# Statistical Analysis of Employment Education in Colleges and Universities Based on Improved Clustering Algorithm

Authors: Bin Liu
Journal: Security and Communication Networks
 (2022)

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## Abstract

In order to improve the effect of employment education in colleges and universities, this study combines the improved clustering algorithm to carry out statistical analysis of employment education in colleges and universities and analyzes the current situation of employment education in colleges and universities. In cluster analysis, considering the complexity of the distribution of statistics after the reestimation of the sample size and the possible complex correlation between the series of statistics in the group sequential design, on the premise that the statistics used will not cause type I error expansion after sample size adjustment, some rules for reestimating the sample size can be formulated. Through the simulation analysis, it can be seen that the statistical analysis system of college employment education based on the improved clustering algorithm proposed in this study has a good effect in the clustering of employment education data and has a certain role in promoting the employment of college graduates.


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## Body

## 1. Introduction

At present, under the guidance of “employment-oriented,” some colleges and universities in China put students’ professional skills training in a very prominent position, while students’ quality education has been neglected. In addition to the two compulsory courses, foreign language, physical education, and other compulsory courses stipulated by the Ministry of Education, other humanistic quality education courses have been neglected, resulting in the disadvantaged position of humanistic quality education courses in colleges and universities. Humanistic quality education and vocational and technical education play an equally important role in the growth and success of college students, and they are in a position that cannot be ignored in the employment and career development of college students. However, at present, the quality of education for student development in China’s colleges and universities is not in place, and quality education and practice are not enough. Moreover, education has not deeply analyzed the characteristics of college students, and the quality of talents demanded by the market needs to be improved, so that the problems existing in all aspects of students cannot be answered correctly and effectively. Second, quality education lacks pertinence. At present, the quality education of many colleges and universities is the traditional “big pot rice” education, which is the same as the education model of ordinary undergraduate colleges and does not educate students according to the actual situation of college students’ love of outdoor activities and lack of learning motivation. Third, the effect of quality education is not good. Colleges and universities generally adopt various forms and methods to carry out quality education, but the effect is not obvious. Moreover, the ideological level, learning ability, and daily behavior of students have not been significantly improved and improved, and the content of quality education has not been truly implemented.At present, under the guidance of “employment-oriented,” some colleges and universities in our country have placed the professional skills training of students in a very prominent position, while the quality education of students has been neglected. In addition to the two compulsory courses, foreign language, physical education, and other compulsory courses stipulated by the Ministry of Education, other humanistic quality education courses have been neglected, resulting in the disadvantaged position of humanistic quality education courses in colleges and universities. Humanistic quality education and vocational and technical education play an equally important role in the growth and success of college students, and they are in a position that cannot be ignored in the employment and career development of college students [1]. In order to achieve full employment, students in colleges and universities must shape themselves into an all-round development, with comprehensive quality and ability of senior professionals. The basic abilities it should have include the ability to adapt to society, practical ability, innovation ability and interpersonal communication ability, management ability, expression ability, core competitiveness, decision-making ability, team spirit, both ability and political integrity, and learning ability, in the final analysis, with the improvement of quality in all aspects [2]. However, at present, the quality of education for the development of students in various colleges and universities in our country is not in place, quality education and practice are not enough, there is no in-depth analysis of the characteristics of college students, and the quality of talents demanded by the market needs to be improved. Correct and effective answer: Second, quality education lacks pertinence. At present, many colleges and universities develop quality education, which is a traditional “big pot rice” education, which is the same as the education model of ordinary undergraduate colleges and is not aimed at college students. If students lack learning motivation due to their love of outdoor activities, they should be educated according to the actual situation [3]; third, the effect of quality education is not good; colleges and universities generally adopt various forms and methods to carry out quality education, but the effect is not obvious; students’ ideological level, learning ability, and daily behavior have not been significantly improved and improved, and the content of quality education has not been truly implemented [4].According to the research content of Western employment theory by Chinese and Western scholars, it is generally believed that Keynes’ previous employment theory (i.e., Western traditional employment theory) includes automatic employment equilibrium theory, equilibrium wage employment theory, and employment cycle fluctuation theory. The theory of automatic equilibrium emphasizes that the government should not intervene in the economy, because according to the spontaneous adjustment of the price mechanism, the commodity market and the production factor market will gradually tend to the equilibrium of supply and demand, which will lead to full employment. The unbalanced state of supply and demand is only temporary, and the self-regulation of the market will automatically restore it to an equilibrium state [5]. What the government can do is best limited to the role of encouraging production. The core content of the equilibrium wage employment theory is that the wage of labor is determined by demand and supply, while the amount of employment is determined by the equilibrium wage. The employment cycle fluctuation theory refers to the cyclical fluctuations of employment caused by the cyclical fluctuations of the economy, such as insufficient consumption, and the social demand for consumer goods cannot keep up with the growth of consumer goods supply; then the surplus of labor will lead to underemployment. Austrian economist Hayek believes that excessive investment will cause the supply of money to fail to meet the demand for money in real economic life. It will also lead to the phenomenon of underemployment [6]. Tavani and Zamparelli [7] pointed out that the old equilibrium caused by innovation is broken, and when transitioning to the new equilibrium, the labor force whose skills cannot keep up with the pace of innovation is eliminated, and unemployment becomes a helpless necessity. And society progresses in the process of breaking the old equilibrium from the new equilibrium, and unemployment caused by technological innovation will be inevitable. With Keynesian employment theory (i.e., modern employment theory), through Keynesian theoretical analysis, full employment can only appear when the total social supply and total demand are in the best state [8]. However, in the actual operation of the market economy, in order to achieve a balance between total social supply and total demand, we can only hope for economic contraction, which is contrary to the law of social progress. Portella-Carbó [9] believed that the realization of full employment must be done by vigorously stimulating demand and carrying out demand management. The lack of effective demand is the irreconcilable product of the market mechanism itself. In order to break through this practical bottleneck and expand the functions of the government, implementing the means of government intervention in the economy is an effective way to solve the problem. Keynes therefore also extended the macroeconomic policy proposition on solving the unemployment problem. Its main contents include tax policy, monetary policy, fiscal policy, and foreign trade policy. The core of Keynes’s policy proposition on solving the unemployment problem is to change laissez-faire and implement the policy of government intervention in the economy to increase the effective demand of the society and achieve full employment. The emergence of modern employment theory is due to the fact that the contradictions inherent in capitalist society have not been fundamentally eliminated by the Keynesian policy, and although the state intervention promoted by this policy has stimulated production to a certain extent, it has also contributed to a more serious crisis. Condition [10] is provided. In order to solve the inflation problem plaguing the capitalist economy, various new theories and theories have emerged one after another. The more important theoretical schools after Keynes are supply school, monetary school, rational expectation school, development economics, and new Keynesian school. In employment theory [11], the point of [12] is that the most convenient way to stimulate economic growth and expand employment can be achieved through tax cuts; any practice that increases the cost of labor use will hinder the expansion of employment. Clarkson [13] proposed the monetarist policy of “market unemployment rate” and “natural rate of unemployment.” By envisioning the formulation of a single monetary policy rule, the money supply will increase at a fixed rate, so as to achieve the goal of maintaining the stability of the capitalist economy, and under such an economic environment, the employment problem will be gradually solved.Promoting the employment of engineering students in colleges and universities is of great significance to the country, schools, and individuals. In addition, as colleges continue to expand enrollment and it is difficult for college students to find employment, it is particularly important to carry out employment promotion work to enhance the competitiveness of advanced engineering students in the job market and increase their employment rate [14].With the continuous expansion of the enrollment scale, the pressure of the oversupply of labor force across the country is increasing, and the graduates of colleges and universities have also encountered unprecedented employment pressure. In the face of the lack of sophisticated technical talents in high-end industries and the saturated supply of talents in low-end industries, the embarrassing situation of college graduates can be imagined. Explore scientific and reasonable employment education countermeasures for students in colleges and universities, while increasing students’ employment skills, guide students to establish correct employment values, improve students’ income chips, open up ideas for students’ employment, and help students pursue life goals and achieve life value which has become the driving force behind the reform of employment education.This study combines the improved clustering algorithm to conduct statistical analysis of employment education in colleges and universities to analyze the current situation of employment education in colleges and universities, which provides a reference for better development of employment education in the future.


