Transforming Data

• non-parametric tests are less powerful
• non-parametric test include the Mann-Whitney U and Kruskal-Wallis
• transforming data


  applying consistent mathematical expression to each point in the data to change the distribution to normal
• if the transformed data meets parametric assumptions, the new data can be used instead of the original
• all data must be transformed for it to be mathematically valid
• transforming data does not change the relationship, just the difference
• for testing skewed difference data, transform all samples
• for testing skewed regression only transform the problem data
• types of ways the transform data

  log, square root, arsin
• log transformations are use when there is a positive skew or unequal variance
• to tranform data with log you do log(X) or log10(X+1)
• log squashes the right tail of the distribution reducing the positive skew
• cant use log if the data contains 0 or negatives
• square root transformation used for positive skew or unequal variance
• to transform data with square root you do √X or √X+1
• square root transformations cannot be used if there are negative numbers
• square root transformations are good for very large data
• arsin transformations used for binomial distribution and percentages
• arsin flattens the distribution by stretching both tails
• for an arsin transformation (√(X%/100))
• for presenting data you must always back-transform
• always report that you have transformed your data in the methods