Measurement

There are four levels of measurement: Nominal, Ordinal, Interval and Ratio.

Interval and Ratio Scales

The interval scales and ratio scales are sometime classified together and called the Cardinal Scale.
Also known as counting numbers because they indicate how many / size
1,2,3,4 50. 100
These can be used for ordering and ranking
Cardinal numbers can be divided into two groups:
     ● Discrete - These are units where each value is clearly separated from its neighbour (eg 3 people)
     ● Continous - These can be divided up again and again (eg 2 inches)

Nominal Scale

more
These are used for identification, naming or to provide names
Nominal data comes from counting things and putting them in a category.
These categories are based on names and there is no order to these names.
telephone numbers, account numbers, "20".
When measuring using a nominal scale you use categories and there is no concept of ordering
This only represents equivalence / names of categories

This data does not have any numerical values.
This data can only be separated into categories.
(examples: colours or favourite types of food)

Ordinal Scale

Has Ordering and Ranking
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These indicate the order or position in a set
1st, 2nd, third

Ordinal data is nominal data where the categories stand in a clear ordered, ranked relationship.
You can use the terms "more than" or "less than"

This is nominal data where the categories stand in a clear order, ranked relationship
(examples provide a rating out of 1 to 5)
This data has no sense of relative size.
5 is better than 1 but there is no scale associated with these numbers

Interval Scale

Has Ordering, Ranking and Interval size

Interval data is ordinal data where the categories are ranked on a scale.
This means the distance between the categories is a known Quantity and can be used in the analysis.
You can use the terms "how much more" or "how much less"

This allows direct comparison as well as addition and subtraction

Examples - calendar years
You can measure central tendency

Ratio Scale

Has Ordering, Ranking, Interval Size and Absolute Zero

Ratio data is interval data where the categories exist on a scale that has a "true zero" or absolute point of reference

This allows multiplication and division
For example a Ruler (centimters and inches)

Examples - What type of measurement are these:

The salaries of people aged 30
The exam scores for a particular course
Number of exams passed
IQ scores
The size of famalies in the UK