## 2. Improved Clustering Algorithm

### 2.1. Adaptive Design

Considering the complexity of the statistic distribution after the reestimation of the sample size and the possible complex correlations between the statistic series in the group sequential design, Bauer and Kohne [15] proposed to carry out hypothesis test analysis on the stage data between each two analyses separately and finally merge the P values obtained by each hypothesis test in a certain form. Figure 1 shows an example of a two-stage adaptive sequential design. That is, first calculate the P1 of the first stage; if P1>β1, the null hypothesis H0 is not rejected in the early stage. If P1<α1, the null hypothesis H0 is rejected early. If α1≤P1≤β1, we continue to enroll subjects in the second stage, and after the enrollment is completed, the hypothesis test probability P2 of the second-stage samples is calculated separately, and P1 and P2 are combined into CP1,P2 in a certain form. If CP1,P2<β2, the null hypothesis H0 is rejected; otherwise, the null hypothesis H0 is not rejected.Figure 1
Two-stage adaptive sequential design diagram.There are many ways to combineP1 and P2. In fact, it can be shown that the MSP statistic is the general form of the Cui-Hung-Wang statistic, the latter were combined using the standard normal distribution statistic Zi, and the parameters w1′w2 were specified as the square root of the two-stage sample size percentage before sample size adjustment, the reason why a statistic is defined as a function of probability P. On the one hand, the probability P is simply distributed under the null hypothesis H0 and obeys the uniform distribution U (0, 1) on [0, 1]. On the other hand, it is due to the fact that the t-statistic is considered to be complicated in the correlation between the statistic series in the traditional group sequential design. When the probability P is used to construct the statistic and the sample size is readjusted, the conditional distribution P2|P1=p1∼U0,1 under the null hypothesis H0 is the same as the case where the variance is known.Although the above two statistics can accurately control the type I error at the presetα level, they also have certain defects. When P1⟶α1 or β2, the MPP statistic can almost 100% reject the null hypothesis H0 at the end of the period analysis. The MSP statistic is more prone to type II errors in interim analysis than the former. Based on the above two points, this study deduces a new statistic—MCP statistic.For brevity, the following assumes that the population variance is known and uses a two-stage adaptive sequential design as an example. In fact, based on the theory of two-stage adaptive design, it can be generalized to multistage adaptive design, and the generalization method will be introduced in the sample size adjustment based on conditional type I error.


