Levels of measurement | AQA A-Level Psychology Revision
- Revision Notes
- Aug 5
- 15 min read
Updated: 6 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 55 minutes
This Levels of measurement A-Level Psychology revision page explains how psychologists classify numerical and categorical data as nominal, ordinal or interval. You will learn how to identify each level from an unfamiliar research scenario and explain why the level of measurement affects the choice of statistical test. This topic builds on quantitative and qualitative data and is essential preparation for selecting and justifying inferential statistical tests in AQA Research Methods.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Define nominal, ordinal and interval data.
Explain the differences between the three levels of measurement.
Identify the level of measurement used in an unfamiliar psychological study.
Justify your identification using features of the data.
Explain how level of measurement affects statistical test choice.
Select a possible statistical test using the level of measurement and other features of a study.
Revision Notes 📚
Levels of measurement in A-Level Psychology
A level of measurement describes how data have been recorded and what the resulting values represent.
AQA requires students to distinguish between:
nominal data;
ordinal data;
interval data.
The level of measurement affects:
how the data can be organised;
which descriptive statistics may be appropriate;
how the results can be displayed;
which inferential statistical test may be selected.
Correctly identifying the level of measurement is therefore an important step when analysing psychological data.
A quick comparison
Level of measurement | What the data represent | Ordered? | Equal intervals? |
Nominal | Separate categories or labels | No | No |
Ordinal | Ordered categories, ranks or ratings | Yes | Not necessarily |
Interval | Numerical measurements with equal units | Yes | Yes |
The key questions are:
Are the values only category labels?
Can the values be placed in a meaningful order?
Are the intervals between values equal?
Nominal data
Nominal data place people, behaviours or responses into separate categories.
The categories are different from one another, but they do not have a meaningful numerical order.
Examples include:
attachment classification;
type of treatment received;
whether a participant answered correctly or incorrectly;
whether a behaviour occurred or did not occur;
category of questionnaire response where the categories are not ordered.
Nominal data may be represented by words, letters or numbers. However, numbers used as category codes do not turn the data into numerical measurements.
Numbers used as nominal labels
Suppose a researcher codes attachment classifications as follows:
Attachment classification | Code |
Secure | \(1\) |
Insecure-avoidant | \(2\) |
Insecure-resistant | \(3\) |
The data are still nominal.
The code:
$$3$$
does not represent more attachment than:
$$1$$
The numbers are simply labels used to distinguish the categories.
It would not be meaningful to calculate:
$$3-1=2$$
and claim that one classification contains two more units of attachment than another.
Characteristics of nominal data
Nominal data:
consist of separate categories;
have no meaningful numerical order;
may be represented by labels or codes;
can be counted using frequencies;
can be expressed as percentages or proportions;
cannot be ranked meaningfully.
A frequency table or bar chart may be used to display nominal data. These displays are covered in tables and graphs.
Worked example: identifying nominal data
A researcher records whether each participant:
obeyed;
did not obey.
These results are nominal because:
there are two separate categories;
one category is not a higher numerical measurement than the other;
the researcher can count how many participants fall into each category.
A suitable justification would be:
The data are nominal because participants are classified into separate categories of obeyed or did not obey, and the categories do not represent numerical measurements.
Ordinal data
Ordinal data can be placed into a meaningful order or rank.
The values show relative position, but the intervals between values are not necessarily equal.
Examples include:
finishing positions in a competition;
ranked preferences;
ratings on an ordered scale;
ordered questionnaire response categories;
ratings of pain, anxiety or agreement.
Ordered response categories
A questionnaire might ask participants to choose one of the following responses:
Strongly disagree
Disagree
Neither agree nor disagree
Agree
Strongly agree
These responses have a meaningful order.
For example:
$$\text{Strongly disagree}<\text{Disagree}<\text{Agree}<\text{Strongly agree}$$
However, the psychological difference between strongly disagree and disagree is not necessarily exactly equal to the difference between agree and strongly agree.
The data are therefore ordinal.
Characteristics of ordinal data
Ordinal data:
can be arranged in a meaningful order;
may represent ranks or ordered categories;
show relative position;
do not guarantee equal intervals between values;
may be based on subjective ratings;
contain more information than unordered categories.
The median and mode can be used with ordinal data because the values can be ordered.
Worked example: ranked data
Participants rank four coping strategies from most useful to least useful.
A rank of:
$$1$$
represents the most useful strategy.
A rank of:
$$4$$
represents the least useful strategy.
The data are ordinal because the values show an ordered position.
