Chapter 4: Analysing the Data Part II : Descriptive Statistics

# Transformations

In many ways, the way in which we measure constructs is very arbitrary. If we measured height, we could use a ruler and measure in feet and inches, or a ruler in centimetres and millimetres. If it were a horse you could measure it in "hands" rather than feet. Now these measurements can be converted from one to the other by a rule or formula. One hand = x inches = y centimetres. We do it all the time in the real world. The position of the hands of the clock (angle in degrees) measures the time (in hours and minutes,), level of mercury in a thermometer (centimetres) = temperature (in degrees), scores on a piece of paper (scores or points) = IQ (in some other arbitrary units). Therefore, the data you have are not sacred in terms of the actual numbers assigned. So, there are many options available to us in terms of converting scores from one metric to another or to another set of points on the same metric. The scaling of scores in the Higher School Certificate examination is a common example.

In statistical practice there are a number of transformations that are in common use. The ones we will mention are dichotomisation, standardisation, normalising.