Choosing an inferential test | AQA A-Level Psychology Revision
- Revision Notes
- Aug 5
- 18 min read
Updated: 5 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 60 minutes
This Choosing an inferential test A-Level Psychology revision page explains how psychologists select an appropriate statistical test. You will learn to distinguish tests of difference, association and correlation before using the experimental design and level of measurement to make your final decision. Test selection is a step-by-step process, not a guessing game. It builds on levels of measurement and introduction to statistical testing, so check these topics if any of the terminology feels unfamiliar.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Distinguish tests of difference, association and correlation.
Use the research aim or hypothesis to identify the purpose of a statistical test.
Use experimental design to distinguish related from unrelated data.
Use the level of measurement to help select an appropriate test.
Select an appropriate inferential test from an unfamiliar research scenario.
Justify a test choice using the purpose, design and level of measurement.
Revision Notes 📚
Choosing an inferential test in A-Level Psychology
An inferential statistical test helps a researcher determine whether a result is statistically significant.
AQA requires students to know when to use:
the sign test;
Spearman’s rho;
Pearson’s \(r\);
the Wilcoxon test;
the Mann-Whitney test;
the related \(t\)-test;
the unrelated \(t\)-test;
the Chi-squared test.
The correct test depends on features of the investigation.
A useful summary is:
$$\text{Research purpose}+\text{experimental design}+\text{level of measurement}=\text{test choice}$$
The precise questions you need to ask depend on whether the investigation concerns a difference, correlation or association.
The three main decisions
When choosing an inferential test, work through three decisions.
Decision 1: What is the purpose of the analysis?
Is the researcher investigating:
a difference;
a correlation;
an association?
Decision 2: Are the data related or unrelated?
This is particularly important for a test of difference.
Related data come from:
repeated measures;
matched pairs.
Unrelated data usually come from:
independent groups.
Decision 3: What is the level of measurement?
Are the data:
nominal;
ordinal;
interval?
Do not select a test until you have considered all the relevant features of the study.
Overview of the test-selection process
Purpose | Design or data relationship | Level of measurement | Appropriate test |
Difference | Related | Nominal | Sign test |
Difference | Related | Ordinal | Wilcoxon test |
Difference | Unrelated | Ordinal | Mann-Whitney test |
Difference | Related | Interval | Related \(t\)-test |
Difference | Unrelated | Interval | Unrelated \(t\)-test |
Correlation | Paired scores | Ordinal | Spearman’s rho |
Correlation | Paired scores | Interval | Pearson’s \(r\) |
Association | Categorical frequencies | Nominal | Chi-squared test |
This table provides the central framework for the lesson. However, you must understand why each test fits its particular combination of features.
Step 1: Difference, correlation or association?
The first step is to identify what the researcher is trying to discover.
The wording of the aim or hypothesis will often provide the answer.
Test of difference
A test of difference investigates whether two conditions or groups produce different results.
Examples include:
whether memory scores differ between silence and background-noise conditions;
whether anxiety ratings differ before and after therapy;
whether two groups produce different concentration scores;
whether participants make fewer errors after training.
Words suggesting a test of difference include:
difference;
differs;
higher;
lower;
more;
fewer;
increase;
decrease;
effect.
For example:
There will be a difference in memory scores between participants tested in silence and participants tested with background noise.
This requires a test of difference because two conditions are being compared.
Test of correlation
A test of correlation investigates whether two measured co-variables are related.
Examples include:
hours of sleep and memory score;
stress rating and wellbeing rating;
age and reaction time;
revision time and examination performance.
Words suggesting a correlation include:
correlation;
relationship;
related;
co-variable;
increases as;
decreases as.
For example:
There will be a correlation between the number of hours students revise and their examination scores.
This requires a test of correlation because the researcher measures two co-variables for each participant.
The direction and strength of correlations are covered in scattergrams and correlation coefficients.
Test of association
A test of association investigates whether two categorical variables are associated.
The researcher records how frequently cases fall into different combinations of categories.
Examples include an association between:
treatment type and whether participants improve;
attachment classification and preferred coping strategy;
participant group and choice of response;
sleep category and whether a memory response is correct.
Words suggesting an association include:
association;
categorical variables;
frequencies;
categories;
observed frequency;
expected frequency.
For example:
There will be an association between treatment condition and whether participants show improvement.
Both variables contain categories:
treatment or no treatment;
improved or did not improve.
