CN115062073A - College entrance examination probability verification method based on single-parameter bilateral hypothesis test - Google Patents

Abstract

A college entrance examination admission probability verification method based on single-parameter bilateral hypothesis testing belongs to the technical field of probability testing and solves the problem that admission probability cannot be tested. The method comprises the following steps: the method comprises the following steps: calculating equivalent scores of the current year, which are equivalent to the equivalent scores of the previous year, by combining historical data to obtain an equivalent score sequence; step two: solving the equivalent fraction sequence according to the first step, and solving the mean value and the standard deviation of the equivalent fraction sequence; further obtaining an admission probability function model through batch processing of data; step three: carrying out mean value processing on the admission probability function model obtained in the second step; step four: and performing hypothesis test on the admission probability function model after the three-mean processing to verify the rationality of the model, thereby realizing the method for verifying the admission probability of the college entrance examination based on the single-parameter bilateral hypothesis test. The invention checks the rationality of the admission probability by finding an accurate probability interval, thereby reducing the risk of admission to a great extent.

Description

College entrance examination probability verification method based on single-parameter bilateral hypothesis test

Technical Field

The invention belongs to the technical field of probability test, and particularly relates to a college entrance examination probability verification method based on single-parameter bilateral hypothesis test.

Background

Under the modern big data era, the network platform is more and more accepted by wide examinees and parents, the data of the past years is taken as the basis, the science is more scientific, and the result is more accurate. However, their validity requires further examination.

At present, most platforms directly display the admission probability, and find out a distribution function meeting the score based on various factors such as the score of the past year, the batch line, the scale of an examinee and the like, so as to calculate the admission probability. However, the computed probability of enrollment is rarely checked, and the probability is inherently disturbed by multiple factors, which is difficult to achieve to a certain degree of accuracy.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a college entrance examination probability verification method based on single-parameter bilateral hypothesis test, which solves the problem that the entrance probability cannot be tested.

The technical scheme adopted by the invention for solving the technical problem is as follows:

a college entrance examination probability verification method based on single-parameter bilateral hypothesis test comprises the following steps:

the method comprises the following steps: calculating equivalent scores of the current year, which are equivalent to the equivalent scores of the previous year, by combining historical data to obtain an equivalent score sequence;

step two: solving the equivalent fraction sequence according to the first step, and solving the mean value and the standard deviation of the equivalent fraction sequence; further obtaining an admission probability function model through batch processing of data;

step three: carrying out mean value processing on the admission probability function model obtained in the second step;

step four: and performing hypothesis test on the admission probability function model after the three-mean processing to verify the rationality of the model, thereby realizing the method for verifying the admission probability of the college entrance examination based on the single-parameter bilateral hypothesis test.

Preferably, the equivalent fraction sequence obtained in the first step is X ═ X (X) ₁ ,x ₂ ,…x _n )，

The sample mean value of the equivalent fraction sequence obtained in the second step is as follows:

the sample standard deviation of the equivalent fraction sequence obtained in the second step is as follows:

wherein x _i Is any sample in the equivalent fraction sequence X, i ═ 1,2, …, n;

the admission probability obtained in the second step is as follows:

where X represents a function of X, i.e., X is a sufficient statistic of the variable X; s represents any fraction in the interval from 0 to x, and ω(s) is white noise.

Preferably, the equivalent fractional sequence obtained in step one is represented by (X) ₁ ,x ₂ ,…x _n ) Doing an average value processing, X ═ X ₁ ,x ₂ ,…x _n ) Do y ═ x-mu ₀ Obtaining a sample Y ═ (Y) ₁ ,y ₂ ,…y _n ) Y represents a function of Y, Y is sufficient statistics of the variable Y, and the enrollment probability obtained in step two becomes a single parameter function with the parameters only being standard deviations.

Preferably, the fourth step includes the following steps:

assuming that the level of the test problem is α (0 < α < 1), H ₀ :σ ₁ ² ≤σ ² ≤σ ₂ ² Or H ₁ :σ ² ＞σ ₂ ² Or σ ² ＜σ ₁ ² ，σ ₁ To set the lower limit of the standard deviation, σ ₂ Is the upper limit of the set standard deviation; carrying out unbiased inspection on the consistent optimal potential;

the sample Y ═ Y ₁ ,y ₂ ,…y _n ) The joint density function of (a) is:

p(y；σ ² )＝c(σ ² )·exp{Q(σ ² )·T(y)}，

wherein Q (σ) ² )＝(-2σ ² ) ^-1 Is σ ² Yi represents any one of the sequences Y;

the sufficient statistics are set as follows:

then T (y)/σ ² ～χ ² (n); y represents a function of Y, which is the sufficient statistic of the variable Y; chi-type food processing machine ² (n) denotes a chi-square distribution.

