Summary of The Four Levels of Measurement:
Appropriate Descriptive Statistics and Graphs

James Neill, 2009

Level of Measurement

Properties

Examples

Descriptive statistics

Graphs

Nominal / Categorical

Discrete

Arbitrary
(no order)

Dichotomous

  • Yes / No

  • Gender

Types / Categories

  • colour

  • shape

Frequencies Percentage
Mode

Bar

Pie

Ordinal / Rank

Ordered categories

Ranks

Ranking of favourites

Academic grades

Frequencies

Mode

Median

Percentiles

Bar

Pie

Stem & leaf

Interval

Equal distances between values

Discrete
(e.g., Likert scale)

Metric
(e.g., deg. F)

Interval scales >5 can usually be treated as ratio

Discrete

- Thoughts, behaviours, feelings, etc. on a Likert scale

Metric

- Deg. C or F

Frequencies
(if discrete)

Mode

(if discrete)

Median

Mean

SD

Skewness

Kurtosis

Bar
(if discrete)

Pie
(if discrete)

Stem & Leaf

Boxplot

Histogram
(if metric)

Ratio

Continuous / Metric / Meaningful 0 allows ratio statements
(e.g., A is twice as large as B)

Age

Weight

VO2 max

Deg. Kelvin

Mean

SD

Skewness

Kurtosis

Histogram

Boxplot

Stem&Leaf
(may need to round leafs)

Summary of Descriptive Statistics & Graphical Summaries for the Four Levels of Measurement

Statistic

Nominal

Ordinal

Interval

Ratio

Mode

√

√

√

If meaningful

Median

X

√

√

√

Range, Min. Max

X

√

√

√

Mean

X

X

If metric

√

SD

X

X

If metric

√

 

Graph

Nominal

Ordinal

Interval

Ratio

Bar / Pie

√

√

If discrete

X

Stem & Leaf

X

√

√

√

Boxplot

X

√

√

√

Histogram

X

X

If metric

√