Spearman’s rho and Pearson’s r | AQA A-Level Psychology Revision

For 7182 specification, first teach in September 2025

AQA A-Level Psychology | Free Revision Notes

Estimated study time: 55 minutes

This Spearman’s rho and Pearson’s r A-Level Psychology revision page explains how psychologists select an appropriate inferential test for a correlation. You will learn that Spearman’s rho is used with ordinal data, while Pearson’s \(r\) is used with interval data. Both tests produce a correlation coefficient showing the direction and strength of a relationship. This lesson builds on scattergrams and correlation coefficients and choosing an inferential test.

Learning Objectives 🎯

By the end of this revision page, you should be able to:

• Identify when Spearman’s rho should be used.

• Identify when Pearson’s \(r\) should be used.

• Explain why both tests are tests of correlation.

• Distinguish ordinal from interval co-variable data.

• Compare the similarities and differences between the two tests.

• Select and justify the correct test in an unfamiliar research scenario.

Revision Notes 📚

Spearman’s rho and Pearson’s \(r\) in A-Level Psychology

Spearman’s rho and Pearson’s \(r\) are inferential statistical tests used to investigate a correlation.

A correlation examines whether two measured co-variables are related.

Examples include possible relationships between:

• hours of sleep and memory performance;

• stress ratings and wellbeing ratings;

• revision time and examination score;

• age and response time;

• ranks for anxiety and ranks for confidence.

Both tests produce a correlation coefficient. This coefficient describes:

• the direction of the relationship;

• the strength of the relationship.

The important difference between the tests is the level of measurement of the data.

A useful summary is:

$$\text{Correlation}+\text{ordinal data}=\text{Spearman's rho}$$

$$\text{Correlation}+\text{interval data}=\text{Pearson's }r$$

Both tests investigate correlations

Before selecting either test, establish that the researcher is investigating a relationship between two co-variables.

A correlational hypothesis might state:

There will be a correlation between participants’ stress ratings and their sleep-quality ratings.

The researcher does not compare separate conditions or groups. Instead, each participant provides one score for each co-variable.

For example:

Participant	Stress score	Sleep-quality score
A	\(8\)	\(3\)
B	\(6\)	\(5\)
C	\(4\)	\(7\)
D	\(2\)	\(9\)

Participant A provides the paired scores:

$$(8,3)$$

Participant B provides:

$$(6,5)$$

Each participant or case must provide a value for both co-variables.

Correlation is not a test of difference

Spearman’s rho and Pearson’s \(r\) are not used to compare:

• two experimental conditions;

• two groups of participants;

• scores before and after an intervention;

• treatment and control groups.

These situations require tests of difference.

For example:

Is there a difference in memory scores before and after a revision programme?

This is a test of difference, not a correlation. Neither Spearman’s rho nor Pearson’s \(r\) would be suitable.

Correlation is not an association between categories

Spearman’s rho and Pearson’s \(r\) are also different from the Chi-squared test.

A correlation uses paired scores for two co-variables.

An association uses frequencies showing how cases fall into combinations of categories.

For example:

Is treatment type associated with whether participants improve?

This concerns an association between nominal categories and would require Chi-squared rather than a correlation test.

Paired co-variable scores

In a correlation, every participant or case provides two scores.

For example:

Participant	Hours of sleep	Memory score
A	\(5\)	\(8\)
B	\(6\)	\(11\)
C	\(7\)	\(13\)
D	\(8\)	\(16\)

The paired values are:

$$(5,8)$$

$$(6,11)$$

$$(7,13)$$

$$(8,16)$$

The test analyses whether a consistent relationship exists across these pairs.

Do not confuse paired co-variable scores with a repeated measures design. A correlation measures two co-variables rather than comparing two experimental conditions.

Choosing between the two tests

Once you have established that the study investigates a correlation, identify the level of measurement.

Ask:

Are the co-variables ordinal or interval?

• Ordinal data indicate Spearman’s rho.

• Interval data indicate Pearson’s \(r\).

Your understanding of nominal, ordinal and interval data can be reviewed in levels of measurement.

Spearman’s rho

When should Spearman’s rho be used?

Spearman’s rho is used when:

1. The researcher is testing for a correlation.

2. The two co-variables produce ordinal data.

A useful selection rule is:

$$\text{Correlation}+\text{ordinal data}=\text{Spearman's rho}$$

Spearman’s rho is commonly represented by:

$$r_s$$

The subscript distinguishes it from Pearson’s \(r\).

Ordinal data

Ordinal data can be placed into a meaningful order, but the intervals between adjacent values cannot be assumed to be equal.

Examples include:

• ranks;

• ordered ratings;

• positions;

• Likert-type responses;

• categories such as low, moderate and high.

Suppose participants rank five activities from most stressful to least stressful.