### 2.2. Construction of MCP Statistics

Based on the probabilityP value of each stage, the MCP statistic is constructed: T1=P1,T2=w1P1+w2P22, and the rules for early termination of the experiment similar to the traditional group sequential design are specified:(1)IfT1≤α1,Terminate the test in advance and reject the null hypothesisH0,IfT1≥β1,Terminate the test in advance and do not reject the invalid hypothesisH0,Ifα1<T1<β1,Continue the second stage test.In the final analysis, ifT2≥β2, the null hypothesis H0 is not rejected, and if T2<β2, the null hypothesis H0 is rejected. α1,β1,β2 are the preset boundaries of the rejection domain or the accepted domain, respectively.The properties of this statistic are derived as follows:We assume a continuous variableX, and its distribution function is F(x). Obviously, the function F and its inverse function F−1 are both monotonically increasing functions.For one-sided hypothesis testing, the probabilityP = 1 − F(X), and then the distribution function of P is(2)PP≤p=P1−FX≤p=PX≥F−11−p=1−PX≤F−11−p=1−FF−11−p=pp∈0,1.For the two-sided hypothesis test, the probabilityP = 2(1 − F(|X|)), we assume that the statistic obeys a symmetrical distribution, and then the distribution function of P is(3)PP≤p=P2−2FX≤p=2PX≥F−11−p2=21−PX≤F−11−p2=21−FF−11−p2=pp∈0,1.From the above, it can be proved that the random variableP obeys a uniform distribution on [0, 1]; that is, T1 of the MCP statistic obeys a uniform distribution on [0, 1] under the null hypothesis.SinceP1=1−FZ1, the sample size of the second stage after the reestimation of the sample size is n˜2=N˜−n1=gZ1=hP1, and the conditional probability density function is fp2|p1=fp2|n˜2=1, so the joint distribution of P1 and P2 is fp1,p2=fp2|p1∗fp1=1.It is easy to find the Jacobian determinant fromP1,P2 to T1,T2 as(4)J=10hT1,T21w22−w1w22T1T2=1w22−w1w22T1T2.Then the joint probability density function ofT1,T2 is ft1,t2=J∗fp1,p2=1/w22−w1/w22t1/t2. The subprobability density function of T2 is ft2=∫α1β1ft1,t2dt2dt1.If the results of the interim analysis meet the conditions for rejectingH0 and early termination of the experiment under the premise that H0 is true, then the probability of making a type I error at this time is Prob=α1. Conversely, if the results of the interim analysis do not meet the conditions for early termination of the trial, further phase II trials are required. From the definition of T2, we know that T2≥w12T1. When w12β1≥β2, there is T1>β2/w12, at this time T2=w1T1+w2P22>β2, and H0 can be accepted without a second-stage test. Therefore, when w1β1≥β2, the probability of making a type I error in the end-of-period analysis is(5)Prob2=∫α1β2/w12∫w12t1β2ft1,t2dt2dt1=∫α1β2/w12∫w12t1β21w22−w1w22t1t2dt2dt1=⋯⋯=β226w12w22+4w1α1α1β23w22−w12α122w22−α1β2w22.Whenw1β1<β2, similar to the above calculation process, the probability of making a Type I error in the end-of-period analysis is(6)Prob2=∫α1β1∫w12t1β2ft1,t2dt2dt1=∫α1β1∫w12t1β21w22−w1w22t1t2dt2dt1=⋯⋯=6β2β1−α1+3w12β12−α12+8w1α1α1β2−8w1β1β1β26w22.The rejection of the null hypothesisH0 at the interim analysis and the rejection of the null hypothesis $H_{0}$ at the end of the period are two mutually exclusive and independent events. Therefore, in order to control the overall type I error to the preset inspection level α, it is necessary to satisfy(7)Prob1+Prob2=α.If the early termination of the experiment due to rejection of the null hypothesisH0 is not allowed in the interim analysis, the experiment will no longer make type I errors in the interim analysis, and α1=0 in equations (5) and (6). When w1β1≥β2, the probability of making a type I error in the end-of-period analysis is(8)Prob2=β226w12w22.Whenw1β1<β2, the probability of making a Type I error in the end-of-period analysis is(9)Prob2=6β1β2+3w12β12−8w1β1β1β26w22.Furthermore, it satisfies(10)Prob2=α.Under this constraint, the boundary valuesα1 and β1 can be selected according to the experimental design requirements and relevant regulations, and the boundary value β2 at the end of the period can be calculated.Since the joint distribution ofT1,T2 is not affected by the readjustment of the sample size, the MCP statistic can accurately control the total type I error of the trial at the preset α level.In a simulation of employment data that allows for sample size reestimation, it is not enough for a statistic to draw conclusions about whether to reject the null hypothesis. However, if the probabilityP value of hypothesis testing can be obtained, it will make this statistic more useful. In hypothesis testing, the P value is defined as the probability of the current situation and more extreme situations when the null hypothesis H0 is true. The smaller the P value, the stronger the reason for rejecting the null hypothesis H0. The probability P value of the traditional design is easily obtained according to the monotonicity of the likelihood ratio, while the adaptive design no longer has a monotonic likelihood ratio in the sample space due to the different number of subjects in different analysis stages. Therefore, a number of different definitions for “extreme” have been proposed, including stagewise ordering, maximum likelihood estimation order (MLE ordering), likelihood ratio order, and score test order, among which stage order is the most commonly used.For the MCP statistic, theP values based on the order of stages are(11)Pk=T1k=1,α1+T226w12w22+4w1α1α1T23w22−w12α122w22−α1T2w22k=2,w1β1≥β2,α1+6T2β1−α1+3w12β12−α12+8w1α1α1T2−8w1β1β1T26w22,k=2,w1β1<β2.One of the advantages of using the sequence of stages is that the results of the probabilityP(k) are guaranteed to be consistent with the hypothesis testing results. That is, if the null hypothesis is rejected at any stage at the α level, then Pk<α. Otherwise, Pk≥α.Noninferiority test and bioequivalence test are commonly used test methods in the simulation of new drug employment data. Compared with the traditional hypothesis testing, the confidence interval method has obvious advantages. The MCP statistic can also be used to estimate confidence intervals. Still taking the employment data simulation of the difference test between groups as an example, we assume that the actual difference between the group means isθ. Then, the confidence interval of the parameter to be tested refers to the interval composed of all possible values of θ calculated according to the current sample when the null hypothesis H0 is established. It is easy to obtain Pk′=1−FF−11−Pk−θnk/2σ,k=1,2,F⋅⋅ is the cumulative probability function of the normal distribution, F−1.. is its inverse function, Pk′ is the probability P value when the actual difference is θ, and Pk is the probability P value when the actual difference is equal to the H0 test value. If the trial is terminated at the interim analysis, the confidence interval for θ is the set(12)θ|1−FF−11−p1−θn12σ≥α1.If the trial is terminated at the end-of-period analysis, the confidence interval for $\theta$ is the set(13)θ|w11−FF−11−p1−θn12σ+w21−FF−11−p2−θn22σ2≥β2.


