Statistics: Nominal, Ordinal, Interval and Ration Scales and Testing

Gathering information from various sources plays a crucial role. For a researcher, pieces of information are very important. We collect the data using various tools, one of which is a questionnaire. When we collect the data, we use open-ended and closed-ended questionnaires. When we pose a question with options or choices, such as choosing between two or five options, it clarifies our analysis based on the choices we provide in the questionnaire.

We are all familiar with the terms nominal, ordinal, interval, and ratio; these are all termed scales. We use different statistical tools for the different scales. Have you heard the term parametric or non-parametric? If your answer is yes, then you must know about the analysis tools. If your response is negative, you must have to learn. When we discuss and test the population, we are defining the parametric model. If we don’t know about the population, and this is necessary to test the hypotheses, the test will be non-parametric.

Table of Contents

Parameters

It is a fixed measure that describes the target.

It is a fixed and unknown numerical value.

Variables

This characteristic is specific to a small portion of the population. I liked the sample size.

It is a known and variable number.

The parameters of the population distribution, from which the data originate,

Parametric statistics

That leads to assumptions about the population distribution parameters from which the data are drawn.

They assume that the data has an underlying statistical distribution.

A parametric test’s result must meet several validity conditions.

Non-parametric statistics

They make no assumptions about the parameters of a distribution.

Do not rely on any distributions.

They can be used even if the parametric validation condition is not met.

Difference between Parametric and Non Parametric

Sr	Parametric	Non parametric
1	We make specific assumptions about the population parameter.	We make no assumptions about the population parameter.
2	Ratio and interval scale	Nominal and ordinal scales
3	For the calculation, more information is needed.	The calculation requires less information.
4	Assume a normal bell-shaped distribution curve.	Don’t assume a regular bell-shaped distribution curve.
5	More statistical power	Less statistical power
6	Less robust	More robust
7	The result can be generalized.	Results cannot be generalized.

Table-1 Difference between Parametric and Non Parametric

The Case, Parametric and Non-Parametric Test

Case	Parametric Test	Non Prametric Test
Central Tendency	Mean	Median/ Mode
Correlation	Pearson	Spearman
Independent Sample, 2 Groups	Independent Sample Test	Mann- Whitney Test
Independent Samples, More Than 2 Groups	One Way Analysis Of Variance	Kruskal Wallis Test
Dependent Samples, 2 Conditions	Paired Sample T Test	Wilcoxon Signed Rank Test
Dependent Samples, More Than 2 Conditions	One Way Repeated Analysis Of Variance	Friedman Anova

Table-2 The Case, Parametric and Non-Parametric Test

The Action and Operation

What Can We Do
Operation/Action	Nominal	Ordinal	Interval	Ratio
Categories/Classified	Yes	Yes	Yes	Yes
Arrange In Order (Sorting)		Yes	Yes	Yes
Quantify Difference Between Values			Yes	Yes
Addition & Subtraction			Yes	Yes
True/Absolute Zero				Yes
Multiplication& Division				Yes

Table 3- The Action and Operation

The above table shows that case (the case is the individual unit of the experiment). These are the individuals from whom we collect the data. We refer to the individuals who took part in our research as participants.

We understand that a category refers to a class or division of people who perform certain tasks. Arranging in order refers to assigning the correct positions in relation to each other. The degree of excellence of something is determined by comparing it to other similar objects. The ration scale features a zero, indicating the origin of the character.

The Measurement Scale

Measurement Scales
Nominal	Ordinal	Interval	Ratio
Categories	Categories	Categories	Categories
	Rank	Rank	Rank
		Meaningful Distance	Meaningful Distance
			True Zero

Table-4 Measurement of the Data and Categories

The measurement scale is how the variables are defined and categorized. There are four common scales of measurement that were developed by the psychologist Stanley Stevens. These scales are nominal, ordinal, interval, and ratio. It is the properties of each scale of measurement that determine how the data should be analyzed in the appropriate manner.

Inferential statistics and Testing

Which Statistics Can Be Used
	Non -Parametric Data		Parametric Data
	Discrete Variable		Continuous Variable
Inferential Statistics	Nominal	Ordinal	Interval	Ratio
Chi Square	Yes	Yes
Mann-Whitney, Wilcoxon, Kruskal Wallis and Friedman		Yes
Anova and T-Test			Yes	Yes
Rank Order Correlation		Yes
Product Moment Correlation			Yes	Yes
Factor Analysis			Yes	Yes

Table- 5 Inferential statistics and Testing

The two primary applications of inferential statistics are the establishment of estimates regarding populations and the testing of hypotheses in order to draw conclusions regarding populations.

Which Statistics Can Be Used
Descriptive Statistics	Nominal	Ordinal	Interval	Ratio
Frequency Distribution	Yes	Yes	Yes	Yes
Percentage	Yes	Yes	Yes	Yes
Mode	Yes	Yes	Yes	Yes
Percentile		Yes	Yes	Yes
Median		Yes	Yes	Yes
Range			Yes	Yes
Mean			Yes	Yes
Standard Deviation			Yes	Yes
Geometric Mean				Yes
Harmonic Mean	`			Yes

Table-6: Descriptive statistics and test

The scale serves as a measurement tool for collecting data for further analysis. When we measure the data, it depends on your research questions, objectives, and hypotheses. You must determine the constructs or variables you want to measure, such as attitudes, opinions, behaviors, or perceptions.