Levels of Measurement

Data and Levels of Measurement

Understanding our data is key to analysing its contents using descriptive and inferential statistics.

• Data can be broadly categorised as qualitative (qualities or characteristics) or quantitative (numerical).
• There are also different levels of measurement which tell us how precisely variables are recorded.
• The different levels of measurement limit which descriptive statistics are used to summarise data, and which inferential statistics can be performed on data.
• These levels are: Nominal, ordinal, interval and ratio.

Nominal

Nominal data divides variables into mutually exclusive labeled categoies. Each category is different but cannot be rank ordered.

Examples

Eye Colour

Transport to Work

Inferential statistics

Descriptive Statistics

Chi-squared goodness of fit Chi-squared test of independence

Frequency distribution Mode

Ordinal

Ordinal data classifies variables into categories which have an order or rank. The data can be categorized and ranked although intervals between values are not necessarily equal.

Examples

Exam Grades

Education Level

Inferential statistics

Descriptive Statistics

Mood's median test, Mann-Whitney U-test, Wilcoxon matched pairs signed-rank test, Kruskal-Wallis H test, Spearman's rho.

Frequency distribution Mode, median Range

Interval

Interval data is measured along a numerical scale that has equal intervals between adjacent values. It can be categorized and ranked.

Examples

IQ Scores

Temperature (°C)

50 60 70 80 90 100 110 120 130 140 150

Inferential statistics

Descriptive Statistics

T-test, ANOVA, Pearson's r, simple linear regression

Frequency distribution Mode, median and mean Range, standard deviation and variance

Ratio

Ratio data is measured along a numerical scale that has equal distances between adjacent values and a "true zero".

Examples

Weight (kg)

Annual Household Income (£)

Inferential statistics

Descriptive Statistics

T-test, ANOVA, Pearson's r, simple linear regression

Frequency distribution Mode, median and mean Range, standard deviation, variance, coefficient of variation