The appropriate test is Chi-squared.
Difference and correlation compared
Feature | Test of difference | Test of correlation |
Main question | Do two conditions or groups differ? | Are two co-variables related? |
Variables | Conditions or groups and an outcome measure | Two measured co-variables |
Typical wording | Higher, lower, difference, effect | Related, relationship, correlation |
Example | Silence compared with noise | Sleep related to memory |
Possible tests | Sign, Wilcoxon, Mann-Whitney or \(t\)-tests | Spearman’s rho or Pearson’s \(r\) |
Correlation and association compared
A correlation and an association both concern relationships, but they involve different forms of data.
Correlation
A correlation uses paired scores for two co-variables.
For example:
Participant | Hours of sleep | Memory score |
A | \(5\) | \(8\) |
B | \(6\) | \(11\) |
C | \(7\) | \(14\) |
Each participant provides two measured values.
Association
An association uses frequencies for combinations of categories.
For example:
Improved | Did not improve | |
Therapy | \(18\) | \(7\) |
No therapy | \(9\) | \(16\) |
The table shows how many participants fall into each combination of categories.
A quick purpose check
Ask:
Is the researcher comparing conditions, measuring two co-variables or counting combinations of categories?
Comparing conditions means a test of difference.
Measuring two co-variables means a test of correlation.
Counting combinations of categories means a test of association.
Step 2: Experimental design
Once you identify a test of difference, determine whether the data are related or unrelated.
This decision depends on the experimental design.
The three experimental designs are covered in experimental designs.
Related data
Related data contain scores that are meaningfully paired.
Related scores are produced by:
repeated measures designs;
matched pairs designs.
Repeated measures
In a repeated measures design, the same participants take part in both conditions.
For example, each participant completes a memory test:
once in silence;
once with background noise.
Each participant’s score in one condition is paired with their own score in the other condition.
The scores are therefore related.
Matched pairs
In a matched pairs design, each participant in one condition is matched with a similar participant in another condition.
Participants might be matched according to:
age;
initial ability;
a previous test score;
another relevant characteristic.
Each matched pair produces two related scores.
Unrelated data
Unrelated data come from participants or cases that are not meaningfully paired.
An independent groups design normally produces unrelated data.
For example:
Group A completes a memory task in silence.
Group B completes the task with background noise.
The participants in Group A are different from those in Group B, and no participant is directly paired with a participant in the other condition.
The scores are therefore unrelated.
Related and unrelated data compared
Feature | Related data | Unrelated data |
Repeated measures | Yes | No |
Matched pairs | Yes | No |
Independent groups | No | Yes |
Link between scores | Each score has a corresponding paired score | Scores are independent |
Example | Before and after scores from the same participants | Scores from two separate groups |
Experimental design and test choice
For ordinal tests of difference:
related data require Wilcoxon;
unrelated data require Mann-Whitney.
For interval tests of difference:
related data require the related \(t\)-test;
unrelated data require the unrelated \(t\)-test.
For nominal related data:
the sign test is used.
The importance of related scores in the sign test is explained in the sign test.
Identifying related data from a scenario
Look for phrases such as:
the same participants;
before and after;
each participant completed both conditions;
participants were matched;
each participant was paired with another participant.
These suggest related data.
Identifying unrelated data from a scenario
Look for phrases such as:
separate groups;
different participants;
one group completed Condition A and another completed Condition B;
participants were randomly allocated to one condition only;
independent groups.
These suggest unrelated data.
Step 3: Level of measurement
The level of measurement is the final major factor in selecting a test.
The three levels are:
nominal;
ordinal;
interval.
Nominal data
Nominal data consist of separate categories without a meaningful numerical order.
Examples include:
correct or incorrect;
obeyed or did not obey;
improved or did not improve;
attachment classification;
treatment group.
Nominal data may be represented by category names or number codes.
For example:
$$1=\text{obeyed}$$
$$2=\text{did not obey}$$
These data remain nominal because the numbers are labels rather than measurements.
Nominal data are used in:
the sign test;
Chi-squared.
Ordinal data
Ordinal data can be placed into a meaningful order, but the intervals between values cannot be assumed to be equal.
Examples include:
ranks;
ratings;
ordered categories;
positions;
Likert-type responses.
For example:
$$1=\text{strongly disagree}$$
$$2=\text{disagree}$$
$$3=\text{neither agree nor disagree}$$
$$4=\text{agree}$$
$$5=\text{strongly agree}$$
The responses are ordered, but the psychological difference between adjacent ratings is not necessarily equal.
