Johnson Transformation

Johnson Transformation

Johnson Transformation

DescriptionThe Johnson transformation is a statistical technique that transforms non-normal data into a normal distribution. It extends the Box-Cox transformation and can handle positively and negatively skewed data.

Why to use

To normalize the distribution of a continuous variable.

When to use

  • Non-normality of data

When not to use

  • Data with extreme outliers
  • Categorical or ordinal data
  • Non-linear relationships

Prerequisites

  • A data with non-normal distribution.

Input

Any dataset containing numerical variables.

 Output

A transformed version of the original dataset.

Statistical Methods Used

  • Maximum Likelihood Estimation (MLE)
  • Moment Estimation

 Limitation

  • Data range
  • Parameter estimation
  • Sensitivity to outliers.

Johnson Transformation or Yeo-Johnson Transformation is a statistical method to convert a numerical variable such that its distribution is more closer to normal distribution. Unlike Box-Cox transformation which is not applicable on negative values, Johnson transformation can handle negative values.
The following formula describes the Johnson transformation