發(fā)布時間：2019-05-24 11:44

【摘要】：本文通過蒙特卡洛模擬方法，采用錨題設計，模擬不同參照基準與年級離散程度下，對垂直等值產(chǎn)生的影響。結(jié)果發(fā)現(xiàn)： （1）在均值上，以年級1為基準的各年級的難度均值與1年級距離越遠，其值與真值的差異越大；同時隨著年級間的離散程度增大，所有年級的難度的D值絕對值呈現(xiàn)明顯的遞增趨勢。在基準年級2上，只有年級4呈現(xiàn)遞增趨勢，但是相比較基準年級1，在年級2、年級3與年級4上D值的絕對值明顯下降。在錨題上，基準年級為1年級時，在1與1.5的年級離散上，錨題難度值隨著年級增大，真值與估計值的差異呈現(xiàn)遞增趨勢；同時不同年級間錨題隨著年級離散程度增大，與真值差異有規(guī)律的增大；在2年級的基準上則只有Mm34b隨著效應呈現(xiàn)遞增趨勢，，同時與1年級基準相比，其與真值差異明顯要更小。 （2）在b參數(shù)RMSE上，難度b值在1年級的基準上，1與2年級隨著離散程度增大仍然比較穩(wěn)定；而3與4年級趨近，但是隨著年級離散程度增大而明顯增大，同時在不同效應大小上普遍高于年級1與年級2；在2年級基準上，年級1與年級2、年級3趨近，且隨著年級離散趨勢增大RMSE的變化不明顯，但4年級隨著離散增大明顯上升，且RMSE普遍高于其他年級。 （3）在a參數(shù)RMSE上，無論是參照基準年級1還是參照基準年級2，年級1、年級2與年級3上的區(qū)分度RMSE在不同效應上趨于穩(wěn)定與一致，但是年級4則隨著年級離散程度增大而增大，且同一離散程度上普遍高于其他年級。 （4）θ參數(shù)RMSE值，其與b值的RMSE值基本趨于一致，只是年級3與年級4在不同年級離散程度上起伏程度相對較小。 （5）效應大小ES值，在ES估計與真值的對比上，只有基準年級1的ES值隨著年級與年級離散程度增大而增大，但只呈現(xiàn)微弱的遞增趨勢，而基準年級2只在3與4年級間，隨著效應大小增大呈現(xiàn)遞增趨勢，其余年級間都呈現(xiàn)無規(guī)律現(xiàn)象，且基準年級2比基準年級1的D值的絕對值更小. （6）水平距離HD的均值，HD均值在與真值比較上，無論是基準1或者基準2，隨著年級與年級之間的離散程度ES增加，HD與真值的差呈現(xiàn)明顯的遞增趨勢，但相對而言，基準年級2的D值的絕對更小。 （7）不同比例水平距離HD值，不同的參照基準上，在0.5效應大小上，不同年級與不同百分比的水平距離上的D值沒有明顯的規(guī)律變化，但是隨著效應大小的增大，越遠離基準年級，D值呈現(xiàn)規(guī)律性的增加，且不同百分比上的水平距離也呈現(xiàn)規(guī)律性的增大，但是總體上，基準年級2明顯比基準年級1的精度更好。 綜合上述認為，不同基準與年級離散程度會對垂直等值效果產(chǎn)生較大的影響。
[Abstract]:In this paper, Monte Carlo simulation method is used to simulate the influence of different reference frames and grade discretization on vertical equivalence by using anchor design. The results show that: (1) in the mean value, the farther the distance between the average difficulty of each grade based on grade 1 and grade 1, the greater the difference between the value and the true value; At the same time, with the increase of the degree of dispersion between grades, the absolute value of D value of difficulty in all grades shows an obvious increasing trend. In grade 2, only grade 4 showed an increasing trend, but compared with grade 1, the absolute value of D value in grade 2, grade 3 and grade 4 decreased significantly. On the anchor problem, when the benchmark grade is grade 1, the difficulty value of anchor problem increases with the grade of grade 1 and 1.5, and the difference between the true value and the estimated value shows an increasing trend. At the same time, with the increase of the degree of dispersion of different grades, the difference between anchoring problems and true values increases regularly. On the benchmark of grade 2, only Mm34b showed an increasing trend with the effect, and compared with the benchmark of grade 1, the difference between the benchmark and the true value was significantly smaller. (2) on the b parameter RMSE, the difficulty b value is on the benchmark of grade 1, and the grade 1 and grade 2 are still stable with the increase of the degree of discretization; Grade 3 and grade 4 approach, but it increases obviously with the increase of grade dispersion, and is generally higher than grade 1 and grade 2 in different effect sizes. On the benchmark of grade 2, grade 1 and grade 2 and grade 3 approached, and the change of RMSE was not obvious with the increase of grade discretization, but the RMSE of grade 4 increased obviously with the increase of dispersion, and the RMSE was generally higher than that of other grades. (3) on the a parameter RMSE, the discrimination RMSE on the reference grade 1 or the reference grade 2, grade 1, grade 2 and grade 3 tends to be stable and consistent in different effects. However, grade 4 increases with the increase of grade discretization, and the same degree of discretization is generally higher than that of other grades. (4) the RMSE value of theta parameter tends to be basically consistent with the RMSE value of b value, but the fluctuation degree of grade 3 and grade 4 is relatively small in different grades. (5) in the comparison of ES estimation and true value, only the es value of benchmark grade 1 increases with the increase of grade and grade dispersion, but only shows a weak increasing trend, while the base grade 2 is only between grade 3 and grade 4. With the increase of the effect, there is an irregular phenomenon among the other grades, and the absolute value of the D value of the benchmark grade 2 is smaller than that of the benchmark grade 1. (6) the mean value of horizontal distance HD and the mean value of HD are compared with the true value, whether it is benchmark 1 or benchmark 2, with the increase of ES between grade and grade, the difference between HD and true value shows an obvious increasing trend, but relatively speaking, The D value of benchmark grade 2 is absolutely smaller. (7) there is no obvious regular change in D value between different grades and different percentages of horizontal distance on different proportion horizontal distance HD values and different reference frames, but with the increase of effect size, the D value of different grades and different percentages of horizontal distance does not change regularly, but with the increase of effect size, the D value of different grades and different percentages of horizontal distance does not change regularly, but with the increase of effect size, The farther away from the base grade, the D value increases regularly, and the horizontal distance in different percentages also increases regularly, but on the whole, the accuracy of benchmark grade 2 is obviously better than that of reference grade 1. According to the above, the dispersion degree of different datum and grade will have a great influence on the vertical equivalence effect.
【學位授予單位】：江西師范大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：B841

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