Ordinal data are used in:
Spearman’s rho;
Wilcoxon;
Mann-Whitney.
Interval data
Interval data consist of numerical measurements with equal intervals between values.
Examples include:
time measured in seconds;
distance measured in centimetres;
numerical test scores recorded using equal units;
number of words recalled.
For example, the difference between:
$$12\text{ seconds and }13\text{ seconds}$$
is the same size as the difference between:
$$18\text{ seconds and }19\text{ seconds}$$
Interval data are used in:
Pearson’s \(r\);
the related \(t\)-test;
the unrelated \(t\)-test.
Summary of levels and tests
Level of measurement | Difference tests | Correlation or association test |
Nominal | Sign test for related data | Chi-squared for association |
Ordinal | Wilcoxon for related data or Mann-Whitney for unrelated data | Spearman’s rho |
Interval | Related or unrelated \(t\)-test | Pearson’s \(r\) |
Identifying the level from operationalisation
The level of measurement depends on how a variable has been operationalised.
For example, anxiety could be measured as:
Nominal data
Participants are classified as:
anxious;
not anxious.
Ordinal data
Participants rate anxiety as:
low;
moderate;
high.
Interval data
Participants receive a numerical score measured using equal units.
Do not choose the level from the psychological concept itself. Identify exactly what the researcher records.
Selecting the sign test
The sign test is appropriate when:
The researcher is testing for a difference.
The data are related.
The paired differences are converted into nominal signs.
A useful summary is:
$$\text{Difference}+\text{related}+\text{nominal}=\text{Sign test}$$
Worked example: sign test
A psychologist records whether each participant’s anxiety score:
increases;
decreases;
remains the same after relaxation training.
The same participants provide scores before and after training.
The sign test is appropriate because:
the study investigates a difference;
the scores are related through repeated measures;
each difference is converted into a nominal sign.
The researcher would calculate the test using positive and negative signs.
Selecting Spearman’s rho
Spearman’s rho is appropriate when:
The researcher is testing for a correlation.
The co-variables produce ordinal data.
A useful summary is:
$$\text{Correlation}+\text{ordinal}=\text{Spearman's rho}$$
Worked example: Spearman’s rho
A psychologist investigates whether participants’ rank for stress is related to their rank for sleep quality.
Spearman’s rho is appropriate because:
the study investigates a correlation;
both co-variables are measured using ranks;
ranks are ordinal data.
The use of Spearman’s rho is covered in Spearman’s rho and Pearson’s r.
Selecting Pearson’s \(r\)
Pearson’s \(r\) is appropriate when:
The researcher is testing for a correlation.
The co-variables produce interval data.
A useful summary is:
$$\text{Correlation}+\text{interval}=\text{Pearson's }r$$
Worked example: Pearson’s \(r\)
A researcher investigates the relationship between:
hours of sleep;
numerical memory scores measured in equal units.
Pearson’s \(r\) is appropriate because:
the study investigates a correlation;
both co-variables produce interval data.
Spearman’s rho and Pearson’s \(r\) compared
Feature | Spearman’s rho | Pearson’s \(r\) |
Purpose | Correlation | Correlation |
Experimental design decision | Not used as a difference-test design decision | Not used as a difference-test design decision |
Level of measurement | Ordinal | Interval |
Example | Ranked stress and ranked sleep quality | Hours of sleep and numerical memory score |
The main distinction is the level of measurement.
Selecting the Wilcoxon test
The Wilcoxon test is appropriate when:
The researcher is testing for a difference.
The data are related.
The data are ordinal.
A useful summary is:
$$\text{Difference}+\text{related}+\text{ordinal}=\text{Wilcoxon}$$
Worked example: Wilcoxon
Participants rate their anxiety from \(1\) to \(5\):
before a relaxation activity;
after the activity.
Wilcoxon is appropriate because:
the study investigates a difference;
the same participants provide both sets of ratings;
the ordered ratings are ordinal data.
Selecting the Mann-Whitney test
The Mann-Whitney test is appropriate when:
The researcher is testing for a difference.
The data are unrelated.
The data are ordinal.
A useful summary is:
$$\text{Difference}+\text{unrelated}+\text{ordinal}=\text{Mann-Whitney}$$
Worked example: Mann-Whitney
One group of participants rates anxiety after Treatment A. A different group rates anxiety after Treatment B.
The ratings are collected using an ordered scale.
Mann-Whitney is appropriate because:
the study investigates a difference;
different participants take part in the two conditions;
the ratings are ordinal.
The distinction between these two tests is developed in Wilcoxon and Mann-Whitney tests.
Wilcoxon and Mann-Whitney compared
Feature | Wilcoxon | Mann-Whitney |
Purpose | Difference | Difference |
Level of measurement | Ordinal | Ordinal |
Data relationship | Related | Unrelated |
Possible design | Repeated measures or matched pairs | Independent groups |
The experimental design determines which of the two ordinal difference tests is selected.
Selecting the related \(t\)-test
The related \(t\)-test is appropriate when:
The researcher is testing for a difference.
The data are related.
The data are interval.
A useful summary is:
$$\text{Difference}+\text{related}+\text{interval}=\text{Related }t\text{-test}$$
Worked example: related \(t\)-test
A psychologist records each participant’s time to complete a task:
before training;
after training.
Time is measured in seconds.
The related \(t\)-test is appropriate because:
the study investigates a difference;
the same participants provide both scores;
time in seconds produces interval data.
Selecting the unrelated \(t\)-test
The unrelated \(t\)-test is appropriate when:
The researcher is testing for a difference.
The data are unrelated.
The data are interval.
A useful summary is:
$$\text{Difference}+\text{unrelated}+\text{interval}=\text{Unrelated }t\text{-test}$$
Worked example: unrelated \(t\)-test
One group completes a reaction-time task after sleep deprivation. A different group completes the task after a normal night’s sleep.
Reaction time is measured in milliseconds.
The unrelated \(t\)-test is appropriate because:
the study investigates a difference;
different participants take part in the two conditions;
reaction time is measured using equal numerical units.
The distinction between these tests is covered in related and unrelated t-tests.
Related and unrelated \(t\)-tests compared
Feature | Related \(t\)-test | Unrelated \(t\)-test |
Purpose | Difference | Difference |
Level of measurement | Interval | Interval |
Data relationship | Related | Unrelated |
Possible design | Repeated measures or matched pairs | Independent groups |
Selecting the Chi-squared test
The Chi-squared test is appropriate when:
The researcher is testing for an association.
The variables are categorical.
The data consist of nominal frequencies.
A useful summary is:
$$\text{Association}+\text{nominal frequencies}=\text{Chi-squared}$$
Worked example: Chi-squared
A psychologist investigates whether treatment condition is associated with improvement.
The categories are:
Treatment A or Treatment B;
improved or did not improve.
The researcher counts how many participants fall into each combination of categories.
Chi-squared is appropriate because:
the study investigates an association;
both variables are categorical;
the results are nominal frequency data.
The calculation and interpretation of this test are covered in Chi-squared test.
Chi-squared and the sign test compared
Both tests use nominal data, but they have different purposes.
Feature | Sign test | Chi-squared |
Purpose | Difference | Association |
Data | Positive and negative signs | Frequencies in categorical combinations |
Relationship | Related paired data | Categorical frequency data |
Example | Increase or decrease after treatment | Treatment type associated with improvement |
Do not choose a test from the level of measurement alone. Both tests involve nominal data, but the research purpose is different.
Complete test-selection table
Test | Difference, association or correlation? | Related or unrelated? | Level of measurement |
Sign test | Difference | Related | Nominal |
Spearman’s rho | Correlation | Paired co-variable scores | Ordinal |
Pearson’s \(r\) | Correlation | Paired co-variable scores | Interval |
Wilcoxon | Difference | Related | Ordinal |
Mann-Whitney | Difference | Unrelated | Ordinal |
Related \(t\)-test | Difference | Related | Interval |
Unrelated \(t\)-test | Difference | Unrelated | Interval |
Chi-squared | Association | Categorical frequency data | Nominal |
The decision tree
Use this sequence in an examination.
Question 1: Is the study testing a difference?
If yes, ask whether the data are related or unrelated.
Related nominal data
$$\text{Sign test}$$
Related ordinal data
$$\text{Wilcoxon}$$
Related interval data
$$\text{Related }t\text{-test}$$
Unrelated ordinal data
$$\text{Mann-Whitney}$$
Unrelated interval data
$$\text{Unrelated }t\text{-test}$$
Question 2: Is the study testing a correlation?
If yes, identify the level of measurement.
Ordinal data
$$\text{Spearman's rho}$$
Interval data
$$\text{Pearson's }r$$
Question 3: Is the study testing an association?
If the data are nominal category frequencies:
$$\text{Chi-squared}$$
Worked selection example 1
A psychologist investigates whether there is a relationship between participants’ ranked anxiety and ranked self-esteem scores.
Purpose
The study investigates a relationship between two co-variables:
$$\text{Correlation}$$
Level of measurement
Both variables are ranks:
$$\text{Ordinal}$$
Test
$$\boxed{\text{Spearman's rho}}$$
Worked selection example 2
A researcher compares numerical memory scores before and after a revision programme. The same participants complete both tests.
Purpose
Two conditions are compared:
$$\text{Difference}$$
Design
The same participants complete both conditions:
$$\text{Related}$$
Level of measurement
Memory scores are measured using equal numerical units:
$$\text{Interval}$$
Test
$$\boxed{\text{Related }t\text{-test}}$$
Worked selection example 3
Two separate groups rate the usefulness of different therapies using an ordered scale.
Purpose
Two groups are compared:
$$\text{Difference}$$
Design
Different participants are used:
$$\text{Unrelated}$$
Level of measurement
The responses are ordered ratings:
$$\text{Ordinal}$$
Test
$$\boxed{\text{Mann-Whitney}}$$
Worked selection example 4
A researcher records whether participants in two treatment conditions improve or do not improve.
Purpose
The researcher investigates whether treatment condition is associated with improvement:
$$\text{Association}$$
Level of measurement
Both variables consist of categories:
$$\text{Nominal}$$
Test
$$\boxed{\text{Chi-squared}}$$
Worked selection example 5
A psychologist compares anxiety ratings before and after relaxation. The same participants rate anxiety as low, moderate or high.
Purpose
The study compares anxiety before and after relaxation:
$$\text{Difference}$$
Design
The same participants provide both responses:
$$\text{Related}$$
Level of measurement
Low, moderate and high are ordered categories:
$$\text{Ordinal}$$
Test
$$\boxed{\text{Wilcoxon}}$$
Worked selection example 6
A researcher investigates whether the number of hours slept is related to response time measured in milliseconds.
Purpose
Two measured co-variables are being related:
$$\text{Correlation}$$
Level of measurement
Both variables are measured using numerical units:
$$\text{Interval}$$
Test
$$\boxed{\text{Pearson's }r}$$
Writing a complete justification
A question may ask you to identify and justify an inferential test.
A strong justification should name every relevant feature.
For a test of difference, include:
The purpose of the analysis.
Whether the data are related or unrelated.
The level of measurement.
For example:
The Wilcoxon test is appropriate because the researcher is testing for a difference, the same participants provide scores in both conditions so the data are related, and the rating-scale data are ordinal.
For a correlation, include:
The study investigates a correlation.
The level of measurement.
For example:
Spearman’s rho is appropriate because the researcher is testing for a correlation between two co-variables and both variables have been measured using ordinal ranks.
For an association:
Chi-squared is appropriate because the researcher is testing for an association between two categorical variables and the data consist of nominal frequencies.
Why naming the test is not enough
An answer such as:
Use Mann-Whitney.
may earn credit for identifying the correct test, but it does not show why the test is appropriate.
A complete response should explain:
that the study tests a difference;
that the groups are unrelated;
that the data are ordinal.
This demonstrates understanding rather than recall alone.
Selecting from the name of the design
Do not assume that repeated measures always means Wilcoxon.
Repeated measures tells you that the data are related, but you must still identify the level of measurement.
For repeated measures:
nominal data suggest the sign test;
ordinal data suggest Wilcoxon;
interval data suggest the related \(t\)-test.
Similarly, independent groups do not automatically mean Mann-Whitney.
For independent groups:
ordinal data suggest Mann-Whitney;
interval data suggest the unrelated \(t\)-test.
Selecting from the level alone
Do not assume that ordinal data always mean Spearman’s rho.
Ordinal data could require:
Spearman’s rho for a correlation;
Wilcoxon for a related difference;
Mann-Whitney for an unrelated difference.
Do not assume that interval data always mean Pearson’s \(r\).
Interval data could require:
Pearson’s \(r\) for a correlation;
a related \(t\)-test for a related difference;
an unrelated \(t\)-test for an unrelated difference.
