Types of scales

When collecting data, often it is useful to group the results and apply them to a scale.

But not all scales are the same.

I will explain the similarities and differences between the 4 types of scales, and clarify some aspects of the scales that can be confusing.

• Nominal

• Ordinal

• Interval

• Ratio

The scales are distinguished by two properties:

1. Distance: The meaning of the "space between" elements of the scale

2. Operations: Which operations are defined on elements of the scale

The simplest scale is barely a scale. It consists of simply naming things, aka labeling, and grouping the elements by the names.

Of course, there is power in naming! See True Name.

It allow for comparison of sizes of sets.

Typical example: Count of Preferred Public Transportation Modes

CareerForge "What is Nominal Data?"

1. Distance: Meaningless

2. Operations: Labeling, Counting

If you have ever rated something using a "5 star" system, you have used an ordinal scale.

Similar to the nominal scale, elements are labeled. These labels, however, can be sorted. The sorting can be by numbers, letters, or anything else that can be ordered.

Famous example: Cooper-Harper Handling Qualities Rating Scale

1. Distance: Meaningless

2. Operations: Labeling, Counting, Sorting

NOTE Ordinal scales CANNOT be averaged in any meaningful way. To communicate the values of an ordinal scale, it's best to just use a bar chart to indicate counts.

Be like Drake

If you have ever talked about the temperature outside when looking at the weather, you have used an interval scale, whether Fahrenheit or Celsius.

Famous example: Fahrenheit and Celsius Temperature Scales

1. Distance: Fixed distance between units, arbitrary distance from zero

2. Operations: Labeling, Counting (See Countability below), Sorting, Addition/Subtraction

NOTE Because "zero" is arbitrary in an interval scale, multiplication and division are not defined. "100℉" is not "twice as hot as 50℉"

If you have ever had school work graded on a scale of 0 to 100, you have experienced a ratio scale. A 90 is twice as many points as a 45, because "zero" has meaning. Therefore, elements of the scale can be multiplied and divided in meaningful ways.

Famous example: Kelvin Temperature Scale

1. Distance: Fixed distance between units, fixed distance from zero

2. Operations: Labeling, Sorting, Addition/Subtraction, Multiplication/Division

Discrete

• Countable

• "Chunked"

Continuous

• Uncountable

• "Smoothed"

All four of the scales can use discrete values, but only interval and ratio scales can meaningfully use continuous values.

Numeric: Associated with "numbers"

Often, nominal and ordinal are not considered "numeric" scales, however, numbers can be used as labels for all four of the scales.

When numbers are applied to a nominal scale, they do not imply a numeric value, just a unique identifier, in the sense that "1" is distinct from "2."

When numbers are applied to an ordinal scale, they do not imply anything other than a sortable sequence, in the sense that "2" is "between" "1" and "3", but NOT that "2" is "twice" "1".

Categorical: associated with "categories"

Often, categorical is solely associated with nominal data, but more broadly, categories may be assigned that can be used on any of the four scales.

The arithmetic operations are addition/subtraction and multiplication/division.

Qualitative: no arithmetic operations may be meaningfully applied to the elements of the scale

Quantitative: some arithmetic operations may be meaningfully applied to the elements of the scale

However, once items are labeled and counted, their counts are quantitative. So just because nominal and ordinal scales are composed of elements that are qualitative, the results of grouping items labeled with the scale elements can be quantitative

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