However, the difference between ranks:
$$1\text{ and }2$$
is not necessarily equal to the difference between ranks:
$$3\text{ and }4$$
Likert-type ratings
A Likert-type rating scale contains ordered response categories.
For example:
Rate how anxious you feel from \(1\) to \(5\), where \(1\) means not anxious and \(5\) means extremely anxious.
The response values have an order:
$$1<2<3<4<5$$
However, the psychological difference between adjacent ratings cannot automatically be assumed to be equal.
The ratings are therefore ordinal.
Interval data
Interval data consist of numerical measurements in which the intervals between values are equal.
This means that the difference between one pair of adjacent values is the same size as the difference between another pair.
Examples may include:
time measured in seconds;
distance measured in centimetres;
numerical test scores treated as equal units;
the number of words recalled;
numerical measures collected using a standardised procedure.
Equal intervals
Suppose response time is measured in seconds.
The difference between:
$$2\text{ seconds and }3\text{ seconds}$$
is the same size as the difference between:
$$7\text{ seconds and }8\text{ seconds}$$
In each case, the difference is:
$$1\text{ second}$$
The data therefore have equal intervals.
Characteristics of interval data
Interval data:
consist of numerical measurements;
can be placed in order;
contain equal intervals between values;
allow differences between scores to be compared meaningfully;
support a wider range of mathematical and statistical analysis.
The mean, median and mode may be calculated for interval data. Measures of dispersion, such as the range and standard deviation, may also be used.
Worked example: response times
A psychologist records the time taken by participants to complete a task:
$$12.4,\ 13.1,\ 14.8,\ 15.2,\ 16.0\text{ seconds}$$
These data are interval because:
the scores are numerical measurements;
the values can be ordered;
the difference of one second has a consistent meaning across the scale.
A suitable justification would be:
The data are interval because completion time is measured numerically in seconds and the intervals between values are equal.
Worked example: memory scores
Participants complete a memory task, and the researcher records the number of words recalled:
$$6,\ 8,\ 10,\ 11,\ 14$$
These results are numerical scores.
The difference between:
$$6\text{ and }8$$
is two recalled words, as is the difference between:
$$8\text{ and }10$$
The scores may therefore be treated as interval data within the study.
Comparing nominal, ordinal and interval data
Feature | Nominal | Ordinal | Interval |
Separate categories | Yes | Yes | Values may be grouped, but are measurements |
Meaningful order | No | Yes | Yes |
Equal intervals | No | Not guaranteed | Yes |
Frequencies can be calculated | Yes | Yes | Yes |
Mode can be identified | Yes | Yes | Yes |
Median can be identified | No meaningful ordering | Yes | Yes |
Mean can be calculated meaningfully | No | Usually not appropriate for ranks | Yes |
A decision process for identifying the level
Use the following steps.
Step 1: Are the data categories only?
Ask whether the values merely identify different groups.
If the answer is yes and there is no meaningful order, the data are nominal.
Examples:
correct or incorrect;
secure or insecure attachment;
treatment A or treatment B.
Step 2: Can the categories or values be ordered?
If the values can be ranked but equal gaps cannot be assumed, the data are ordinal.
Examples:
first, second and third place;
low, medium and high anxiety;
ratings from strongly disagree to strongly agree.
Step 3: Are the intervals equal?
If the values are numerical measurements with equal units, the data are interval.
Examples:
time measured in seconds;
distance measured in centimetres;
performance scores recorded in consistent numerical units.
Identifying the level from the operationalisation
The level of measurement depends on how the variable is operationalised, meaning how it is defined and measured in the study.
The same psychological concept could produce different levels of measurement depending on the procedure.
Worked example: measuring anxiety in different ways
A researcher could measure anxiety using three different procedures.
Procedure A
Participants are classified as:
anxious;
not anxious.
This produces nominal data because there are two unordered categories.
Procedure B
Participants rate their anxiety as:
low;
moderate;
high.
This produces ordinal data because the categories have a meaningful order, but the intervals are not known to be equal.
Procedure C
The researcher records a numerical score using a procedure that produces equal numerical units.
This produces interval data.
The psychological concept remains anxiety, but the level of measurement changes because the operationalisation changes.
Worked example: measuring memory in different ways
A researcher investigates memory performance.
Method 1
Participants are recorded as:
recalled the target word;
did not recall the target word.
This produces nominal data.
Method 2
Participants are ranked from best to worst according to performance.
This produces ordinal data.
Method 3
The researcher records the number of words recalled.
