We discussed about different Measurement Scales of data in a previous post.
The diagram below depicts the hierarchy among the different scales of measurement.
Nominal scale of data contains the least amount of information and hence a limited set of statistical methods can only be applied on this data. This is represented by the inner most circle in the diagram.
Ordinal scale is one level above. The statistical methods that can be applied on ordinal scale includes all that belongs to the nominal scale and few more.
Interval scale is the next higher circle. The statistical methods that can be applied on ordinal scale is a subset of what can be applied on interval scale.
Ratio scale is the highest level super set. Any statistical method that can be applied on any of the other three measurement scales can be applied on ratio scale data. More methods are applicable on top of that.
Let us validate this understanding using the other post on Central Tendency that we covered earlier.
Mode is the only measure of central tendency that can be applied on nominal scale of data. For example, if the number of students belonging to “Yellow” sports house is higher than the count for the other three houses, Yellow is the mode for this data. Other measures of central tendency like median or mean cannot be applied on Nominal data.
Median can be computed for ordinal data. Because ranking is possible for ordinal data, it can be sorted based on the ranking order and the value occurring at the center is the median. Also, as per the hierarchy diagram shown above, mode is also applicable for ordinal data. It has to be, because anything that can be applied on nominal scale is a subset that can be applied on ordinal data too. Here again, the category against which the frequency of observations is maximum is the mode for the data.
Mean can be computed for a minimum of interval scale data. This is because interval scale has numeric values and hence it is possible to add them up and divide by the number of observations. Ordinal (and hence nominal too) is a subset of interval scale in terms of the statistical methods that can be applied. So, mode and median can be applied on interval scale data too.
Ratio scale data can take mode, median as well as mean. In addition, it can take geometric & harmonic means as well which any of the other lower scales of measurement cannot take.
The intention of this post is to recap on our Measurement Scales topic and connect the understanding of hierarchy using Central Tendency as example. The same hierarchy logic illustrated here with central tendency holds good for any of the umpteen number of statistical methods that we will learn going forward.