The ranks might be:

$$1,\ 2,\ 3,\ 4,\ 5$$

The values have a meaningful order, but the difference between ranks:

$$1\text{ and }2$$

is not necessarily equal to the difference between:

$$4\text{ and }5$$

The data are ordinal.

Worked example: ranked co-variables

A psychologist investigates whether participants’ rank for examination stress is related to their rank for hours of sleep.

The data are:

Participant	Stress rank	Sleep rank
A	\(1\)	\(6\)
B	\(2\)	\(5\)
C	\(3\)	\(4\)
D	\(4\)	\(3\)
E	\(5\)	\(2\)
F	\(6\)	\(1\)

The researcher is investigating a correlation.

Both co-variables are expressed as ranks, so the data are ordinal.

The appropriate test is:

$$\boxed{\text{Spearman's rho}}$$

A complete justification would be:

Spearman’s rho is appropriate because the researcher is investigating a correlation between two co-variables and both co-variables are measured using ordinal ranks.

Ordered rating scales

Spearman’s rho may also be appropriate when both co-variables are measured using ordered rating scales.

For example, participants might rate:

• anxiety from very low to very high;

• confidence from very low to very high.

The ratings are ordered, but equal intervals between adjacent ratings cannot be assumed.

The data are therefore ordinal.

Worked example: rating scales

A researcher asks participants to rate:

• their current stress from \(1\) to \(5\);

• their sleep quality from \(1\) to \(5\).

The researcher wants to find out whether the two ratings are correlated.

The purpose is:

$$\text{Correlation}$$

The level of measurement is:

$$\text{Ordinal}$$

The appropriate test is:

$$\boxed{\text{Spearman's rho}}$$

Spearman’s rho and original score data

A question may state that scores have been converted into ranks.

For example, a researcher might record numerical test scores and then rank the participants from highest to lowest on both co-variables.

Once the analysis uses ranked positions, the data entered into the test are ordinal.

Spearman’s rho would therefore be appropriate.

Interpreting a Spearman’s rho coefficient

A Spearman’s rho coefficient lies between:

$$-1\leq r_s\leq+1$$

A positive value indicates a positive correlation.

For example:

$$r_s=+0.78$$

indicates a strong positive correlation.

A negative value indicates a negative correlation.

For example:

$$r_s=-0.81$$

indicates a strong negative correlation.

A value close to zero indicates a weak or absent correlation.

For example:

$$r_s=+0.06$$

indicates little or no consistent positive relationship.

Spearman’s rho does not show causation

A statistically significant Spearman’s rho result shows that two ordinal co-variables are related.

It does not demonstrate that one co-variable caused the other.

For example, a significant negative correlation between stress rank and sleep-quality rank does not show that stress definitely caused poorer sleep.

Another variable could influence both.

Pearson’s \(r\)

When should Pearson’s \(r\) be used?

Pearson’s \(r\) is used when:

1. The researcher is testing for a correlation.

2. The two co-variables produce interval data.

A useful selection rule is:

$$\text{Correlation}+\text{interval data}=\text{Pearson's }r$$

Pearson’s test is commonly represented by:

$$r$$

Interval data

Interval data consist of numerical measurements with equal intervals between values.

Examples include:

• response time measured in seconds or milliseconds;

• duration measured in minutes;

• distance measured in centimetres;

• numerical performance scores measured using equal units;

• the number of words recalled.

For interval data, equal numerical differences have a consistent meaning.

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.

Worked example: sleep and memory

A psychologist investigates whether hours of sleep are related to the number of words correctly recalled.

Participant	Hours of sleep	Words recalled
A	\(4.5\)	\(7\)
B	\(5.0\)	\(9\)
C	\(6.0\)	\(12\)
D	\(7.0\)	\(14\)
E	\(8.0\)	\(17\)

The researcher is investigating a correlation between two measured co-variables.

Hours of sleep and the number of words recalled are numerical data measured using consistent units.

The appropriate test is:

$$\boxed{\text{Pearson's }r}$$

A complete justification would be:

Pearson’s \(r\) is appropriate because the researcher is investigating a correlation between two co-variables and both variables produce interval data.

Worked example: two time measurements

A researcher investigates whether the time participants spend revising is related to the time they take to complete a test.

Both co-variables are measured in minutes.

The purpose is:

$$\text{Correlation}$$

The level of measurement is:

$$\text{Interval}$$

The appropriate test is:

$$\boxed{\text{Pearson's }r}$$

Numerical scores and Pearson’s \(r\)

A research scenario may use numerical scores rather than direct physical measurements.

For example, a researcher could correlate:

• numerical scores on a memory task;

• numerical scores on a concentration task.

Where these scores are treated as having equal units, Pearson’s \(r\) is the appropriate test.

Always use the information given in the question to determine the level of measurement.

