Data Transformations

Data transformation is a process in which the measurements on the original scale are converted to a new scale. A transformation is the re-expression of a variable, typically the dependent variable. It is used to stabilize the variance of the variable, to normalize the variable, and to linearize the regression model. For example, if a quantity y grows at a rate r per unit time then:

Data transformation presents one way to simplify this nonlinear model into a linear model. In this case taking the natural logarithms of both sides leads to a linear model:

IC-CAP Statistics provides a number of ways to transform data where each method is better suited to a particular data set. As a whole the available methods provide a comprehensive range of data transformation options.

Exponential

The exponential transformation is used to stabilize random variance, and to approximate solutions to difficult distributions. One of the situations in which this works is when time has no effect on the future outcomes. That is, the future distribution is not affected by the past.

Natural Log

The log transformation is used to stabilize marked increases in variance, to normalize the dependent variable in a positively skewed distribution of residuals, and to linearize the regression model in the case of models with a consistently increasing slope.

Square Root

The square root transformation is used to stabilize a variance that is proportional to the mean. It is a particularly appropriate transformation if the dependent variable has the Poisson distribution, which describes the number of occurrences for a given interval.

Square

The square transformation is used to stabilize a variance that decreases with the mean, to normalize the dependent variable in a negatively skewed distribution of residuals, and to linearize the model if the dependent variable consistently decreases with any increase in the independent variable.

Constant Value

The constant value transformation simply replaces your data with the specified constant.

Mean

The mean transformation replaces your data with the calculated mean value for this column of data.