## Introduction

This post is part of a series I’ve been chipping away at, where I teach basic statistics and probability. The other posts in the series include:

- Measures of Central Tendency
- Frequency Distributions
- Dispersion and Variability (Standard Deviation)
- Z-Scores
- Z-Test Hypothesis Testing
- Correlation (Calculating Pearson’s r)
- Least-Squares Regression
- Statistical Coding and Classification

Variables are the outcomes of a psychological measurement. As the Australian Bureau of Statistics notes, a variable is “any characteristics, number, or quantity that can be measured or counted.” Also called data items, they are called variables because the “value may *vary*” and may change over time.

There are four scales of measurement used to distinguish variables:

- Nominal/Categorical
- Ordinal
- Interval
- Ratio

## Nominal Variables

Nominal variables are those that separate a value into different categories. Examples of nominal variables are gender (male, female, other) or type of transportation (car, bus, train). These are categories and have no intrinsic value that allows them to be compared on their own.

## Ordinal Variables

Ordinal variables are similar to nominal variables but they are ranked. These are like nominal variables but they are ranked. One example of an ordinal variable is educational achievement. A scale might look like this:

- Less than a high school diploma
- High school or GED
- Bachelor’s degree
- Graduate or first professional degree
- Doctorate degree

These can be ranked from least education to most education, but there is no way to tell necessarily how much “more” education a Bachelor’s degree is when compared to a graduate or professional degree.

## Interval Variables

An interval variable is an ordinal variable where the different items are evenly spaced. For example, income level:

- $0-4,999
- $5,000-9,999
- 10,000-14,999
- 15,000-20,000

Each one of these is evenly spaced. There must be a continuum to measure an interval variable.

## Ratio Variables

Ratio variables are like interval variables but with the notable exception that “0” indicates an absence of the value. For example, in our previous example income level happens to mean no money. If we look at temperature however, 0 degrees Celsius does not mean there is no temperature. This makes Celsius an Interval Variable.

On the other hand, Kelvin is a ratio variable because 0 Kelvin really means no heat or temperature at all (as we say, absolute zero.)

## Continuous vs. Discrete Variables

One more distinction is the difference between continuous and discrete variables. Continuous variables are those that can take on any value. For example, a variable that can have any number between 10 and 11 (10.48938, 10.74982, 10.9999) is continuous.

If the survey only has two values with with nothing in between (like 10 or 11) then this is a discrete variable, also known as an integer.

## Why Separate Variables into Categories

It’s important to understand whether the variables we are working with are nominal, ordinal, interval, ratio, because we’ll use different statistical tests when working with different data. Coding, and other manipulations and processing of the data may also differ depending on the variable.

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