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percentile

百分位数、百分位等级、插值法 (Percentile, percentile rank and interpolation)

百分位数、百分位等级 (Percentile and percentile rank)

百分位等级 (Percentile rank)

某一分布中,分数 (score) 在某一值之下或等于该值的个体所占的百分比。1)
In a distribution, the percentage of individuals whose scores are below or equal to a certain value. 2)

百分位数 (Percentile)

恰取这一值的分数称为这一百分位等级的百分位数。
The score that takes exactly this value is called the percentile of this percentile rank.

例子 (Example)

有 58% 的同学分数为 7 分或在 7 分下,则分数 X=7 的百分位等级为 58% ,这个分数就是第 58 个百分位数。
If 58% of the students have a score of 7 or below, the percentile rank of X=7 is 58% , so the X=7 is the 58th percentile.

注意事项 (Notes)

在某一个案例中,分数有 1 - 5 分,对于分数 4 , 算得其对应的累积百分比是 95% ;但注意,分数 4 意味着一个人得分在 3.5 和 4.5 之间,第 95 百分位数是 4.5 ,而不是 4.0 。
In one case, the score is 1 - 5 , and for a score of 4 , the corresponding cumulative percentage is 95% ; but note that a score of 4 means that a person scores between 3.5 and 4.5 , and the 95th percentile is 4.5 , not 4.0 .


插值法 (Interpolation)

插值法是一种求解两个数值之间某位置数值的方法,其假设是在所求解点的附近1个组距单位区间之内的分数和对应的百分比的变化是线性的。
Interpolation is a method to calculate the value of a certain number between two numbers. The hypothesis of interpolation is that, the change in scores and percentages within a unit interval of 1 group distance around the solved point is linear.

插值法步骤 (The steps of interpolation)

假设要求的数值如图所示:
Suppose the value to be solved is shown as follows:

1. 找到距求解点最近的两个区间(较远的区间不满足分数和对应的百分比线性变化的假设)。
Find the 2 nearest intervals to the value to be solves (Further intervals do not requires the hypothesis of scores and percentages changing linearly).

2. 根据数据列出方程:
Make an equation based on the data:

3. 由等式求得结果
Calculate the equation, and get the result of .

1)
《心理学名词》(第二版):百分位数,指在整个分布中,某一值之下或等于该值的分数的百分比所对应的分数。百分等级,指在频率分布或分数群中低于给定值的那个分数的百分位数。与给定值对应。
2)
APA Dictionary: Percentile, the location of a score in a distribution expressed as the percentage of cases in the data set with scores equal to or below the score in question. Thus, if a score is said to be in the 90th percentile this means that 90% of the scores in the distribution are equal to or lower than that score. Also called percentile rank.
percentile.txt · 最后更改: 2024/03/12 07:29 由 hant_g._cavendish