# Statistics » Measurement scales

## Inhoud

NominalOrdinal

Interval

Ratio

Qualitative or quantitative

Discrete or continuous

Nominal | Ordinal | Interval | Ratio | ||||

categories | categories | categories | categories | ||||

order | order | order | |||||

equal differences | equal differences | ||||||

natural zero |

## Nominal

If a variable is only a distinction between different categories, then there is a nominal measurement scale. In that case the values of the variable can be indicated with names or categories, so that they can be distinguished from each other.

Examples are gender, places or your favourite food.

## Ordinal

If, in addition to a distinction, a sequence can also be indicated, then there is an ordinal measurement scale.

Examples are 'Agree, neutral, disagree' or the star system used for hotels.

With ordinal data, you are able to use numbers, like in the example of the star system for the hotels. However, there is no equal difference between the number of stars.

## Interval

If in a variable there is a distinction, an order and a equal difference between values there is an interval scale. There is no natural zero, so no ratio. There can be a zero, but it is chosen. The zero does not point to an absence.

Examples are the year we live in, times and temperature.

In these examples there is no ratio because when it is 30 °C outside, it is not twice as warm as when it is 15 °C.

## Ratio

With this measurement scale you have all the properties mentioned above (category, order and equal differences) and a natural zero. The natural zero points to an absence. So if a variable has all four properties, there is a ratio scale.

Examples are age, weight and amount of money.

Now there is a ratio because something weighing 40 kg is twice as heavy as something of 20 kg.

## Qualitative or quantitative

Variables 'measured' on a nominal or ordinal scale are also called qualitative, categorical or attributive variables.

Variables measured on an interval or ratio scale are also called quantitative variables.

## Discrete or continuous

A **discrete** variable cannot have all values.

You can buy one or two tomatoes, but not a half tomato. The number of tomatoes is a discrete variable. The amount you pay for the tomatoes is also discrete. This variable can be a lot more different values, but still not all imaginable numbers.

A **continuous** variable can (in theory) have all values. Looking at the tomatoes again, the weight of the tomatoes is a continuous variable. It could be anything. They can weigh 325 grams, but also 327.568 grams. Between these two examples are an infinite number of other numbers. All these numbers could be the weight of these tomatoes.

### Continuous can seem discrete

A continuous variable can (in theory) have all values. Why I wrote the 'in theory' between parenthesis I will explain now. Let us look at the weight of the tomatoes again, which is continuous. However, the scale in the supermarket only shows the weight in grams. In the supermarket your tomatoes will therefore always weigh a whole number. This happens to a lot of things we measure. Think about time or a length. No matter how accurately you measure, there is always a moment when you round off.

So: the weight of the tomatoes is a continuous variable. The weight shown on the scale is discrete.