Z (Johnson transformation)

A set of standard normal percentiles used to select and estimate the Johnson transformation. The optimum transformation is that which produces normalized data with the greatest p-value in an Anderson-Darling normality test.

Minitab uses four symmetric standard normal deviates (-3Z, -Z, Z, and 3Z) to optimize transformation, where Z is a positive value between 0.25 to 1.25 inclusive. For each value of Z in this range, in increments of 0.01, Minitab calculates the standard normal CDF of the four symmetric deviates and finds the percentiles associated with these CDF values in your original untransformed data. Based on these sample percentiles, Minitab selects a distribution, estimates its parameters, and applies the Anderson-Darling normality test. The distribution with the greatest p-value from this normality test is the distribution Minitab uses to transform your data. The distribution, the values of its parameters, and the value of Z that produces the optimum transformation are displayed in the Johnson Transformation graphical output.

If no value of Z produces a distribution with an Anderson-Darling p-value greater than the specified critical value (0.10 is the default), then Minitab repeats the procedure, calculating distributions with Z-intervals of 0.005 instead of 0.01. If it still finds no distribution with a p-value greater than the critical value, then no Johnson transformation is available.