Measurement scales

Qualitative: Nominal

Items are in mutually-exclusive categories, and can only belong to a single category

There is no natural order - quantitative comparisons don’t make sense

Nominal scale examples

Species	🐌 🌲 🦡
Sex
Boolean / Logical	TRUE FALSE
Observer name	Layla Miguel

Distance sampling

Does density differ between land-cover classes?

Does detectability depend on team size or equipment?

Qualitative: Ordinal

Ordinal categories occur along a scale from low to high, where the order of categories has meaning

The absolute value does not have meaning because the intervals between values are not equal. For example, ‘big’ is not twice the size of ‘medium’. Therefore it doesn’t make sense to make numerical calculations such as averaging

Ordinal scale examples

Age class	🌱 🌿 🌳
Dominance rank	Dominant Subordinate

Distance sampling

Are experienced observers more likely to detect the species than novices?

Density declines from primary forest through secondary forest into agricultural land

Quantitative: Discrete and continuous

Quantitative variables can be discrete or continuous

Discrete

Discrete values are used when only whole numbers (integers) make sense and intermediate values are impossible

For example, number of parasites or offspring

Continuous

Continuous values can have decimals, and there is theoretically an infinite number of values between any two integers

For example: weight or area

Quantitative: Interval

Interval variables have an equal-interval ordering¹, i.e. the difference between 1 and 2 is the same as the difference between 4 and 5

It makes sense to calculate averages

There is no natural zero point: zero is placed at an arbitrary point (for example the date when the calendar year begins). This means that calculating a ratio isn’t meaningful, i.e. 20°C is not twice as hot as 10°C

Interval scale examples

Temperature in Celsius	0°C 23°C
Calendar date	📆

Distance sampling examples

• Does detectability decline with rising temperature, as animals become less active?

1. Equal interval: The distance between two adjacent values is the same throughout the scale

Quantitative: Ratio

Ratio variables have equal-interval ordering and a true zero point

A zero implies the absence of the variable being measured, quite literally ‘none’

This means it makes sense to calculate ratios, e.g. a breeding pair with four offspring has twice as many as a pair with two

Ratio scale examples

Temperature in Kelvin	0°K 287°K
Survey effort	🚶 🚶
Species diversity	🐬 🐠 🐢

Distance sampling

Is density correlated with food availability?

Quantitative - Cyclic

In cyclic¹ variables, the highest number on the scale falls next to the lowest

For example, 23:59 is followed by 00:00, or December is followed by January

Cyclic variables need to be treated differently to other continuous data, to take into account they are circular

Cyclic scale examples

Bearing or azimuth	🧭
Time	⌚
Season	🍃 🍂

Distance sampling

Does detectability vary with time of day?

1. Also known as drectional

Measurement scales in R

R treats Quantitative variables as:

• Factors if categories are denoted by text names, i.e. character vectors
• Integers if categories are denoted by numeric codes

You need to apply the factor() function to convert numeric codes to categories, and use the ordered subcommand to impose the correct order of categories for ordinal variables

Qualitative variables in R:

• R distinguishes between discrete (integer), continuous (numeric) and circular
• Interval and ratio variables are both numeric in R

Measurement scales in unmarked

unmarked also deals with categorical covariates intuitively:

• Define them as a factor with factor() if R hasn’t automatically recognised categorical variables as factors when you imported your data
• unmarked automatically understands how to treat your multiple categories