transformTukey function

Tukey's Ladder of Powers

Conducts Tukey's Ladder of Powers on a vector of values to produce a more-normally distributed vector of values.

transformTukey(
  x,
  start = -10,
  end = 10,
  int = 0.025,
  plotit = TRUE,
  verbose = FALSE,
  quiet = FALSE,
  statistic = 1,
  returnLambda = FALSE
)

Arguments

• x: A vector of values.
• start: The starting value of lambda to try.
• end: The ending value of lambda to try.
• int: The interval between lambda values to try.
• plotit: If TRUE, produces plots of Shapiro-Wilks W or Anderson-Darling A vs. lambda, a histogram of transformed values, and a quantile-quantile plot of transformed values.
• verbose: If TRUE, prints extra output for Shapiro-Wilks W or Anderson-Darling A vs. lambda.
• quiet: If TRUE, doesn't print any output to the screen.
• statistic: If 1, uses Shapiro-Wilks test. Will report NA if the sample size is greater than 5000. If 2, uses Anderson-Darling test.
• returnLambda: If TRUE, returns only the lambda value, not the vector of transformed values.

Returns

The transformed vector of values. The chosen lambda value is printed directly.

Details

The function simply loops through lamdba values from start

to end at an interval of int.

The function then chooses the lambda which maximizes the Shapiro-Wilks W statistic or minimizes the Anderson-Darling A statistic.

It may be beneficial to add a constant to the input vector so that all values are posititive. For left-skewed data, a (Constant - X) transformation may be helpful. Large values may need to be scaled.

Examples

### Log-normal distribution example
Conc = rlnorm(100)
Conc.trans = transformTukey(Conc)

References

https://rcompanion.org/handbook/I_12.html

Author(s)

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu