ratio scale vs interval scale

Interval scale and ratio scale are the two variable measurement scales where they define the attributes of the variables quantitatively. There are four scales of measurement that have been mentioned time and again. Apart from the two mentioned here, there is nominal scale and ordinal scale.

This concept was first introduced by the noted psychologist Stanley Smith in the year 1946. He wrote an article titled, “On the theory of the scales of measurements”. This article was widely accepted and was published in the “Nature” magazine.

Out of the four scales of measurement nominal and ordinal are qualitative in nature.

What is Ratio Scale?

A ratio scale is a measurement scale which has more or less all the properties of an interval scale. Ratio data on this scale has measurable intervals. Where the ratio scale differs is, it has a zero point or character of origin. For example, the temperature outside is 0-degree Celsius, this doesn’t mean that it is neither hot nor cold. It means there is a value assigned to measuring the temperature.

The most common examples of a ratio scale are height, weight, money, age and similar. For example:

What age bracket do you fall in?

  • Blow 20 years
  • 21-30 years
  • 31-40 years
  • 41-50 years
  • Above 50 years

Ratio scale is the most informative scale and it tells precisely about the order and number of objects between the value of the scale. Ratio scale allows a researcher to apply any statistical technique including geometric and harmonic mean.

What is Interval Scale?

In an interval scale, all the quantitative attributes can be measured. Any measurement belonging to this category of interval scale can be ranked, counted, subtracted, added but by no means it will give any sense of ratio between the two measurements.

Let’s take an example to understand interval scale better. A good example in this category would be measuring temperature. The temperature in an air-conditioned room is 16-degree Celsius and the temperature outside the AC room is 32-degree Celsius. It is reasonable to say that the temperature outside is 16 degrees higher than inside the room.

But, if you said that it is twice as hot outside than inside, then you would thermodynamically incorrect. The selection of this reference point is considered as zero, which is also the freezing point of water. So the difference in temperature inside the room and outside the room has to a number, not a mere comparison.

Zero point in an interval scale is arbitrary and negative values can also be defined. The variables that are measured on an interval scale are commonly known as interval variables or scaled variables. Observations say it is common that these variable carry unit. Statistically, mean, mode and median can be used as a measure of central tendency for interval variables.

Differences between Interval Scale and Ratio Scale

Interval Scale

Ratio Scale

All variables that are measured in interval scale can be added, subtracted, multiplied but calculating ratio is not possible. Ratio scale has all the characteristics of an interval scale, in addition, to be able to calculate ratios.
Zero point in an interval scale is arbitrary.   Ratio scale has an absolute zero or character of origin.
Statistically, in interval scale arithmetic mean is calculated. Statistically in ratio scale geometric or harmonic mean is calculated.  
Interval scale can measure size and magnitude as multiple factors of a defined unit. Ratio scale can measure size and magnitude as a factor of one defined unit in terms of another.  
A classic example of an interval scale is a temperature in Celsius. For example, the difference in temperature between 50 degrees and 60 degree is 10 degree which is the same difference between 70 degrees and 80 degrees. Classic examples of a ratio scale are any variable which possesses an absolute zero characteristic like age, weight, height, sales figure, ruler measurement, income earned in the last month and so on.

 

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