### 2.3. Reestimation of Sample Size

On the premise of ensuring that the statistics used will not cause type I error expansion after sample size adjustment, some rules for sample size reestimation can be formulated. From the derivation process of the statistic distribution, as long as the conditional probability density functionfp2|p1=1 of P2 is guaranteed, that is, when the sample size in the second stage is a function of the variable P1, the sample size can be adjusted “arbitrarily.” The commonly used adjustment rules are as follows:As mentioned earlier, the sample size estimation formula isN=2σ2Z1−α+Z1−β2/θ2. We assume that the initial estimated sample size of an experiment is N0 and the effect size is E0=θ/σ. Then, the effect size estimated from the sample of n1 cases in the interim analysis is E˜=θ˜/σ˜. The total sample size can be reestimated intuitively to be N˜=E0/E˜2N0, so that the sample size of the second phase trial is n˜2=N˜−n1. Generally, a minimum value n2min and a maximum value n2max are specified for n˜2, so the second-stage sample size of reestimation is n˜2re=minmaxn˜2,n2min,n2max.In an adaptively designed experiment, the conditional power is often more important than the total power. Based on conditional test power, it is possible not only to compare different experimental designs and statistical methods, but also to make decisions such as sample size reestimation. The so-called conditional test power refers to the probability of rejection of the null hypothesisH0 at the end of the period analysis after obtaining the results of the interim analysis under the alternative hypothesis H1, that is, the probability of T2|P1=p1,H1<β2. For the MCP statistic, conditional test power refers to the probability that P2|P1=p1,H1<β2−w1p12/w22.Taking the simulation of employment data comparing the means of the two groups as an example, we assume that, under the alternative hypothesisH1, θ is the actual difference between the means of the two groups, the variance of the variable is known as σ2,F is the standard normal distribution function, the sample size of each group in the second stage is n2, and then, the conditional distribution of P2 is Dp2|p1=PP2≤p2|p1=P1−FZ2≤p2|p1=PZ2≥F−11−p2|p1=1−FF−11−p2−θn2/2σ; therefore, the conditional test power of the MCP statistic is(14)cP=1−FF−11−β2−w1p12w22−θn22σ,(15)n˜2=2σ2θ2F−11−β2−w1p12w22−F−11−cP2.The sample sizen2 of the second stage can be estimated by specifying the conditional test power cP. Since σ and θ are often unknown, they can be replaced by the corresponding estimated values obtained from the interim analysis.Due to the constraints of human, financial, and material resources, a maximum sample sizen2max is specified for the second stage. At the same time, in order to make the sample size of the second stage not too small, a minimum sample size n2min is specified. We assume that the reestimated sample size calculated according to equation (15) is n˜2; then the sample size of the second stage is n˜2re=minmaxn˜2,n2min,n2max. According to equation (14), the probability density function of conditional test power cP can be obtained as f(cP). If the trial is terminated early, the expected sample size in the second stage is(16)En˜2stage=∫01minmaxn˜2,n2min,n2maxfcPdcP.The probability of terminating the experiment early because the data is valid ispe=ϕθRn1/2σ−ϕ−11−α1. And the probability of terminating the experiment early due to invalid data is pf=ϕϕ−11−β1−θRn1/2σ. Then, the expected total sample size is(17)En˜=pe+pf∗n1+1−pe−pf∗En˜2stage.It is worth mentioning that when the conditional test power is very low, it is possible that the sample size obtained by reestimating is larger than the sample size of starting a new simulation of employment data. At this point, it is necessary to discuss whether to continue the employment data simulation.Based on this idea, we can make(18)2σ˜2θ˜2ϕ−11−β2−w1p12w22−ϕ−11−cP2≤2σ˜2ϕ−11−α+ϕ−11−β2θ˜2.We assume that the conditional test power iscP=1−β and then simplify the above formula to get(19)p1≤β2−w2αw12.That is, whenp1>β2−w2α/w12, it would be a better choice to abandon the current experiment and start a new experiment purely from the point of view of saving the sample size statistically. Of course, researchers generally prefer to keep the employment data simulation intact. At the same time, it must be taken into account that the preparation of a new employment data simulation is also a rather complicated process. Therefore, this study proposes to set a multiple upper limit Δ, and when the reestimated sample size is greater than Δ times the sample size of a new employment data simulation, comprehensively consider various factors to decide whether to stop the current employment data simulation.The so-called conditional type I error refers to the probability of rejection of the null hypothesisH0 at the end of the period analysis after obtaining the results of the interim analysis under the null hypothesis H0, that is, the probability of T2|P1=p1,H0<β2. For the MCP statistic, that is the probability of P2|P1=p1,H0<β2−w1p12/w22. Since the conditional distribution of P2 is Fp2|p1=p2 under the H0 condition, the conditional type I error is Ap1=β2−w1p12/w22. In fact, if θ=0 in the conditional test efficiency formula, the above formula can also be obtained. It is easy to know from the definition that the unconditional type I error of the second stage is ∫α1β1Ap1dp1, and it satisfies α1+∫α1β1Ap1dp1=α; this formula is equation (14).The reason why it is called “staged” sample size readjustment is that the conditional type I error is mainly used to adjust the number of experimental stages compared to the conditional test power mainly used for sample size readjustment. Consider adding another interim analysis to the current design. We assume that, after adding a new experimental stage, the conditional type I error based onp1 becomes A∗p1, which is sufficient to keep the total type I error at the α level. Considering the following interim analysis and final analysis as a new two-stage adaptive sequential design experiment, the total type I error of these two stages needs to be controlled at the Ap1 level. We assume that the boundary values of the rejection domain and the acceptance domain are α2,β2′, respectively, in the second interim analysis, and the boundary value in the end-of-period analysis is β3. As before, when w1β2′≥β3, it needs to satisfy(20)Ap1=β326w12w22+4w1α2α2β33w22−w12α222w22−α2β3w22+α2.WhenQ = 1, it needs to satisfy(21)Ap1=6β3β2′−α2+3w12β2′2−α22+8w1α2α2β3−8w1β2′β2′β36w22+α2,α2,β2′, and β3 can be calculated.If the experimental stage is added in the above manner during the interim analysis, the corresponding parameters should also be adjusted in the reestimation of the sample size based on the conditional test power or the total test power. Referring to this idea, in the second interim analysis, we can also calculate the conditional type I error and continue to increase the analysis stage and make a reasonable sample size adjustment under the premise of controlling the conditional type I error.The MCP statisticT1=P1,T2=P1+2P22 is used. After the interim analysis results are obtained, the sample size is reestimated, and the reestimation formula is(22)n˜2=S˜2θ˜2ϕ−11−β2−p122−ϕ−11−cP2.Among them,S˜2 is the combined variance obtained from the interim analysis, θ˜2=μ˜experience group−μ˜control group+12,μ˜control groupμ˜experience group is the mean of the control group and the experimental group in the interim analysis, respectively.


