A Common Misconception About Log Transformation

...and here's what it does.

Log transform is commonly used to eliminate skewness in data.

Yet, it is not always the ideal solution for eliminating skewness.

It is important to note that log transform:

• Does not eliminate left-skewness.

• Only works for right-skewness, that too when the values are small and positive.

This is also evident from the image above.

It is because the log function grows faster for lower values. Thus, it stretches out the lower values more than the higher values.

Graph of log(x)

Thus,

• In case of left-skewness:

  

  Left-skewness with log transform

  • The tail exists to the left, which gets stretched out more than those to the right

  • Thus, skewness isn't affected much.

• In case of right-skewness:

  

  Right-skewness with log transform

  • Majority of values and peak exists to the left, which get stretched out more.

  • However, the log function grows slowly when the values are large. Thus, the impact of stretch is low.

There are a few things you can do:

• See if transformation can be avoided as it inhibits interpretability.

• If not, try box-cox transform. It is often quite effective, both for left-skewed and right-skewed data. You can use it using Scipy’s implementation: Scipy docs.

👉 Over to you: What are some other ways to eliminate skewness?

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