StatTools : Numerical Transformation Explained

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Related Links:
Numerical Transformation Program Page

Introduction Linear Curve Miscellaneous
All mathematics involves the transformation of one set of numbers to another set, but transformations provided by StatTools are those commonly used in clinical statistics.

Data Input :

  • The data is a single column of numbers to be transformed
  • Where additional parameters are necessary, input is either via values for text boxes, or alternatives in action buttons.
  • Example data and parameters are available for each transformation procedure to guide the user. Specific requirements and pitfalls for each procedure are described in the following panels
Result output : One or more of the following are provided after transformation
  • A table comparing the following parameters from the original and transformed data
    • Mean and Standard Deviation
    • Skewness and Kurtosis
    • Chi Square (with 2 degrees of freedom) to test the combination of skewness and kurtosis against the null hypothesis that the data is normally distributed. A critical value of chi square = 5.99 provides the Type I Error α=0.05, so that higher values indicates a significant departure from normal distribution
    • A correlation coefficient ρ between the values against theoretical values from a normal distribution. This provides a numerical representation of how close the data is to normal distribution.
  • A table listing all values before and after transformation
  • Two plots, for data before and after transformation, to allow visual inspection of the distribution of the data
    • The data is converted into Standard Deviation (z) values, where z = (v-mean) / Standard Deviation
    • The values are then placed into an array at one Standard Deviation intervals
    • The number of values in each array is represented as a percent of the total number
    • The final plot is the percent of total in each Standard Deviation array
  • A x/y scatterplot, with x=before and y=after transformation, the demonstrate the shape of the relationship that is affected by the transformation.
  • Please note that the MacroPlot Program Page provides programs to produce publishable quality plots should the user wishes to replicate some of the plots produced by Numerical Transformation Program Page .