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接着看3.2 scaling过程:
3.2.2 Raw HSC marks
Raw HSC marks, rather than the Board’s reported HSC marks, are used in the scaling process.
A student’s raw HSC mark in a course is the average of their raw examination mark and their raw
moderated school assessment. These marks are not reported to students.
scaling过程使用HSC原始分而不是boardofstudies报告的HSC分数。学生的HSC原始分是原始的考试分和调整后的学校考试分想加后的平均值。这些分数不告诉学生。
3.2.4 Initial standardisation
Before the scaling algorithm is implemented, a linear transformation is applied to the raw HSC marks in
each course to set the top mark to a common value. The marks in each course are then standardised to
a mean of 25 and standard deviation of 12 on a one-unit basis.
在应用scaling算法之前,先对HSC原始分进行线性处理,这样每门课的最高分都变成一样的一个值。接着,每门课中的所有分数都按照一个unit为基础转换成均值为25,标准差为12的正态分布分数。
举个例子说明一下经过以上两步以后数值的变化:
以物理和化学为例:
物理的最高分原始分是95,化学的最高原始分是89;小A的物理原始分是82。
根据3.2.4,第一步是线性变化,假设那个common value是100,那么物理的最高分变成了100,化学的最高分也变成了100;小A的物理原始分变成了82*100/89=92.1;下一步,小A的化学分按照一个unit计算就是92.1/2=46.05,然后这个分数再按照均值为25,标准差为12进行标准化处理,得到另外一个数,让我们说是48。
3.2.5 Calculating scaled means and standard deviations
The model underpinning the scaling algorithm specifies that the scaled mean in a course is equal to the
average academic achievement of the course candidature where, for individual students, the measure
of academic achievement is taken as the average scaled mark in all courses completed. The model
specification leads to a set of simultaneous equations from which the scaled means of 2 unit courses
are calculated.
The scaled standard deviation for a 2 unit course is the standard deviation of the measure of overall
academic achievement of the candidature of that course.
下一步是计算scaled mean和标准差。
第一小段由两个句子组成。都是复合句。第一个句子的主语是 The model,谓语是specifies 然后是specifies的以that引导宾语从句。宾语从句的主语是scaled mean,系动词is equal to,然后是表语部分 average academic achievement。在表语部分之后,继续对表语部分进行解释说明。翻译如下:
scaling算法的模型指定scaled mean等于所有本门课程考生的平均学术成就。每个学生的学术成就的衡量是其在所有完成的课程的scaled mark的平均值。根据模型的要求产生一系列的联立方程来计算书一门2u课程的scaled mean。
注意,我理解第一个句子中的scaled mark是上一步3.2.4中标准化处理后的数,对于小A就是那个48。
注意以上是2u课程scaled mean的计算。
3.2.5剩下部分说明SD如何计算,一些特殊的情况如数学,英语,历史extension如何计算等。略过。
3.2.6 Setting maximum marks
The maximum possible scaled mark in a course is determined according to the academic quality of
the course candidature in such a way that the maximum possible scaled mark for the combined 2 unit
English candidature is 50 on a one-unit basis.
In 2011 the maximum possible scaled mark in a course was given by the smaller of 50 and the scaled
mean + 2.47 times the initial scaled standard deviation, where the scaled mean and initial scaled
standard deviation of the course are determined using the scaling algorithm.
The number, 2.47, was determined on the basis that the maximum possible scaled mark in the
combined 2 unit English course is 50. This number is calculated afresh each year.
3.2.6说明scaling后每门课的最高分是如何得到的。简单说是50或者3.2.5中算出的scaled mean+2.47*SD两者中的分数小的。
3.2.7 Scaling individual marks
Once the scaled means and standard deviations are determined, individual raw marks are scaled using
a non-linear transformation which preserves the scaled mean and standard deviation of a course and
restricts the scaled marks to the range (0–50).
If the actual maximum scaled mark in a course is less than the maximum possible scaled mark a further
linear transformation is applied. The effect of this linear transformation is that, while the scaled mean
for a course is not changed, the standard deviation is increased when the actual maximum scaled mark
in the course is changed to be the same as the maximum possible scaled mark. In all tables presented
in this report the modified scaled standard deviations rather than the initial scaled standard deviations
are shown.
For some courses with very small candidatures the non-linear transformation is not always appropriate,
in which case alternative transformations, which are consistent with the principles of the scaling
algorithm, are used.
3.2.7说明每个个人的是如何scaled。简单来说,就是3.2.5得出scaled mean和SD之后,在用学生的HSC原始分计算scaled分数。按照以前的例子,小A的化学原始分82/2=41以及由3.2.5得出的scaled mean和SD折算小A在化学这科目上的scaled分数。
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