Introduction to Statistics - Measurement scales and statistical tools

As we know every subject has its origin, development stages, scope, uses and limitations. In “Introduction to Statistics”, we will discuss origin and development, definition, scope, uses and limitations of statistics. In our daily life we are using statistics knowingly or unknowingly, because

1. Most of the decisions taken by us being are based on past experience
2. Future events are also predicted by using the past behavior of that particular event

Statistics is a branch of science which deals with collection, classification, tabulation, analysis and interpretation of data.

MEASUREMENT SCALES

In Statistics, act of counting and measurement is divided into 4 levels of measurement scales known as

1. Nominal Scale
2. Ordinal Scale
3. Interval Scale
4. Ratio Scale

1. Nominal Scale
Under Nominal Scale we divide the objects under study into two or more categories by giving them unique names. Nominal scale is used when we want to categories the data based on the characteristics such as gender, race, region, religion, etc.

Example, (i) Classification into different categories based on gender

(ii) Classification into different categories based on Meal

(iii) Classification into different countries based on Continents

2. Ordinal Scale

As we already know order does not make any sense in nominal scale. So if in a measurement scale orders also make sense then, this scale comes under Ordinal scale. It is used when we want to measure the attitude scores towards the level of liking, satisfaction, preference, etc. 

Example, based on economic condition of a family, generally families of a society are divided into three categories: Higher class family > Middle class family > Lower class family. But the actual difference cannot be measured, as we can only give order/rank. 

3. Interval Scale

In interval scale actual differences can be found. Say, if I = [12, 18], then length of this interval (here we are using the concept of interval) is 18-12 = 6, i.e. difference between 12 and 18 is 6, i.e. we can find the difference between any two points of the interval. Interval scale includes +, - in addition to >, < and =, ≠.

From above three definitions we have learned,

• Nominal scale gives only names to the different categories
• Ordinal scale moving one step further and provides the concept of order between the categories also
• Interval scale moving one step ahead to ordinal scale and also provides the characteristics of the difference between any two categories

4. Ratio Scale

Ratio scale is the highest level of measurement because other than names, orders and characteristics of difference; ratio scale also provides natural zero (absolute zero). In ratio measurement scale values of characteristics cannot be negative.

Ratio scale is used when we want to measure weight, height, length, age, mass, time, etc. Ratio scale includes x, ÷ in addition to +, -, >, <, =, ≠ . 

One of the advantages of measurement scale is that these help us to decide which statistical tool should be used in a given situation.

Based on information provided by measurement scales, their levels from lowest to highest are nominal, ordinal, ratio and interval

That is why all the Statistical tools applicable on the lower scale will automatically be applicable on the next level. It is understood that statistical tools which are permissible for nominal will be permissible in case of ordinal and so on. Advantages of measurement scale are that these help us to decide which statistical tool should be used in a given situation.

MEASUREMENT SCALE	PERMISSIBLE STATISTICAL TOOLS	LOGIC/REASON
NOMINAL SCALE	Mode, chi-square test and run test	Here counting is only permissible operation
ORDINAL SCALE	Median all positional averages like quartile, Decile, percentile, rank correlation	Here other than counting, order relation (less than or greater than) also exists
RATIO SCALE	Mean, SD, t-test, f-test, ANOVA, sample multiple and moment correlations, regression	Here counting, order and difference operations hold
INTERVAL SCALE	Geometric mean (GM), Harmonic mean (HM), Coefficient of variation	Here counting, order, difference and natural zero exist

Permissible Statistical Tools

For my next blog post, we will discuss on different types of data.