levels of measurement

Nominal Level of Measurement

• Nominal data are categorical. They label or name things but have no numerical meaning, order, or value.

• Characteristics:

  • Categories are mutually exclusive: each participant or data point can only belong to one category.

  • There is no ranking or order.

  • You cannot perform arithmetic calculations on nominal data.

• Examples:

  • Gender (male, female)

  • Favourite colour (red, blue, green)

  • Type of therapy attended (CBT, psychodynamic, humanistic)

Statistical Tests and Analysis:

• Use non-parametric tests such as the chi-squared test.

• The mode is the only appropriate measure of central tendency.

Advantages:

• Easy to collect and classify.

• Useful for qualitative, categorical information.

Limitations:

• Cannot measure magnitude or direction of differences.

• Limited statistical analysis is possible.

Ordinal Level of Measurement

• Ordinal data can be ordered or ranked, but the distance between ranks is not equal or meaningful.

• Characteristics:

  • Shows relative position or order.

  • The differences between ranks are unknown or unequal.

  • You can say which is more or less, but not by how much.

Examples:

• Likert scales on surveys (e.g., 1 = strongly disagree, 5 = strongly agree)

• Socioeconomic status (low, middle, high)

• Education level (GCSE, A-Level, degree)

Statistical Tests and Analysis:

• Use non-parametric tests, for example Spearman’s rho or Mann–Whitney U test.

• Median or mode can be used as measures of central tendency.

Advantages:

• Captures order and ranking.

• Useful for surveys, questionnaires, and subjective measures.

Limitations:

• Cannot perform arithmetic calculations.

• Differences between ranks are not equal, limiting precision.

Interval Level

Interval data are numerical, ordered, and have equal intervals between values, but there is no true zero point.

Characteristics:

• Can measure differences between values.

• Zero is arbitrary; it does not indicate the absence of the variable.

• Allows addition and subtraction, but multiplication or division is not meaningful.

Examples:

• Temperature in Celsius or Fahrenheit

• IQ scores

• Standardised test scores

Statistical Tests and Analysis:

• Use parametric tests if assumptions are met, e.g., Pearson’s r or t-tests.

• Mean, median, and mode are all appropriate measures of central tendency.

Advantages:

• Precise measurement with meaningful differences between scores.

• Allows a wider range of statistical analyses than nominal or ordinal data.

Limitations:

• No true zero, so ratios are meaningless (e.g., 20°C is not twice as hot as 10°C).

summary

Nominal – “Labels”

• Meaning: Nominal data are just names or labels. They don’t have a number value or order.

• Key idea: You can group things, but you can’t say one is bigger or smaller than the other.

• Example: Eye colour. Blue, green, brown.

  • You can count how many people have each colour.

  • You cannot say blue is “more” than green.

Simple analogy: Nominal is like putting things into boxes. Each thing goes into a box, but the boxes don’t have any order.

Ordinal – “Ranks”

• Meaning: Ordinal data can be put in order (first, second, third), but the distance between them is not equal.

• Key idea: You can say which is bigger or better, but you can’t measure by how much.

• Example: Finishing positions in a race.

  • 1st, 2nd, 3rd place.

  • You know 1st is faster than 2nd, but you don’t know exactly how much faster.

Simple analogy: Ordinal is like a ranking system. You know the order, but you don’t know the exact difference between ranks.

Interval – “Numbers with equal gaps”

• Meaning: Interval data are numbers where the gaps between values are equal, but there’s no true zero.

• Key idea: You can measure the difference between numbers, but zero doesn’t mean “nothing.”

• Example: Temperature in Celsius.

  • 20°C is 10°C warmer than 10°C (difference makes sense).

  • But 0°C does not mean “no temperature.”

  • You cannot say 20°C is “twice as hot” as 10°C.