各级难度试题分值比例的确定

在考分呈正态分布,最高分≤98的概率为99.7%的假设下,获得了考分分布的各项常模参数,据此提出了考分期望值μ的合理值域为〔65,81〕(百分制).根据"难度越大得分越低,分值比例越小"的一般规律,按统计学观点导出了三级、六级和五级难度下每级试题的得分期望值{Hi},继而在一定的约束条件下通过求解方程∑aiHi=μ的最优合理解,求得各级试题的分值比例{ai}.本文的结果不仅为6∶3∶1,7∶2∶1,8∶1∶1等组卷经验方案提供了理论依据,而且为进一步确定各级难度试题的题量比例奠定了基础.

The Confirmation of Point Percentage for Test Questions of Difficulties at all Levels

In this paper, by supposition that test points assume normal distribution and the probability of the highest test point≤98 equal to 99.7%, parameters of normal modes under the distributions are gained. Hereby, the range of the desired values of test points is 65,81] (percentage). The greater the difficulty scale, the smaller the point percentage. According to statistics principle, {H_i}:the desired values of test points of questions for difficulty levels 3, levels 6 and levels 5 are exported. Afterwards, under constraint conditions, by solutions of optimization for the equation ∑a_iH_i=μ, {ai}:the point percentage of questions for difficulty levels3, levels 6 and levels 5 are gained. The results of this paper provide the theoretical bases for 6:3:1,7:2:1,8:1:1,etc. experience schemes for builder of paper, and the foundation for deciding the percentage of test questions of difficulties at all levels.