In the previous post we looked at the different measurement scales and variable types. Though we covered some description about Interval scale in that post itself, I thought I will follow it up with another post dedicated only for Interval Scale.
Interval scale of measurement is one topic that I personally found little tough to grasp. That is because it most cases the numeric data looks pretty much like ratio scale. The only aspect that separates interval scale from ratio measurement scale is the fact that interval data doesn’t have an absolute zero. With nominal or ordinal scales I feel it is relatively easier to spot the difference.
The difficulty with interval scale may be compounded by the fact that whatever examples or case studies I came across so far didn’t have to deal with many examples of interval data. May be, I just didn’t come across a domain where interval scale is more prevalent. We keep working with nominal, ordinal and ratio data over and over in most of our statistical modelling tasks.
If you go for different training programs or search in the web to get more clarity around interval data, you will encounter the same temperature example most of the times. You will almost be driven to a point where you wonder “Did they create interval scale exclusively to deal with the temperature data scenario?!”.
Not really ! There are just few more examples that I found from other blogs and statistics books. I have listed my understanding of the other examples of interval scale below to make it easier for you.
Example 1 – Percentage return on stock:
Percentage return on stock is measured as an incremental change over the previous day’s closing stock price. So, the reference point for each measurement is different and ratio calculation cannot be made on this data.
Example 2 – Dollar change in stock price:
This is similar to the previous example. Dollar change in stock price is computed with reference to price at a previous point in time and not with reference to zero. Such values cannot be used for ratio computation.
Example 3 – Percentage change in employment:
Percentage change in employment is again not an absolute number with zero as the reference point. These calculations are made using previous employment rates as the reference.
Example 4 – SAT score:
SAT score is listed as example for interval scale in some texts and I googled to find out why. For some reason, the scoring is done starting from 200 for a section in SAT and from there it ranges up to a maximum of 800. The numbers from 0 to 200 are not used when they scale the raw score (number of questions answered correctly) to the section score. The reference point is not an absolute zero and it becomes obvious why it qualifies as an interval measure.
Example 5 – Time listed in 12-hour format:
Time listed in 12-hour format for example (or even 24 hour format) is a rotational measure that keeps restarting from zero at set periodicity. These numbers are on interval scale as the distances between them are measurable and comparable. But ratios will not work as there is no single zero reference point.
If time is measured using stop watch for a 100m dash and Usain Bolt runs at 9.58 seconds compared to my 20 seconds, the readings in this context are ratio scale. Both have zero reference to the gun shot where we started off the mark. Ratios of these two timings are meaningful. So, time can be interpreted as interval or ratio scale depending on how a particular case is represented.
Hope this helps !