Square Root Transformation

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Definition: Square Root Transformation

In statistics and quantitative techniques, data transformation refers to replacing each data point by a value defined by a predetermined function, e.g.each data point ‘Xi’ is replaced with the transformed value ‘Zi’ = f(Xi), where ‘f’ is the predetermined function.Transforms are usually applied so that the data appear more relevant for statistical inferences and improve the interpretability or appearance of the plotted graphs. Transforming the data makes it fit the statistical assumptions better.

‘Square root transformation’ is one of the many types of standard transformations.This transformation is used for count data (data that follow a Poisson distribution) or small whole numbers. This transformation also may be appropriate for percentage data where the range is between 0 and 20% or between 80 and 100%.Each data point is replaced by its square root. Negative data is converted to positive by adding a constant, and then transformed.

Transformation of data as in the above cases, where sample means are approximately proportional to the variances often results in homogeneous variances.

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