Statistics 简明教程

Statistics - Transformations

数据转换是指对数据集中的每一项应用一个函数。在这里，$ x_i $ 被其转换后的值 $ y_i $ 替换，其中 $ y_i = f(x_i) $。通常执行数据转换是为了使图表的外观更易于解释。

Data transformation refers to application of a function to each item in a data set. Here $ x_i $ is replaced by its transformed value $ y_i $ where $ y_i = f(x_i) $. Data transformations are carried out generally to make appearance of graphs more interpretable.

有四个主要函数用于转换。

There are four major functions used for transformations.

$ log x $ - logarithm transformations. For example sound units are in decibels and is generally represented using log transformations.
$ \frac{1}{x} $ - Reciprocal Transformations. For example Time to complete race/ task is represents using speed. More the speed lesser the time taken.
$ \sqrt{x} $ - Square root Transformations. For example areas of circular ground are compared using their radius.
$ {x^2} $ - Power Transformations. For example to compare negative numbers.

对正数使用对数和平方根转换，而对负数和正数则可以使用等效和幂转换。

logarithm and Square root Transformations are used in case of positive numbers where as Reciprocal and Power Transformations can be used in case of both negative as well as positive numbers.

下面的图表说明了如何使用对数转换来比较人口分布。

Following diagrams illustrates the use of logarithm transformation to compare population graphically.

Before transformation

After transformation