The rejection region of UMPT with the level of test problem α is W ═ y: (t) (y) ≦ c ₁ Or T (Y) ≧ c ₂ }，c ₁ And c ₂ Is determined by the following two equations:

to obtain

Wherein x ² (y | n) represents χ with degree of freedom n ² A density function of the distribution; c. C ₁ And c ₂ Upper and lower bounds representing sufficient statistics rejection regions, respectively;

and

representing the probability of the upper and lower bounds of the variance with a confidence level of alpha in the test question.

The invention is to get

In time, the college entrance examination probability verification method based on single-parameter bilateral hypothesis testing is realized.

The invention has the beneficial effects that: the invention checks the rationality of the admission probability by finding an accurate probability interval, thereby reducing the risk of admission to a great extent.

Drawings

FIG. 1 is a schematic diagram of a method for verifying the probability of college entrance examination based on single-parameter bilateral hypothesis testing.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

As shown in fig. 1, a method for verifying the probability of college entrance examination based on single-parameter bilateral hypothesis test includes the following steps:

the method comprises the following steps: calculating equivalent scores of the current year, which are equivalent to the equivalent scores of the previous year, by combining historical data to obtain an equivalent score sequence; the historical data comprises data such as the lowest admission score, the average admission score, the number of examinees, the score ranking, the number of recruits in the enrollment plan of the year and the reference year and the like. The reference year may be a year or a few years before the current year, the current year is the year to be measured, the method for seeking the equivalent score is equivalent to the method for discounting the option price, and the difference is only that the discount basis in the invention is data such as the number of examinees and the plan for enrollment. Converting the college entrance examination score of the year to be tested into an equivalent score of the corresponding reference year college entrance examination, wherein the sequence of the equivalent score is X ═ X (X) ₁ ,x ₂ ,…x _n )

Step two: solving the equivalent fraction sequence according to the first step, and solving the mean value and the standard deviation of the equivalent fraction sequence; further obtaining an admission probability function model through batch processing of data;

the sample mean value of the equivalent fraction sequence obtained in the second step is as follows:

the sample standard deviation of the equivalent fraction sequence obtained in the second step is as follows:

wherein x _i Is any sample in the equivalent fraction sequence X, i ═ 1,2, …, n;

the score is wholly obeyed to normal distribution, white noise is added to characterize uncertain factors influencing the admission probability, and the admission probability obtained in the second step is as follows:

where X represents a function of X, i.e., X is a sufficient statistic of the variable X; s represents any fraction in the interval 0 to x, and ω(s) is white noise, is a derivative form of brownian motion, and generally describes irregular motion of particles in physics, and is used for describing random uncertain factors influencing recording probability, such as policies of different years and the like; .

Step three: carrying out mean value processing on the admission probability function model obtained in the second step;

preferably, the equivalent fractional sequence obtained in step one is represented by (X) ₁ ,x ₂ ,…x _n ) Doing an average value processing, X ═ X ₁ ,x ₂ ,…x _n ) Processing Y to x-mu to obtain sample Y to (Y) ₁ ,y ₂ ,…y _n ) Y represents a function of Y, Y is sufficient statistics of the variable Y, and the enrollment probability obtained in step two becomes a single parameter function with the parameters only being standard deviations.

Step four: and performing hypothesis test on the admission probability function model after the three-mean processing to verify the rationality of the model, thereby realizing the method for verifying the admission probability of the college entrance examination based on the single-parameter bilateral hypothesis test.

The invention adopts the sample mean value and standard deviation which are respectively satisfied by the equivalent fraction sequence of a certain fraction to carry out bilateral hypothesis test based on single parameter.

Assuming that the level of the test problem is α (0 < α < 1), H ₀ :σ ₁ ² ≤σ ² ≤σ ₂ ² Or H ₁ :σ ² ＞σ ₂ ² Or σ ² ＜σ ₁ ² In the present embodiment, σ ₁ And σ ₂ The selection is based on the college professions' past year specific admission score, sigma ₁ To set the lower limit of the standard deviation, σ ₂ Is the upper limit of the set standard deviation; carrying out unbiased test on the consistent optimal potential;

the sample Y ═ Y ₁ ,y ₂ ,…y _n ) The joint density function of (a) is:

p(y；σ ² )＝c(σ ² )·exp{Q(σ ² )·T(y)}，

wherein Q (σ) ² )＝(-2σ ² ) ^-1 Is σ ² Yi represents any one of the sequences Y;

let the sufficient statistics be:

then T (y)/σ ² ～χ ² (n); y represents a function of Y, which is the sufficient statistic of the variable Y; chi-type food processing machine ² (n) denotes a chi-square distribution.

The rejection region of UMPT with the level of test problem α is W ═ y: (t) (y) ≦ c ₁ Or T (Y) ≧ c ₂ Therein, X is utilized ² The method of (1).

c ₁ And c ₂ Is determined by the following two equations:

to obtain

Wherein x ² (y | n) represents χ with degree of freedom n ² A density function of the distribution; c. C ₁ And c ₂ Upper and lower bounds representing sufficient statistics rejection regions, respectively;

and

representing the probability of the upper and lower bounds of the variance with a confidence level of alpha in the test question.

In the present embodiment: the probability of enrollment is reasonable when and only when t (y) is not in the rejection region, indicating that the mean and variance are within reasonable ranges. c. C ₁ And c ₂ The interval with the determined rejection area is determined, and the reasonable area with the determined rejection area is determined

The invention is to get

In time, the college entrance examination probability verification method based on single-parameter bilateral hypothesis testing is realized.

Claims (4)

1. A college entrance examination probability verification method based on single-parameter bilateral hypothesis test is characterized by comprising the following steps:

the method comprises the following steps: calculating equivalent scores of the current year, which are equivalent to the equivalent scores of the previous year, by combining historical data to obtain an equivalent score sequence;

step two: solving the equivalent fraction sequence according to the first step, and solving the mean value and the standard deviation of the equivalent fraction sequence; further obtaining an admission probability function model through batch processing of data;

step three: carrying out mean value processing on the admission probability function model obtained in the second step;

step four: and performing hypothesis test on the admission probability function model after the three-mean processing to verify the rationality of the model, thereby realizing the method for verifying the admission probability of the college entrance examination based on the single-parameter bilateral hypothesis test.

2. The method for verifying the probability of college entrance examination based on the uni-parameter bilateral hypothesis test as claimed in claim 1, wherein the equivalent score sequence obtained in the first step is X ═ (X ═ X) ₁ ,x ₂ ,…x _n )，

The sample mean value of the equivalent fraction sequence obtained in the second step is as follows:

the sample standard deviation of the equivalent fraction sequence obtained in the second step is as follows:

wherein x _i Is any sample in the equivalent fraction sequence X, i ═ 1,2, …, n;

the admission probability obtained in the second step is as follows:

where X represents a function of X, i.e., X is a sufficient statistic of the variable X; s represents any fraction in the interval from 0 to x, and ω(s) is white noise.

3. A substrate according to claim 1The method for verifying the probability of college entrance examination by single-parameter bilateral hypothesis test is characterized in that the equivalent score sequence X obtained in the first step is (X ═ X ₁ ,x ₂ ,…x _n ) Doing an average value processing, X ═ X ₁ ,x ₂ ,…x _n ) Do y ═ x-mu ₀ Obtaining a sample Y ═ (Y) ₁ ,y ₂ ,…y _n ) Y represents a function of Y, Y is sufficient statistics of the variable Y, and the enrollment probability obtained in step two becomes a single parameter function with the parameters only being standard deviations.

4. The method for verifying the probability of college entrance examination based on the single-parameter bilateral hypothesis test as claimed in claim 1, wherein the fourth step comprises the steps of:

assuming that the level of the test problem is α (0 < α < 1), H ₀ :σ ₁ ² ≤σ ² ≤σ ₂ ² Or H ₁ :σ ² ＞σ ₂ ² Or σ ² ＜σ ₁ ² ，σ ₁ To set the lower limit of the standard deviation, σ ₂ Is the upper limit of the set standard deviation; carrying out unbiased inspection on the consistent optimal potential;

the sample Y ═ Y ₁ ,y ₂ ,…y _n ) The joint density function of (a) is:

p(y；σ ² )＝c(σ ² )·exp{Q(σ ² )·T(y)}，

wherein Q (σ) ² )＝(-2σ ² ) ^-1 Is σ ² Yi represents any one of the sequences Y;

let the sufficient statistics be:

then T (y)/σ ² ～χ ² (n); y represents a function of Y, which is the sufficient statistic of the variable Y; chi shape ² (n) denotes a chi-square distribution;

rejection of UMPT with level of inspection problem alphaThe absolute area is W ═ { y: T (Y) ≦ c ₁ Or T (Y) ≧ c ₂ }，c ₁ And c ₂ Is determined by the following two equations:

to obtain

Wherein x ² (y | n) represents χ with degree of freedom n ² A density function of the distribution; c. C ₁ And c ₂ Upper and lower bounds representing sufficient statistics rejection regions, respectively;

and

representing the probability of the upper and lower bounds of the variance with the confidence level alpha in the test question;

the invention is to get

In time, the college entrance examination probability verification method based on single-parameter bilateral hypothesis testing is realized.

Images