NOMINAL, ORDINAL, INTERVAL, AND RATIO

Variables can be classified into different groups based on how they are measured. Machine number, cost, and weight are all different types of variables. Machine number is called a nominal variable because the numerical codes assigned to the possible responses convey no information. They are merely labels or names . (That is why the level of measurement is called nominal ” from the Latin word for " name .") Codes assigned to possible responses merely identify the response. The actual code number means nothing.

If the possible responses can be arranged in order, as with the exciting-routine-dull variable, the variable is called ordinal : its codes have an order, nothing more. (The word ordinal comes from ” you guessed it ” a Latin word meaning "order.") Variables such as dollars, job satisfaction, condition of health, and happiness with one's social life, all of which are usually measured on a scale going from much to little, are ordinal variables. The numbers assigned to the responses allow you to put the responses in order, but the actual distances between the numeric codes mean nothing.

Temperature can be measured and recorded on a scale that is much more precise than job satisfaction. The interval or distance between values is meaningful everywhere on the scale. The difference between 100 degrees Fahrenheit and 101 degrees Fahrenheit is the same as the difference between 102 degrees and 103 degrees. Since temperature measured on the Fahrenheit scale does not have a true zero, however, you cannot say that an 80-degree day is twice as hot as a 40-degree day. A temperature of zero does not mean that there is no heat. The zero point is determined by convention. (If you insist, I will admit that temperatures do have an absolute zero point; but that has very little to do with the measurement of body or environmental temperatures .) Thus temperature can be called an interval variable.

The last type of measurement scale is called a ratio scale. The only difference between a ratio scale and an interval scale is that the ratio scale has an absolute zero. Zero means zero . It is not just an arbitrary point on the scale that somebody happened to label with zero. Height, weight, distance, age, and education can all be measured on a ratio scale. Zero education means no education at all, and zero weight means no weight at all. On a ratio scale, the proportions or ratios between items are meaningful. A 200-pound person is twice as heavy as a 100- pound person. A 1000-meter race is twice as long as a 500-meter race. I suppose I need not tell you what language the words interval and ratio come from.

Why all the fuss? Why have we spent all this time describing these "levels of measurement?" The reason is straightforward ” the way in which you analyze your data depends on how you have measured it. Certain analyses make sense with certain types of data. Even something as simple as interpreting cumulative percentages requires you to know what scale your data are measured on. For example, cumulative percentages do not make much sense for variables measured on a nominal scale. So, depending on the level of measurement, the appropriate technique, test, and analysis must be selected. Otherwise, the results will be meaningless.