# Session: 7 Scales of Measurement_Section B Group 4_Avik Chatterjee

Origin

In research methodology data used to measure phenomena has been devided into types by  psychologist Stanley Stevens in his treatise “On the theory of scales of measurement” published in 1946. The types are nominal, ordinal, interval, and ratio.

He proposed that all scientific data measurements can be divided into the aforementioned types. The types thus covered both quantitative and qualitative attributes. His work received further mathematical support from the rigorous works of mathematical psychologists Theodore Alper, Louis Narens and R. Duncan Luce.

Nominal Scale

The nominal scale is used to place qualitative data into some categories without having any order. Naturally no arithmetic operations can be performed on them.

For example gender when coded and measured as a parameter does not follow any particular order in the data. Arithmetic operations make no sense just on the code.

Another example can be the jersey number of cricketers. They do not necessarily signify anything and can be arbitrarily assigned.

Mode is used as the most appropriate tool for Measure of Central Tendency of Nominal data.

Ordinal scale

Ordinal scale is concerned with the ranking. The respondent giving his list of favourite TV shows in order of most favourite to least favourite forms a typical example of ordinal type. Here the researcher is not concerned about the actual difference between the ranked quantities. The information is just limited to the relative order.

As an example the colour range of white, grey and black can also form ordinal data as it shows a gradual order of deepening of the dark component.

The Median and the Mode can be used as a measure of Central Tendency for Ordinal data based on the measuring objective.

Interval

The Interval scale is designed to measure the degree of difference between the data points. However the Interval scale is not to measure how many times one aspect of the data is of another. That is, it does not measure the ratios between items.

For example Temperature with the Celsius scale. A temperature of 40 degree Celsius does not automatically mean twice that of 20 degree Celsius.

Ratio Scale

A scale with equidistant intervals along with a meaningful zero is called a ratio scale. For example when asked about age, zero would mean not yet born and the difference between two years would always be constant. Most measurements for scientific purposes is done in ratio scale.

Examples of ratio scale measured data include age, length, mass, time, energy amongst many others.

The measures of Central Tendency of Ratio Scale variables are measured by Median , Mode and Arithmetic, Geometric and Harmonic mean.

Criticism

This method of typifying data into separate scales have been contested by statisticians and other theorists. For the ordinal type the use of mean as a Measure of Central Tendency is well debated. However behavioural scientists often use mean of Ordinal types and justify it by saying that ordinal type in behavioural science lies bears characteristics of both ordinal and interval types.

Another point of view put forward by R.Crisman states that range-bound and repeating measurements do not fit to Stevens original work.

However these classifications are extensively used to understand, organize and analyse data in our everyday professional and academic practice.

SectionB_Group 4_Avik Chatterjee_13PGP072

Other members of Section B,Group 4 are Alok Paul, Aniruddh Mukerji, Anusha C, Rohit Garg, Chanyo YL, Gurjot Singh, Anwesha Dasgupta.