## 2.1. Adaptive Design

Considering the complexity of the statistic distribution after the reestimation of the sample size and the possible complex correlations between the statistic series in the group sequential design, Bauer and Kohne [15] proposed to carry out hypothesis test analysis on the stage data between each two analyses separately and finally merge the P values obtained by each hypothesis test in a certain form. Figure 1 shows an example of a two-stage adaptive sequential design. That is, first calculate the P1 of the first stage; if P1>β1, the null hypothesis H0 is not rejected in the early stage. If P1<α1, the null hypothesis H0 is rejected early. If α1≤P1≤β1, we continue to enroll subjects in the second stage, and after the enrollment is completed, the hypothesis test probability P2 of the second-stage samples is calculated separately, and P1 and P2 are combined into CP1,P2 in a certain form. If CP1,P2<β2, the null hypothesis H0 is rejected; otherwise, the null hypothesis H0 is not rejected.Figure 1
Two-stage adaptive sequential design diagram.There are many ways to combineP1 and P2. In fact, it can be shown that the MSP statistic is the general form of the Cui-Hung-Wang statistic, the latter were combined using the standard normal distribution statistic Zi, and the parameters w1′w2 were specified as the square root of the two-stage sample size percentage before sample size adjustment, the reason why a statistic is defined as a function of probability P. On the one hand, the probability P is simply distributed under the null hypothesis H0 and obeys the uniform distribution U (0, 1) on [0, 1]. On the other hand, it is due to the fact that the t-statistic is considered to be complicated in the correlation between the statistic series in the traditional group sequential design. When the probability P is used to construct the statistic and the sample size is readjusted, the conditional distribution P2|P1=p1∼U0,1 under the null hypothesis H0 is the same as the case where the variance is known.Although the above two statistics can accurately control the type I error at the presetα level, they also have certain defects. When P1⟶α1 or β2, the MPP statistic can almost 100% reject the null hypothesis H0 at the end of the period analysis. The MSP statistic is more prone to type II errors in interim analysis than the former. Based on the above two points, this study deduces a new statistic—MCP statistic.For brevity, the following assumes that the population variance is known and uses a two-stage adaptive sequential design as an example. In fact, based on the theory of two-stage adaptive design, it can be generalized to multistage adaptive design, and the generalization method will be introduced in the sample size adjustment based on conditional type I error.


