Statistics Notes: Percentage differences, symmetry, and natural logarithms
Statistics Notes: Percentage differences, symmetry, and natural logarithms
复制标题
DOI：
10.1136/bmj.j3683
复制
发表时间：
2017-08-16
影响因子：
105.7
通讯作者：
Altman, Douglas G.
中科院分区：
文献类型：
--
作者：
Cole, Tim J.;Altman, Douglas G.
尽管对数变换在统计学中被广泛使用，但它可能会让非统计学家感到不舒服。这是一个耻辱，因为对数具有非常有用的性质，包括一个甚至在统计学家中也不广为人知的秘密。两种常见的对数形式是以10为底的普通对数和以e为底的自然对数。[1]这里我们关注自然对数（或简称“ln”），它有以下“自然”解释：如果我们取两个数字a和B，那么它们的对数之差ln（a）− ln（B）就是a和B之间的分数差。乘以100，即100× ln（a）− 100× ln（B），它就是a和B之间的百分比差。5
Despite its wide use in statistics, the logarithmic transformation can make non-statisticians uncomfortable. 1 2 3 4 This is a shame because logarithms have very useful properties, including a secret not widely known even among statisticians.The two familiar forms of logarithm are common logs, to base 10, and natural logs, to base e. 1 Here we focus on natural logs (or “ln” for short), which have the following “natural” interpretation: if we take two numbers a and b, then the difference between their logs, ln (a)− ln (b), is the fractional difference between a and b. And multiplied by 100—that is, 100× ln (a)− 100× ln (b)—it is the percentage difference between a and b. 5