8.3.6

Levels of Measurement (A2 only)

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Nominal and Ordinal Data

There are four main types of data: nominal, ordinal, interval and ratio. The types of data will influence how they are statistically analysed.

Nominal data

Nominal data

  • Nominal data is essentially data that fits into distinct categories.
  • Nominal data is collected by counting the frequency of each category.
    • An example of nominal data, in terms of biology, would be hair colour (brown, black, red, etc.)
Nominal data example

Nominal data example

  • In a study on the bystander effect, a researcher could observe the behaviour of passing individuals.
  • Do they A) help or B) not help a person in need.
  • This is an example of nominal data because there are two distinct categories.
  • The frequency of people in both categories can be counted (out of 30 people, five were helpful and 25 were not helpful).
Ordinal data

Ordinal data

  • Ordinal data is data that falls along a scale.
  • It relates measurements to the same variable.
  • Ordinal data is often seen in surveys.
Ordinal data example

Ordinal data example

  • An example is a Likert scale:
    • Participants select from a 5-7 point scale (strongly disagree, disagree, neutral, agree, and strongly agree).
    • Another example in psychological studies could be a questionnaire on depression:
    • Participants could rate their symptoms on scales of 1-to-10.

Interval and Ratio Data

Both are data measured on a scale. They both use objective units and intervals. Ratio data cannot have negative readings.

Interval data

Interval data

  • Interval data is also a measurement taken on a scale.
  • But the difference is that the unit is equally sized and is objective.
  • Students can get confused between ordinal and interval data.
    • For example, 1-to-10 scales can be miscategorised. As these scales can be subjective (a person’s own opinion on their depression symptoms), they are ordinal and not interval.
Objectivity

Objectivity

  • For data to be interval, the set units and intervals must be objective.
    • Examples of interval data would include time and temperature.
      • Seconds are equally sized and objective. No one would argue that seconds are subjective.
      • Temperature would also be interval as there is a universal standard of degrees Celsius and standardised measuring equipment.
Ratio data

Ratio data

  • Ratio data, like interval data, are measurements taken on a scale.
  • But ratio data is set to an absolute zero and there can be no negative values.
    • For example, length measured in centimetres by a ruler is set to 0cm. There is no “negative length”.
Examples

Examples

  • Another example would be percentage grades on exam (0-100%). There would be no negative scores.
  • Temperature (measured in Celsius) would be interval and not ratio because you can have negative temperatures.
  • An example of ratio data in psychological studies would be IQ tests. There is no negative IQ score.
Tests

Tests

  • The different type of data is analysed using different statistical tests.
  • Nominal data can be analysed using the sign test or the Chi-squared test.
  • Ordinal data is analysed using Spearman’s rho, the Wilcoxon test or the Mann-Whitney test.
  • Interval and ratio data is analysed using either Pearson’s r test, the unrelated t-test or the related t-test.
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