## 2.2. Construction of MCP Statistics

Based on the probabilityP value of each stage, the MCP statistic is constructed: T1=P1,T2=w1P1+w2P22, and the rules for early termination of the experiment similar to the traditional group sequential design are specified:(1)IfT1≤α1,Terminate the test in advance and reject the null hypothesisH0,IfT1≥β1,Terminate the test in advance and do not reject the invalid hypothesisH0,Ifα1<T1<β1,Continue the second stage test.In the final analysis, ifT2≥β2, the null hypothesis H0 is not rejected, and if T2<β2, the null hypothesis H0 is rejected. α1,β1,β2 are the preset boundaries of the rejection domain or the accepted domain, respectively.The properties of this statistic are derived as follows:We assume a continuous variableX, and its distribution function is F(x). Obviously, the function F and its inverse function F−1 are both monotonically increasing functions.For one-sided hypothesis testing, the probabilityP = 1 − F(X), and then the distribution function of P is(2)PP≤p=P1−FX≤p=PX≥F−11−p=1−PX≤F−11−p=1−FF−11−p=pp∈0,1.For the two-sided hypothesis test, the probabilityP = 2(1 − F(|X|)), we assume that the statistic obeys a symmetrical distribution, and then the distribution function of P is(3)PP≤p=P2−2FX≤p=2PX≥F−11−p2=21−PX≤F−11−p2=21−FF−11−p2=pp∈0,1.From the above, it can be proved that the random variableP obeys a uniform distribution on [0, 1]; that is, T1 of the MCP statistic obeys a uniform distribution on [0, 1] under the null hypothesis.SinceP1=1−FZ1, the sample size of the second stage after the reestimation of the sample size is n˜2=N˜−n1=gZ1=hP1, and the conditional probability density function is fp2|p1=fp2|n˜2=1, so the joint distribution of P1 and P2 is fp1,p2=fp2|p1∗fp1=1.It is easy to find the Jacobian determinant fromP1,P2 to T1,T2 as(4)J=10hT1,T21w22−w1w22T1T2=1w22−w1w22T1T2.Then the joint probability density function ofT1,T2 is ft1,t2=J∗fp1,p2=1/w22−w1/w22t1/t2. The subprobability density function of T2 is ft2=∫α1β1ft1,t2dt2dt1.If the results of the interim analysis meet the conditions for rejectingH0 and early termination of the experiment under the premise that H0 is true, then the probability of making a type I error at this time is Prob=α1. Conversely, if the results of the interim analysis do not meet the conditions for early termination of the trial, further phase II trials are required. From the definition of T2, we know that T2≥w12T1. When w12β1≥β2, there is T1>β2/w12, at this time T2=w1T1+w2P22>β2, and H0 can be accepted without a second-stage test. Therefore, when w1β1≥β2, the probability of making a type I error in the end-of-period analysis is(5)Prob2=∫α1β2/w12∫w12t1β2ft1,t2dt2dt1=∫α1β2/w12∫w12t1β21w22−w1w22t1t2dt2dt1=⋯⋯=β226w12w22+4w1α1α1β23w22−w12α122w22−α1β2w22.Whenw1β1<β2, similar to the above calculation process, the probability of making a Type I error in the end-of-period analysis is(6)Prob2=∫α1β1∫w12t1β2ft1,t2dt2dt1=∫α1β1∫w12t1β21w22−w1w22t1t2dt2dt1=⋯⋯=6β2β1−α1+3w12β12−α12+8w1α1α1β2−8w1β1β1β26w22.The rejection of the null hypothesisH0 at the interim analysis and the rejection of the null hypothesis $H_{0}$ at the end of the period are two mutually exclusive and independent events. Therefore, in order to control the overall type I error to the preset inspection level α, it is necessary to satisfy(7)Prob1+Prob2=α.If the early termination of the experiment due to rejection of the null hypothesisH0 is not allowed in the interim analysis, the experiment will no longer make type I errors in the interim analysis, and α1=0 in equations (5) and (6). When w1β1≥β2, the probability of making a type I error in the end-of-period analysis is(8)Prob2=β226w12w22.Whenw1β1<β2, the probability of making a Type I error in the end-of-period analysis is(9)Prob2=6β1β2+3w12β12−8w1β1β1β26w22.Furthermore, it satisfies(10)Prob2=α.Under this constraint, the boundary valuesα1 and β1 can be selected according to the experimental design requirements and relevant regulations, and the boundary value β2 at the end of the period can be calculated.Since the joint distribution ofT1,T2 is not affected by the readjustment of the sample size, the MCP statistic can accurately control the total type I error of the trial at the preset α level.In a simulation of employment data that allows for sample size reestimation, it is not enough for a statistic to draw conclusions about whether to reject the null hypothesis. However, if the probabilityP value of hypothesis testing can be obtained, it will make this statistic more useful. In hypothesis testing, the P value is defined as the probability of the current situation and more extreme situations when the null hypothesis H0 is true. The smaller the P value, the stronger the reason for rejecting the null hypothesis H0. The probability P value of the traditional design is easily obtained according to the monotonicity of the likelihood ratio, while the adaptive design no longer has a monotonic likelihood ratio in the sample space due to the different number of subjects in different analysis stages. Therefore, a number of different definitions for “extreme” have been proposed, including stagewise ordering, maximum likelihood estimation order (MLE ordering), likelihood ratio order, and score test order, among which stage order is the most commonly used.For the MCP statistic, theP values based on the order of stages are(11)Pk=T1k=1,α1+T226w12w22+4w1α1α1T23w22−w12α122w22−α1T2w22k=2,w1β1≥β2,α1+6T2β1−α1+3w12β12−α12+8w1α1α1T2−8w1β1β1T26w22,k=2,w1β1<β2.One of the advantages of using the sequence of stages is that the results of the probabilityP(k) are guaranteed to be consistent with the hypothesis testing results. That is, if the null hypothesis is rejected at any stage at the α level, then Pk<α. Otherwise, Pk≥α.Noninferiority test and bioequivalence test are commonly used test methods in the simulation of new drug employment data. Compared with the traditional hypothesis testing, the confidence interval method has obvious advantages. The MCP statistic can also be used to estimate confidence intervals. Still taking the employment data simulation of the difference test between groups as an example, we assume that the actual difference between the group means isθ. Then, the confidence interval of the parameter to be tested refers to the interval composed of all possible values of θ calculated according to the current sample when the null hypothesis H0 is established. It is easy to obtain Pk′=1−FF−11−Pk−θnk/2σ,k=1,2,F⋅⋅ is the cumulative probability function of the normal distribution, F−1.. is its inverse function, Pk′ is the probability P value when the actual difference is θ, and Pk is the probability P value when the actual difference is equal to the H0 test value. If the trial is terminated at the interim analysis, the confidence interval for θ is the set(12)θ|1−FF−11−p1−θn12σ≥α1.If the trial is terminated at the end-of-period analysis, the confidence interval for $\theta$ is the set(13)θ|w11−FF−11−p1−θn12σ+w21−FF−11−p2−θn22σ2≥β2.