This produces numerical score data that may be treated as interval data.
This shows why you must examine what was actually recorded rather than identifying the
level from the topic alone.
Nominal or ordinal?
A common difficulty is distinguishing nominal categories from ordinal categories.
Ask whether the categories have a meaningful sequence.
For example:
Data | Level |
Therapy A, Therapy B, no therapy | Nominal |
Low anxiety, moderate anxiety, high anxiety | Ordinal |
Correct, incorrect | Nominal |
Strongly disagree to strongly agree | Ordinal |
First, second, third | Ordinal |
Secure, insecure-avoidant, insecure-resistant | Nominal |
The attachment categories are different, but they are not arranged from lower to higher attachment.
Ordinal or interval?
To distinguish ordinal from interval data, ask whether equal numerical differences have a consistent meaning.
For ordinal data:
$$4-3=1$$
does not necessarily represent the same psychological difference as:
$$2-1=1$$
For interval data, equal numerical differences represent equal measurement intervals.
For example:
$$8\text{ seconds}-7\text{ seconds}=1\text{ second}$$
and:
$$15\text{ seconds}-14\text{ seconds}=1\text{ second}$$
Both differences represent the same amount of time.
Level of measurement and descriptive statistics
The level of measurement affects which measure of central tendency is appropriate.
Level | Appropriate measures of central tendency |
Nominal | Mode |
Ordinal | Median and mode |
Interval | Mean, median and mode |
Nominal data
The mode can be identified because the most frequently occurring category can be found.
The mean and median are not meaningful because the categories do not have numerical distances or an ordered middle.
Ordinal data
The median can be identified because the values can be ranked.
The mode can also be identified.
The mean may not be appropriate because the intervals between ranks or ratings are not known to be equal.
Interval data
The mean, median and mode can all be calculated because the data are ordered numerical measurements with equal intervals.
These measures are explained in measures of central tendency.
Level of measurement and data displays
The level of measurement also influences how results may be displayed.
Level | Possible display |
Nominal | Frequency table or bar chart |
Ordinal | Ordered frequency table or bar chart |
Interval | Table, histogram or another suitable numerical display |
Two measured co-variables | Scattergram, where appropriate |
For example, a scattergram may be used to display a relationship between two measured co-variables. Scattergrams are covered in scattergrams and correlation coefficients.
Level of measurement and inferential testing
The AQA specification requires students to understand how the level of measurement affects the selection of an inferential statistical test.
The level of measurement is not the only factor used to select a test. Researchers must also consider:
whether the study investigates a difference, association or correlation;
whether the data come from related or unrelated groups;
the experimental design.
The full selection process is covered in choosing an inferential test.
Statistical tests associated with nominal data
Tests that may use nominal data include:
the sign test;
the Chi-squared test.
Sign test
The sign test is used for a test of difference when:
the data are nominal;
the data are related;
participants can be assigned a positive or negative sign based on the direction of change.
The sign test is studied in the sign test.
Chi-squared test
The Chi-squared test is used with nominal frequency data when investigating an association between variables.
It is covered in Chi-squared test.
Statistical tests associated with ordinal data
Tests that may be selected for ordinal data include:
Spearman’s rho;
Wilcoxon;
Mann-Whitney.
Spearman’s rho
Spearman’s rho may be used to investigate a correlation using ordinal data.
Wilcoxon test
The Wilcoxon test may be used to test a difference using related ordinal data.
Mann-Whitney test
The Mann-Whitney test may be used to test a difference using unrelated ordinal data.
These tests are covered in Spearman’s rho and Pearson’s r and Wilcoxon and Mann-Whitney tests.
Statistical tests associated with interval data
Tests that may be selected for interval data include:
Pearson’s \(r\);
the related \(t\)-test;
the unrelated \(t\)-test.
Pearson’s \(r\)
Pearson’s \(r\) may be used to investigate a correlation using interval data.
Related \(t\)-test
A related \(t\)-test may be used to test a difference using related interval data.
Unrelated \(t\)-test
An unrelated \(t\)-test may be used to test a difference using unrelated interval data.
The two \(t\)-tests are covered in related and unrelated t-tests.
Summary of measurement level and statistical tests
Research purpose | Data level | Relationship between scores | Possible test |
Difference | Nominal | Related | Sign test |
Association | Nominal | Independent frequencies | Chi-squared |
Correlation | Ordinal | Paired scores | Spearman’s rho |
Correlation | Interval | Paired scores | Pearson’s \(r\) |
Difference | Ordinal | Related | Wilcoxon |
Difference | Ordinal | Unrelated | Mann-Whitney |
Difference | Interval | Related | Related \(t\)-test |
Difference | Interval | Unrelated | Unrelated \(t\)-test |
This table is a guide rather than a complete test-selection method. You must consider all the relevant features of the investigation.
