Summary of The Four Levels of Measurement
& Appropriate Descriptive Statistics & Graphs
(James Neill, revised 15/03/05)

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 V02 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	ü	ü	ü	If meaningful
Median	û	ü	ü	ü
Range, Min. Max	û	ü	ü	ü
Mean	û	û	If metric	ü
SD	û	û	If metric	ü

Graph	Nominal	Ordinal	Interval	Ratio
Bar / Pie	ü	ü	If discrete	û
Stem & Leaf	û	ü	ü	ü
Boxplot	û	ü	ü	ü
Histogram	û	û	If metric	ü