## 2.3. Reestimation of Sample Size

On the premise of ensuring that the statistics used will not cause type I error expansion after sample size adjustment, some rules for sample size reestimation can be formulated. From the derivation process of the statistic distribution, as long as the conditional probability density functionfp2|p1=1 of P2 is guaranteed, that is, when the sample size in the second stage is a function of the variable P1, the sample size can be adjusted “arbitrarily.” The commonly used adjustment rules are as follows:As mentioned earlier, the sample size estimation formula isN=2σ2Z1−α+Z1−β2/θ2. We assume that the initial estimated sample size of an experiment is N0 and the effect size is E0=θ/σ. Then, the effect size estimated from the sample of n1 cases in the interim analysis is E˜=θ˜/σ˜. The total sample size can be reestimated intuitively to be N˜=E0/E˜2N0, so that the sample size of the second phase trial is n˜2=N˜−n1. Generally, a minimum value n2min and a maximum value n2max are specified for n˜2, so the second-stage sample size of reestimation is n˜2re=minmaxn˜2,n2min,n2max.In an adaptively designed experiment, the conditional power is often more important than the total power. Based on conditional test power, it is possible not only to compare different experimental designs and statistical methods, but also to make decisions such as sample size reestimation. The so-called conditional test power refers to the probability of rejection of the null hypothesisH0 at the end of the period analysis after obtaining the results of the interim analysis under the alternative hypothesis H1, that is, the probability of T2|P1=p1,H1<β2. For the MCP statistic, conditional test power refers to the probability that P2|P1=p1,H1<β2−w1p12/w22.Taking the simulation of employment data comparing the means of the two groups as an example, we assume that, under the alternative hypothesisH1, θ is the actual difference between the means of the two groups, the variance of the variable is known as σ2,F is the standard normal distribution function, the sample size of each group in the second stage is n2, and then, the conditional distribution of P2 is Dp2|p1=PP2≤p2|p1=P1−FZ2≤p2|p1=PZ2≥F−11−p2|p1=1−FF−11−p2−θn2/2σ; therefore, the conditional test power of the MCP statistic is(14)cP=1−FF−11−β2−w1p12w22−θn22σ,(15)n˜2=2σ2θ2F−11−β2−w1p12w22−F−11−cP2.The sample sizen2 of the second stage can be estimated by specifying the conditional test power cP. Since σ and θ are often unknown, they can be replaced by the corresponding estimated values obtained from the interim analysis.Due to the constraints of human, financial, and material resources, a maximum sample sizen2max is specified for the second stage. At the same time, in order to make the sample size of the second stage not too small, a minimum sample size n2min is specified. We assume that the reestimated sample size calculated according to equation (15) is n˜2; then the sample size of the second stage is n˜2re=minmaxn˜2,n2min,n2max. According to equation (14), the probability density function of conditional test power cP can be obtained as f(cP). If the trial is terminated early, the expected sample size in the second stage is(16)En˜2stage=∫01minmaxn˜2,n2min,n2maxfcPdcP.The probability of terminating the experiment early because the data is valid ispe=ϕθRn1/2σ−ϕ−11−α1. And the probability of terminating the experiment early due to invalid data is pf=ϕϕ−11−β1−θRn1/2σ. Then, the expected total sample size is(17)En˜=pe+pf∗n1+1−pe−pf∗En˜2stage.It is worth mentioning that when the conditional test power is very low, it is possible that the sample size obtained by reestimating is larger than the sample size of starting a new simulation of employment data. At this point, it is necessary to discuss whether to continue the employment data simulation.Based on this idea, we can make(18)2σ˜2θ˜2ϕ−11−β2−w1p12w22−ϕ−11−cP2≤2σ˜2ϕ−11−α+ϕ−11−β2θ˜2.We assume that the conditional test power iscP=1−β and then simplify the above formula to get(19)p1≤β2−w2αw12.That is, whenp1>β2−w2α/w12, it would be a better choice to abandon the current experiment and start a new experiment purely from the point of view of saving the sample size statistically. Of course, researchers generally prefer to keep the employment data simulation intact. At the same time, it must be taken into account that the preparation of a new employment data simulation is also a rather complicated process. Therefore, this study proposes to set a multiple upper limit Δ, and when the reestimated sample size is greater than Δ times the sample size of a new employment data simulation, comprehensively consider various factors to decide whether to stop the current employment data simulation.The so-called conditional type I error refers to the probability of rejection of the null hypothesisH0 at the end of the period analysis after obtaining the results of the interim analysis under the null hypothesis H0, that is, the probability of T2|P1=p1,H0<β2. For the MCP statistic, that is the probability of P2|P1=p1,H0<β2−w1p12/w22. Since the conditional distribution of P2 is Fp2|p1=p2 under the H0 condition, the conditional type I error is Ap1=β2−w1p12/w22. In fact, if θ=0 in the conditional test efficiency formula, the above formula can also be obtained. It is easy to know from the definition that the unconditional type I error of the second stage is ∫α1β1Ap1dp1, and it satisfies α1+∫α1β1Ap1dp1=α; this formula is equation (14).The reason why it is called “staged” sample size readjustment is that the conditional type I error is mainly used to adjust the number of experimental stages compared to the conditional test power mainly used for sample size readjustment. Consider adding another interim analysis to the current design. We assume that, after adding a new experimental stage, the conditional type I error based onp1 becomes A∗p1, which is sufficient to keep the total type I error at the α level. Considering the following interim analysis and final analysis as a new two-stage adaptive sequential design experiment, the total type I error of these two stages needs to be controlled at the Ap1 level. We assume that the boundary values of the rejection domain and the acceptance domain are α2,β2′, respectively, in the second interim analysis, and the boundary value in the end-of-period analysis is β3. As before, when w1β2′≥β3, it needs to satisfy(20)Ap1=β326w12w22+4w1α2α2β33w22−w12α222w22−α2β3w22+α2.WhenQ = 1, it needs to satisfy(21)Ap1=6β3β2′−α2+3w12β2′2−α22+8w1α2α2β3−8w1β2′β2′β36w22+α2,α2,β2′, and β3 can be calculated.If the experimental stage is added in the above manner during the interim analysis, the corresponding parameters should also be adjusted in the reestimation of the sample size based on the conditional test power or the total test power. Referring to this idea, in the second interim analysis, we can also calculate the conditional type I error and continue to increase the analysis stage and make a reasonable sample size adjustment under the premise of controlling the conditional type I error.The MCP statisticT1=P1,T2=P1+2P22 is used. After the interim analysis results are obtained, the sample size is reestimated, and the reestimation formula is(22)n˜2=S˜2θ˜2ϕ−11−β2−p122−ϕ−11−cP2.Among them,S˜2 is the combined variance obtained from the interim analysis, θ˜2=μ˜experience group−μ˜control group+12,μ˜control groupμ˜experience group is the mean of the control group and the experimental group in the interim analysis, respectively.


