- Understand what it means for a scale to be ordinal and its relationship to interval scales.
- Determine whether an investigator can be misled by computing the means of an ordinal scale.
This is a demonstration of a very complex issue. Experts in the field disagree on how to interpret
differences on an ordinal scale, so do not be discouraged if it takes you a while to catch on. In this
demonstration you will explore the relationship between interval and ordinal scales. The demonstration
is based on two brands of baked goods.
The data on the left side labeled "interval scores" shows the amount of sugar in each of 12 products.
The column labeled "Brand 1" contains the sugar content of each of 12 brand-one products. The second
column ("Brand 2") shows the sugar content of the brand-two products. The amount of sugar is measured on
an interval or ratio scale.
A rater tastes each of the products and rates them on a 5-point "sweetness" scale. Rating scales are
typically ordinal rather than interval.
The scale at below shows a "mapping" of sugar content onto the ratings. Sugar content between 37
and 43 is rated as 1, between 43 and 49, 2, etc. Therefore, the difference between a rating of 1 and a
rating of 2 represents, on average a "sugar difference" of 6. A difference between a rating of 2 and a
rating of 3 also represents, on average a "sugar difference" of 6. The original ratings are rounded off.
It is all but certain that a rater's ratings would not be so close to an interval
The mean amount of sugar in Dataset 1 is 50 for the first brand and 55 for the second brand. The obvious
conclusion is that, on average, the second brand is sweeter than the first. However, pretend that you
only had the ratings to go by and were not aware of the actual amounts of sugar. Would you reach the
correct decision if you compared the mean ratings of the two brands. This demonstration is
designed to shed light on this question.
Keep in mind that in realistic situations, you only know the ratings and not the "true" interval scale
that underlies them. If you knew the interval scale, you would use it.