Nominal scales of measurement
At the nominal level the numbers assigned to an attribute are simply representations so they can’t be added or subtracted or subjected to any arithmetic process. But the numbers in each category can be counted.
In the spreadsheet shown, a team of footballers was asked whether they were left or right footed. Left footed players are entered onto the spreadsheet as 1 and right footed players as 2. How many left footed and right footed players are there in this team?
Similarly adding up all the numbers on footballers shirts is possible – it comes to 66 – but this figure doesn’t mean anything!
Ordinal scales of measurement
Arithmetic operations that can be performed on values assigned to ordinal scales are also limited. As well as counting the numbers in each category on the scale it is possible to indicate relative size using equals (=), greater than (>) or less than (<) symbols.
Any operation involving addition and subtraction is not allowed – for example calculating the mean. Calculating the median and mode as measures of central tendency is appropriate as these only involve counting the numbers in each category on the scale.
Interval scales of measurement
Because the size between intervals is equal within any one scale, you can add and subtract these values. Multiplication and division is not permitted because there is no absolute zero, and, for instance, a temperature of 40°C is not twice as hot as a temperature of 20°C.
Comparisons across different scales (for example centigrade to fahrenheit) should be handled with care, because they’re not starting from the same zero point and although the intervals within a scale are equal, the size of the intervals on different scales will vary
Ratio scales of measurement
Multiplication and division should only be carried out on ratio measurements. Naturally, addition and subtraction are also permitted.
So an increasingly complex level of calculation can be performed for each level of measurement.
|Mastering Statistics: A Guide for Health Service Professionals and Researchers||Authors: Kelvin Jordan, Bie Nio Ong, Peter Croft, Publication Date: 1998, Publisher: Stanley Thornes (Publishers) Limited, ISBN: 0748733256|
|Levels of Measurement RLO||To understand the different levels of measurement and the arithmetic operations that can be performed on them|