Worked example: choosing between correlation tests
A researcher investigates the relationship between two ranked variables:
participants’ rank for stress;
participants’ rank for sleep quality.
The research is investigating a correlation, and the data are ordinal.
A suitable test would therefore be:
$$\text{Spearman's rho}$$
If both co-variables had been measured using interval data, a possible test would be:
$$\text{Pearson's }r$$
Worked example: related ordinal data
Participants rate anxiety before and after a relaxation activity using an ordered scale from:
$$1\text{ to }5$$
The study investigates a difference.
The same participants provide both sets of scores, so the data are related.
The ratings are ordinal.
A suitable test would therefore be:
$$\text{Wilcoxon test}$$
Worked example: unrelated interval data
A researcher compares memory scores from:
one group that revises in silence;
a different group that revises while listening to speech.
The study investigates a difference.
The groups are unrelated because different participants take part in each condition.
The memory scores are treated as interval data.
A suitable test would therefore be:
$$\text{Unrelated }t\text{-test}$$
Explaining a statistical test choice
A complete explanation should normally include three features:
The purpose of the analysis.
The experimental design or relationship between scores.
The level of measurement.
For example:
The Mann-Whitney test is appropriate because the researcher is testing for a difference, the study uses unrelated groups, and the data are ordinal.
Naming the test without explaining these features may not fully answer the question.
Level of measurement is not the same as data type
Do not confuse level of measurement with the distinction between quantitative and qualitative data.
Quantitative data are numerical.
Qualitative data are expressed in words or other non-numerical forms.
Nominal data may involve words or numerical category codes. Ordinal and interval data may also be represented numerically.
The level of measurement concerns what the values mean and how they relate to one another.
Coding qualitative material
In a content analysis, qualitative material may be placed into behavioural or thematic categories.
The researcher may then count the frequency of each category.
The frequencies are numerical, but the categories themselves are usually nominal because they represent different types of content without a necessary order.
For example:
Coded category | Frequency |
Positive reference | \(12\) |
Negative reference | \(9\) |
Neutral reference | \(7\) |
The category labels are nominal, and the researcher has counted their frequencies.
Writing a strong examination answer
When asked to identify a level of measurement:
Name the level.
Refer directly to the data in the scenario.
Explain the defining feature.
For example:
The data are ordinal because the participants place the treatments in rank order. The ranks have a meaningful order, but the intervals between the ranks cannot be assumed to be equal.
For interval data:
The data are interval because response time is measured numerically in seconds, using equal units.
For nominal data:
The data are nominal because participants are placed into separate categories of correct or incorrect, with no meaningful numerical order.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Level of measurement | A classification describing what recorded data represent and how their values relate to one another. | You may identify the level and use it to help select a statistical test. |
Nominal data | Data consisting of separate, unordered categories. | You may identify nominal data from categories such as correct or incorrect. |
Ordinal data | Data that can be ranked or placed in order, but which do not necessarily have equal intervals. | You may identify ordinal data from ranks or ordered rating scales. |
Interval data | Numerical data measured using equal units or intervals. | You may identify interval data from measurements such as time in seconds. |
Category | A group into which a participant, response or behaviour is classified. | Unordered categories produce nominal data. |
Rank | A position within an ordered sequence. | Ranked results are ordinal because the positions are ordered. |
Equal interval | A consistent difference between adjacent values on a numerical scale. | Equal intervals are a defining feature of interval data. |
Frequency | The number of times a score, behaviour or category occurs. | Nominal categories may be summarised using frequencies. |
Operationalisation | The precise way in which a variable is defined and measured. | The operationalisation may determine the resulting level of measurement. |
Statistical test | A procedure used to analyse data and determine whether a result is statistically significant. | Level of measurement helps determine which test should be selected. |
Related data | Scores that are connected, such as scores from the same participants in two conditions. | Relatedness affects statistical test choice. |
Unrelated data | Scores obtained from different participants or independent groups. | Unrelated groups require different tests from related groups. |
Correlation | An investigation of the relationship between two co-variables. | The data level helps determine whether Spearman’s rho or Pearson’s \(r\) may be used. |
Test of difference | An analysis examining whether two conditions or groups differ. | The design and data level determine the appropriate difference test. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Assuming that all data represented by numbers are interval.
Why this is incorrect:
Numbers may be category codes or ranks rather than equal numerical measurements.
For example:
$$1=\text{secure attachment}$$
$$2=\text{insecure-avoidant attachment}$$
The numbers are labels, so the data remain nominal.
How to improve:
Ask what the numbers mean rather than looking only at how they are written.
Mistake: Describing ordered categories as nominal.
Why this is incorrect:
Categories such as low, moderate and high have a meaningful order.
How to improve:
Check whether the categories can be arranged from lower to higher. If they can, the data may be ordinal.
Mistake: Treating all rating scales as interval data.
Why this is incorrect:
An ordered rating scale does not automatically have equal intervals between response options.
How to improve:
If the values represent ordered subjective ratings and equal gaps cannot be assumed, identify the data as ordinal.
Mistake: Confusing the level of measurement with the research method.
Why this is incorrect:
Experiments, observations and questionnaires may produce different levels of measurement depending on what is recorded.
How to improve:
Identify the exact data collected rather than naming the research method.
Mistake: Identifying the level from the psychological topic alone.
Why this is incorrect:
The same concept can be measured using nominal, ordinal or interval data.
How to improve:
Examine how the variable has been operationalised.
Mistake: Saying that ordinal data have equal intervals.
Why this is incorrect:
Ordinal values show order, but equal distances between ranks or categories cannot be assumed.
How to improve:
Use the phrase:
The values can be ordered, but the intervals are not necessarily equal.
Mistake: Calculating a mean from nominal category codes.
Why this is incorrect:
Category codes do not represent measured quantities, so their total and average have no meaningful interpretation.
How to improve:
Use frequencies, percentages or the mode to summarise nominal categories.
Mistake: Selecting a statistical test using only the level of measurement.
Why this is incorrect:
Test choice also depends on the purpose of the investigation and whether the scores are related or unrelated.
How to improve:
Check three features:
Difference, association or correlation.
Related or unrelated scores.
Level of measurement.
Mistake: Naming a test without justifying the choice.
Why this is incorrect:
A question asking why a test is appropriate requires explanation using features of the study.
How to improve:
State the purpose, design and measurement level.
Mistake: Confusing Spearman’s rho and Pearson’s \(r\).
Why this is incorrect:
Both test for a correlation, but they are associated with different levels of measurement.
How to improve:
Remember:
$$\text{Ordinal correlation}\rightarrow\text{Spearman's rho}$$
$$\text{Interval correlation}\rightarrow\text{Pearson's }r$$
Exam-Style Questions ✍️
Question 1
Define nominal data.[2 marks]
Question 2
Explain one difference between ordinal and interval data.[2 marks]
Question 3
A researcher classifies each participant’s response as:
correct;
incorrect.
Identify the level of measurement. Explain your answer.[2 marks]
Question 4
Participants rank five revision strategies from most useful to least useful.
Identify the level of measurement produced by the ranking task. Explain your answer.[2 marks]
Question 5
A psychologist records the time taken by each participant to solve a problem, measured in seconds.
Identify the level of measurement. Explain your answer.[2 marks]
Question 6
A researcher measures stress in three different ways.
Measure A: Participants are classified as stressed or not stressed.
Measure B: Participants rate their stress as low, moderate or high.
Measure C: Participants receive a numerical score measured using equal units.
For each measure, identify the level of measurement and justify your answer.[6 marks]
Question 7
A student codes three types of observed behaviour as follows:
$$1=\text{cooperative}$$
$$2=\text{neutral}$$
$$3=\text{aggressive}$$
The student claims that the data are interval because numbers have been used.
Explain why the student is incorrect.[3 marks]
Question 8
A researcher investigates whether participants’ rank for daily stress is related to their rank for sleep quality.
a) Identify the level of measurement.[1 mark]
b) Identify an appropriate statistical test.[1 mark]
c) Explain why the test is appropriate.[3 marks]
Question 9
Two different groups complete a memory test. The researcher records each participant’s numerical memory score using equal units.
Identify an appropriate statistical test for comparing the two groups. Justify your answer using:
the purpose of the analysis;
the experimental design;
the level of measurement.
[4 marks]
Question 10
A psychologist records whether each participant shows an increase or decrease in anxiety after completing a relaxation activity. The same participants provide scores before and after the activity.
a) Identify the level of measurement used when responses are converted into increase or decrease categories.[1 mark]
b) Identify an appropriate statistical test.[1 mark]
c) Explain why the test is appropriate.[3 marks]
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