## 3. Statistical Analysis of Employment Education in Colleges and Universities Based on Improved Clustering Algorithm

Referring to the existing website and the actual needs of users, the employment distance education platform for graduates is divided into three types of users, namely, the student end, the training lecturer end, and the administrator. Each type of user corresponds to corresponding functional modules, and in the form of mobile applications, it can meet the needs of students to study anytime and anywhere and effectively solve the problem of employment difficulties for college graduates in the computer industry. The overall functional structure is shown in Figure2.Figure 2
The overall functional structure of the employment education platform.By establishing a conceptual model, it is convenient to design the database table structure. According to the overall function diagram, the E-R diagram describing the entity is shown in Figure3.Figure 3
E-R diagram.The shared intelligent warehouse leasing platform uniformly uploads the intelligent warehouse operation data to the enterprise big data platform for classification and screening, aggregation, extraction, mining, and analysis of scattered and repeated data to form valuable big data in logistics and warehousing. After that, the data can be applied to the coordination, management, collaboration, and decision-making of the whole process of enterprise control and management. The big data platform architecture is shown in Figure4 which is divided into four layers: data source, big data acquisition, big data processing, and big data service.Figure 4
Warehouse big data application.The intelligent employment service of colleges and universities based on big data needs to contact various departments of the school. It needs to be based on big data thinking and technology to build an intelligent employment service model for colleges and universities that is oriented by student training and centered on the precise employment of college students, integrating recruitment, education, evaluation, monitoring, and research and judgment, as shown in Figure5.Figure 5
Intelligent employment service model in colleges and universities based on big data.Based on the intelligent employment service model, this research combines the front-end demand analysis to design the overall architecture of the intelligent employment platform based on the principle of “data consistency and on-demand sharing.” The main contents and the logical relationship between them are shown in Figure6.Figure 6
The overall architecture of the college intelligent employment platform based on big data.This study integrates personal information, college career guidance information, and enterprise recruitment information in the three aspects of individual-college-enterprise to increase the communication between units and graduates, provide reliable recruitment channels, and solve the problem of graduate employment difficulties. Figure7 shows an example of college employment information interaction.Figure 7
Example of college employment information interaction. (a) Information exchange between graduates and schools. (b) Information exchange between schools and enterprises. (c) Information exchange between graduates and enterprises.
(a)(b)(c)This study analyzes the effect of the improved clustering algorithm proposed in this study in the statistics of employment education in colleges and universities. The results of the statistical simulation test are shown in Figure8.Figure 8
Simulation analysis of the clustering effect.Through the simulation analysis, it can be seen that the statistical analysis system of college employment education based on the improved clustering algorithm proposed in this study has a good effect in the clustering of employment education data. After that, this study analyzes the effect of the statistical analysis system of employment education in colleges and universities based on the improved clustering algorithm and obtains the results given in Table1.Table 1
Analysis of the effect of the statistical analysis system of employment education in colleges and universities based on the improved clustering algorithm.
NumEmployment educationNumEmployment educationNumEmployment education182.55977.521778.36278.691079.551880.07380.601176.971982.96482.361283.662076.20577.381376.362182.98683.141478.712280.48783.791577.662380.29881.001680.052479.02Through the above analysis, it can be seen that the statistical analysis system of college employment education based on the improved clustering algorithm proposed in this study can effectively improve the effect of employment education and has a certain role in promoting the employment of college graduates.


## 4. Conclusion

In order to achieve full employment, students in colleges and universities must shape themselves into a high-level professional talent with all-round development and comprehensive quality and ability. The basic abilities they should have include the ability to adapt to the society, practical ability, innovation ability and interpersonal communication ability, management ability, expression ability, core competitiveness, decision-making ability, team spirit, both ability and political integrity, and learning ability. This study combines the improved clustering algorithm to conduct statistical analysis of employment education in colleges and universities to analyze the current situation of employment education in colleges and universities. Through the simulation analysis, it can be seen that the statistical analysis system of college employment education based on the improved clustering algorithm proposed in this study has a good effect in the clustering of employment education data and has a certain role in promoting the employment of college graduates.



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*Source: 5776831-2022-07-11.xml*