The research purpose must be identified first.
Hypothesis wording and test choice
The hypothesis can reveal the purpose of the test.
Difference hypothesis
There will be a difference in concentration scores between Condition A and Condition B.
This requires a difference test.
Correlational hypothesis
There will be a correlation between stress ratings and hours of sleep.
This requires a correlation test.
Association hypothesis
There will be an association between treatment group and whether symptoms improve.
This requires an association test.
The hypothesis does not usually provide all the information needed. You must still examine the design and level of measurement.
Test selection and statistical significance
Selecting the correct test is necessary before the researcher can:
calculate an observed value;
use the appropriate statistical table;
identify the correct critical value;
determine statistical significance;
reject or retain the null hypothesis.
Using the wrong test could produce an invalid statistical conclusion.
After selecting the test, the researcher applies the relevant significance rule covered in probability and significance.
A complete exam checklist
Before selecting a test, ask:
Research purpose
Is the researcher testing a difference?
Is the researcher testing a correlation?
Is the researcher testing an association?
Design
For a difference:
Did the same participants take part in both conditions?
Were participants matched?
Were separate groups used?
Are the scores related or unrelated?
Level of measurement
Are the data unordered categories?
Are the values ranks or ordered ratings?
Are the values numerical measurements with equal intervals?
Final selection
Have I matched the purpose, design and level to the correct test?
Can I justify every part of the choice using the scenario?
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Inferential statistical test | A procedure used to determine whether a research result is statistically significant. | You may need to select and justify an appropriate test. |
Test of difference | A test examining whether two conditions or groups produce different results. | Sign, Wilcoxon, Mann-Whitney and \(t\)-tests are tests of difference. |
Test of correlation | A test examining whether two measured co-variables are related. | Spearman’s rho and Pearson’s \(r\) are tests of correlation. |
Test of association | A test examining whether two categorical variables are associated. | Chi-squared is used for an association between nominal variables. |
Related data | Scores that are meaningfully paired through repeated measures or matched pairs. | Relatedness helps distinguish Wilcoxon from Mann-Whitney and the two \(t\)-tests. |
Unrelated data | Scores obtained from independent participants or groups. | Unrelated ordinal data suggest Mann-Whitney. |
Repeated measures | A design in which the same participants take part in every condition. | It produces related data. |
Matched pairs | A design in which participants are paired according to relevant characteristics. | It also produces related data. |
Independent groups | A design in which different participants take part in each condition. | It produces unrelated data. |
Nominal data | Data consisting of separate categories without a meaningful order. | Nominal data may indicate the sign test or Chi-squared. |
Ordinal data | Data that can be ranked or ordered but do not necessarily have equal intervals. | Ordinal data may indicate Spearman’s rho, Wilcoxon or Mann-Whitney. |
Interval data | Numerical data measured using equal units or intervals. | Interval data may indicate Pearson’s \(r\) or a \(t\)-test. |
Co-variable | One of the two measured variables in a correlational investigation. | The level of the co-variables determines the correlation test. |
Frequency | The number of times a category or result occurs. | Chi-squared uses frequencies within combinations of categories. |
Operationalisation | The precise way in which a variable is defined and measured. | It helps determine the level of measurement. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Selecting a test before identifying the research purpose.
Why this is incorrect:
The same level of measurement may be used with several different tests.
For example, ordinal data could require Spearman’s rho, Wilcoxon or Mann-Whitney.
How to improve:
Decide whether the study concerns a difference, correlation or association before examining the design and data level.
Mistake: Assuming that any relationship requires a correlation test.
Why this is incorrect:
A relationship between categorical variables is an association rather than a correlation between measured co-variables.
How to improve:
Check whether the data consist of paired scores or frequencies within categories.
Mistake: Confusing an association with a difference.
Why this is incorrect:
A test of difference compares scores from conditions or groups. An association examines whether categorical variables are linked.
How to improve:
Look for a table containing combinations of categories and their frequencies. This may indicate Chi-squared.
Mistake: Ignoring the experimental design.
Why this is incorrect:
Wilcoxon and Mann-Whitney both use ordinal data, but one requires related scores and the other requires unrelated scores.
How to improve:
Identify whether the same, matched or different participants produced the scores.
Mistake: Treating matched-pairs data as unrelated.
Why this is incorrect:
Each participant is deliberately paired with another participant, creating a relationship between their scores.
How to improve:
Classify both repeated measures and matched pairs as related data.
