CN115062073A - College entrance examination probability verification method based on single-parameter bilateral hypothesis test - Google Patents
College entrance examination probability verification method based on single-parameter bilateral hypothesis test Download PDFInfo
- Publication number
- CN115062073A CN115062073A CN202210684888.XA CN202210684888A CN115062073A CN 115062073 A CN115062073 A CN 115062073A CN 202210684888 A CN202210684888 A CN 202210684888A CN 115062073 A CN115062073 A CN 115062073A
- Authority
- CN
- China
- Prior art keywords
- probability
- equivalent
- parameter
- admission
- entrance examination
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000012360 testing method Methods 0.000 title claims abstract description 35
- 238000000034 method Methods 0.000 title claims abstract description 27
- 230000002146 bilateral effect Effects 0.000 title claims abstract description 20
- 238000012795 verification Methods 0.000 title claims abstract description 10
- 238000007689 inspection Methods 0.000 claims description 3
- 239000000758 substrate Substances 0.000 claims 1
- 230000005653 Brownian motion process Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000005537 brownian motion Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005315 distribution function Methods 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/24—Querying
- G06F16/245—Query processing
- G06F16/2458—Special types of queries, e.g. statistical queries, fuzzy queries or distributed queries
- G06F16/2462—Approximate or statistical queries
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/10—Services
- G06Q50/20—Education
- G06Q50/205—Education administration or guidance
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Probability & Statistics with Applications (AREA)
- Tourism & Hospitality (AREA)
- Strategic Management (AREA)
- Educational Technology (AREA)
- Educational Administration (AREA)
- Computational Linguistics (AREA)
- Health & Medical Sciences (AREA)
- Databases & Information Systems (AREA)
- Data Mining & Analysis (AREA)
- Software Systems (AREA)
- Mathematical Physics (AREA)
- Fuzzy Systems (AREA)
- General Engineering & Computer Science (AREA)
- Economics (AREA)
- General Health & Medical Sciences (AREA)
- Human Resources & Organizations (AREA)
- Marketing (AREA)
- Primary Health Care (AREA)
- General Business, Economics & Management (AREA)
- Complex Calculations (AREA)
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
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;andrepresenting 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 getIn 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;andrepresenting 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
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:
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;andrepresenting the probability of the upper and lower bounds of the variance with the confidence level alpha in the test question;
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202210684888.XA CN115062073A (en) | 2022-06-17 | 2022-06-17 | College entrance examination probability verification method based on single-parameter bilateral hypothesis test |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202210684888.XA CN115062073A (en) | 2022-06-17 | 2022-06-17 | College entrance examination probability verification method based on single-parameter bilateral hypothesis test |
Publications (1)
Publication Number | Publication Date |
---|---|
CN115062073A true CN115062073A (en) | 2022-09-16 |
Family
ID=83201738
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202210684888.XA Pending CN115062073A (en) | 2022-06-17 | 2022-06-17 | College entrance examination probability verification method based on single-parameter bilateral hypothesis test |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN115062073A (en) |
-
2022
- 2022-06-17 CN CN202210684888.XA patent/CN115062073A/en active Pending
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN105184103B (en) | Virtual name based on the database of case history cures system | |
Uebersax | Validity inferences from interobserver agreement. | |
CN107316334B (en) | Personalized precise magnetic resonance imaging method | |
CN110400293A (en) | A kind of non-reference picture quality appraisement method based on depth forest classified | |
CN108363902A (en) | A kind of accurate prediction technique of pathogenic hereditary variation | |
CN116137012B (en) | Online teaching quality supervision and management system based on Internet education | |
CN114676749A (en) | Power distribution network operation data abnormity judgment method based on data mining | |
Treisman | Is signal detection theory fundamentally flawed? A response to Balakrishnan (1998a, 1998b, 1999) | |
Subali et al. | A new model for measuring the complexity of SQL commands | |
Farayola et al. | Massive multisite variability-aware die distribution estimation for analog/mixed-signal circuits test validation | |
CN115062073A (en) | College entrance examination probability verification method based on single-parameter bilateral hypothesis test | |
CN113673609B (en) | Questionnaire data analysis method based on linear hidden variables | |
CN112131752A (en) | Super-collapse pollution rate tolerance estimation algorithm based on quasi-calibration | |
WO2019196437A1 (en) | Index decision method | |
Wheadon | Classification accuracy and consistency under item response theory models using the package classify | |
CN113223700B (en) | Traditional Chinese medicine pulse condition identification method and device based on pulse condition data | |
CN115907461A (en) | Electric power engineering method based on mechanism derivation equation | |
CN112632470A (en) | Method for establishing college entrance probability based on UMPUT probability test | |
CN114582507A (en) | Method for analyzing environmental risk factors of alveolar echinococcosis based on geographic detector | |
CN111091910B (en) | Intelligent evaluation system based on painting clock test | |
CN108874749B (en) | Method for establishing college entrance examination volunteer admission probability model | |
CN108008337A (en) | The computational methods and device of electric energy meter measurement error uniformity | |
CN113408216A (en) | Method and device for acquiring turbulence model | |
Ho-Leung | To evaluate the function point analysis: a case study | |
CN112950035A (en) | Medical institution service quality measurement method for improving D-S algorithm |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination |