among many key senior high school students. If excellent students in a key high school rarely take an exam and many ordinary high school students try their luck, then the candidates in this exam can't represent the level of the candidates in the province, which leads to the problem of declining discrimination.

2. The population should conform to the normal distribution. If the overall distribution does not conform to the normal distribution because of the difficulty of the test paper or the level of the candidates, then the standard score cannot directly reflect the relative position of the candidates in the whole, while Zhejiang Province gives the score according to the percentage, which will lead to the forced normalization of the final score and cannot reflect the actual gap between the candidates.

Step 3 wait

Judging from the significance of psychometric grading, the reform in Zhejiang Province is very valuable. The original rough total score method was revised, and the problems of papers in different subjects were considered, and a more scientific score method was adopted. But from the actual implementation, it seems that something has gone wrong. When the premises of the above two standard scores are not satisfied, it is unfair and not too divorced from the actual situation to use the standard score, which causes some candidates' dissatisfaction.