Change of units and variables, also known as transformation in common statistical terminology, is the change of lists into other lists and variables into other variables. The common types of changes of units and variables are as follows –
Affine transformations – multiply by something and add something. For e.g., y = ax + b is a general affine transformation of x and is similar to the equation of the straight line.
Linear Transformations – multiply by something (y = ax)
Affine transformations are normally used when you want to change the units into Standard Units. The effect of affine transformations on other variables is dependent on the sign of the multiplicative constant. In case of a positive multiplicative constant, the effect of the transformation on the mean, median, mode and percentiles and quartiles is a simple – the new value is calculated by using the same formula as for other variables. In case of a negative constant, the mean, median and mode remain the same but the quartiles and percentiles are reversed (the qth quartile is transformed by subtracting from 1).
Example: Affine transformation - a measure of temperature in degree Celsius is transformed to degree Fahrenheit by multiplying the value by 9/5 and adding 32 to the product. Linear Transformation – a measure of distance in kilometres can be transformed to miles by multiplying the value by 0.621371.