Data Transformation

Logarithmic - used when:

• the variances are not equal (heterogeneity of variances)
• standard deviations are proportional to the means (CV's are equal) or 
• when the data is positively skewed 

Procedure:

1) Convert raw data into their logarithms
2) Perform analysis on log data
3) Convert back into units of the raw data by taking the antilog of the results

Square Root - used usually with counts (number of ......) data and when the variance is:

• proportional to the mean (i.e., variance increases with increasing size of the mean). 

Procedure:

1) Convert raw data into square root transformation
2) Perform analysis on square root data
3) Convert back into units of the raw data by subtracting .5 and squaring the results

Arcsine - used to normalize data in percentages or proportions whose distributions fits the binomial distribution. 

Procedure:

1) Convert raw data into arscin transformations
2) Perform analysis on arscin data
3) Convert back into units of the raw data by taking the sin of squared the results

Reciprocal Transformation - used when: the standard deviation is proportional to the square of the mean. 

Squared Transformation - used when: the standard deviation decreases as the mean increases.