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Johnson Transformation

Transform non-normal data toward normality so that normal-based methods can be applied.

What is the Johnson Transformation?

The Johnson Transformation fits your data with the best member of the Johnson system of distributions and transforms the values through it, producing data that follows a normal distribution as closely as possible. Quantum XL selects among the three Johnson families automatically: SB (bounded), SL (log-normal), and SU (unbounded).

The output shows the transformation side by side with the evidence: probability plots of the original and transformed data, Anderson-Darling normality results before and after, the fitted family and its parameters, and ready-to-use formula cells for converting values in either direction.

When to Use the Johnson Transformation

  • When your data fails a normality test and you need normal-based analyses (for example capability against transformed specification limits)
  • When a simple power transformation (Box-Cox) cannot normalize the data, since the Johnson system covers a much wider range of shapes
  • When you need to convert individual values between the original and transformed scales with an explicit formula

Options

The dialog has a single Data tab: choose the column (or columns) to transform. There are no analysis settings.

  • Each selected data column is transformed separately, producing its own output.
  • A GroupBy column splits the data and transforms each group separately.
  • Frequency columns and combining into a single chart are not supported.

Already-normal check

Before transforming, Quantum XL tests the original data for normality (Anderson-Darling). If the data already looks normal (p-value above 0.1), it asks whether you want to transform anyway. Choosing No skips the transformation for that column; its original-data probability plot and normality table are still written.

Output

A single Johnson Transformation worksheet is written per run, with one block per transformed column or group. Each block contains:

  • A Johnson Parameters table: the family type (SB, SL, or SU) and the fitted parameters \(\eta\) (Eta), \(\gamma\) (Upsilon), \(\lambda\) (Lambda, not used by SL), and \(\varepsilon\) (Epsilon), plus the fit's AD p-Value and the Optimal Z used in the family search
  • Transformation Formulas: live cells where you can enter a value to get its transformed value, or enter a transformed value to get the original back
  • Two normality tables, Normal Fit - Original Data and Normal Fit - Transformed Data, each with the sample size, AD statistic, and AD p-value
  • A data table with the Original Data and Transformed Data columns
  • Two probability-plot charts, one for the original and one for the transformed data

Learn More

  • Math Details: The transformation formulas, family selection, and parameter estimation, exactly as computed