Mistake: Treating independent-groups data as related.
Why this is incorrect:
The scores come from separate participants with no direct pairing.
How to improve:
Classify independent groups as unrelated data.
Mistake: Assuming that all numbered data are interval.
Why this is incorrect:
Numbers may represent category codes or ordinal ratings.
For example:
$$1=\text{strongly disagree}$$
and:
$$5=\text{strongly agree}$$
produce ordered ratings rather than automatically becoming interval measurements.
How to improve:
Ask what the numbers represent and whether the intervals are equal.
Mistake: Selecting Spearman’s rho whenever the data are ordinal.
Why this is incorrect:
Spearman’s rho is specifically a test of correlation.
Ordinal tests of difference require Wilcoxon or Mann-Whitney.
How to improve:
Identify the research purpose before using the level of measurement.
Mistake: Selecting Pearson’s \(r\) whenever the data are interval.
Why this is incorrect:
Pearson’s \(r\) is a correlation test. Interval tests of difference use a related or unrelated \(t\)-test.
How to improve:
Check whether the researcher is relating two co-variables or comparing conditions.
Mistake: Reversing Wilcoxon and Mann-Whitney.
Why this is incorrect:
Wilcoxon requires related ordinal data, while Mann-Whitney requires unrelated ordinal data.
How to improve:
Remember:
$$\text{Wilcoxon}=\text{Related ordinal difference}$$
$$\text{Mann-Whitney}=\text{Unrelated ordinal difference}$$
Mistake: Reversing the related and unrelated \(t\)-tests.
Why this is incorrect:
The name of the test describes the relationship between the two sets of scores.
How to improve:
Remember:
$$\text{Related data}\rightarrow\text{Related }t\text{-test}$$
$$\text{Unrelated data}\rightarrow\text{Unrelated }t\text{-test}$$
Mistake: Selecting Chi-squared only because the results are frequencies.
Why this is incorrect:
Chi-squared is used to test an association between categorical variables. Frequencies may also appear in other descriptive displays.
How to improve:
Confirm that the researcher is investigating whether two nominal categorical variables are associated.
Mistake: Giving only the name of the test when asked to justify the choice.
Why this is incorrect:
A justification requires the features that make the test appropriate.
How to improve:
Include:
difference, correlation or association;
related or unrelated data where relevant;
nominal, ordinal or interval measurement.
Exam-Style Questions ✍️
Question 1
State the three main factors that may be used to select an inferential statistical test.[3 marks]
Question 2
Explain one difference between:
a) a test of difference;[2 marks]
b) a test of correlation.[2 marks]
Question 3
A researcher investigates whether participants’ ranked stress scores are related to their ranked sleep-quality scores.
Identify an appropriate statistical test. Explain your answer.[3 marks]
Question 4
The same participants complete a memory test before and after a revision programme. The researcher records the number of words correctly recalled.
Identify an appropriate statistical test. Justify your answer using:
the purpose of the study;
the experimental design;
the level of measurement.
[4 marks]
Question 5
One group rates anxiety after Treatment A. A separate group rates anxiety after Treatment B. Anxiety is rated on an ordered scale from low to high.
Identify an appropriate statistical test. Explain your answer.[4 marks]
Question 6
A researcher records whether each participant’s anxiety score increases or decreases after a relaxation activity. The same participants provide scores before and after the activity.
Identify an appropriate statistical test. Explain your answer.[4 marks]
Question 7
A psychologist investigates whether hours of sleep are related to response time measured in milliseconds.
Identify an appropriate statistical test. Explain your answer.[3 marks]
Question 8
A researcher records whether participants:
received therapy or did not receive therapy;
improved or did not improve.
The researcher wants to investigate whether treatment condition is associated with improvement.
Identify an appropriate statistical test. Explain your answer.[3 marks]
Question 9
For each investigation, identify the appropriate statistical test.
a) A difference between related ordinal ratings.[1 mark]
b) A correlation between two interval co-variables.[1 mark]
c) A difference between unrelated interval scores.[1 mark]
d) An association between two nominal variables.[1 mark]
e) A correlation between two ordinal co-variables.[1 mark]
f) A difference between related nominal signs.[1 mark]
Question 10
A student selects Spearman’s rho for a study comparing the ordinal anxiety ratings of two independent groups.
Explain why Spearman’s rho is not appropriate and identify the correct statistical test.[4 marks]
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