Interpreting a Pearson’s \(r\) coefficient

A Pearson’s \(r\) coefficient lies between:

$$-1\leq r\leq+1$$

For example:

$$r=+0.91$$

indicates a very strong positive correlation.

$$r=-0.73$$

indicates a strong negative correlation.

$$r=0.04$$

indicates little or no consistent relationship.

As with Spearman’s rho:

• the sign shows direction;

• the distance from zero shows strength.

Pearson’s \(r\) does not show causation

A Pearson’s \(r\) result describes a relationship between interval co-variables.

It does not show that one co-variable caused changes in the other.

For example, a significant positive correlation between sleep duration and memory score does not prove that additional sleep caused better memory performance.

The limitations of causal conclusions are covered in correlations.

Comparing Spearman’s rho and Pearson’s \(r\)

Similarities

Spearman’s rho and Pearson’s \(r\) are similar because both:

• are inferential statistical tests;

• test for a correlation;

• use paired scores from two co-variables;

• produce a correlation coefficient;

• show the direction of a relationship;

• show the strength of a relationship;

• produce values between \(-1\) and \(+1\);

• may be interpreted using statistical tables and critical values;

• cannot demonstrate causation.

Differences

The main difference is the level of measurement.

Feature	Spearman’s rho	Pearson’s \(r\)
Purpose	Correlation	Correlation
Required level of measurement	Ordinal	Interval
Typical data	Ranks or ordered ratings	Numerical measurements using equal units
Symbol	\(r_s\)	\(r\)
Example	Stress rank and sleep-quality rank	Hours of sleep and memory score

The most important distinction

Remember:

$$\text{Spearman's rho}=\text{Ordinal correlation}$$

$$\text{Pearson's }r=\text{Interval correlation}$$

Both tests investigate a correlation. The level of measurement determines which one should be selected.

Identifying the purpose first

Do not choose Spearman’s rho simply because a study contains ordinal data.

Ordinal data could also require:

• Wilcoxon for a related test of difference;

• Mann-Whitney for an unrelated test of difference.

Similarly, interval data could require:

• a related \(t\)-test;

• an unrelated \(t\)-test;

• Pearson’s \(r\).

The research purpose must be identified before the level of measurement is used.

A complete selection process

Use the following steps.

Step 1: Is the research investigating a correlation?

Look for:

• two measured co-variables;

• paired scores for each participant;

• words such as relationship, related or correlation.

If the researcher is comparing conditions, neither test is appropriate.

Step 2: Identify the level of measurement

Ask whether the co-variable data are:

• ordinal;

• interval.

Step 3: Select the test

For ordinal data:

$$\text{Spearman's rho}$$

For interval data:

$$\text{Pearson's }r$$

Step 4: Justify the choice

Name:

• the purpose of the analysis;

• the level of measurement.

Worked selection example 1

A psychologist investigates whether participants’ ranked preference for social activities is related to their ranked wellbeing.

Purpose

$$\text{Correlation}$$

Level of measurement

$$\text{Ordinal}$$

Test

$$\boxed{\text{Spearman's rho}}$$

Worked selection example 2

A researcher investigates whether the number of hours spent revising is related to the number of questions answered correctly.

Purpose

$$\text{Correlation}$$

Level of measurement

$$\text{Interval}$$

Test

$$\boxed{\text{Pearson's }r}$$

Worked selection example 3

The same participants rate anxiety before and after therapy using an ordered scale.

This is not a correlation because the researcher is comparing two occasions.

The study investigates:

$$\text{A difference}$$

The scores are:

$$\text{Related and ordinal}$$

The correct test is:

$$\boxed{\text{Wilcoxon}}$$

Spearman’s rho would be incorrect because the researcher is not investigating a relationship between two co-variables.

Worked selection example 4

Two separate groups complete a memory task, and their numerical scores are compared.

This is a test of difference between unrelated groups.

The correct test is:

$$\boxed{\text{Unrelated }t\text{-test}}$$

Pearson’s \(r\) would be incorrect because the study compares groups rather than correlating two co-variables.

Correlation coefficients

Direction

The direction of the relationship is shown by the sign of the coefficient.

A positive coefficient indicates a positive correlation:

$$r_s=+0.67$$

or:

$$r=+0.67$$

As one co-variable increases, the other tends to increase.

A negative coefficient indicates a negative correlation:

$$r_s=-0.67$$

or:

$$r=-0.67$$

As one co-variable increases, the other tends to decrease.

A value around zero indicates little or no consistent correlation:

$$r_s\approx0$$

or:

$$r\approx0$$

Strength

The strength is shown by how far the coefficient is from zero.

The closer the value is to:

$$+1$$

or:

$$-1$$

the stronger the correlation.

The closer it is to:

$$0$$

the weaker the correlation.

For example:

$$r_s=-0.89$$

is stronger than:

$$r_s=+0.31$$

because:

$$|-0.89|=0.89$$

and:

$$|+0.31|=0.31$$

The negative sign does not make a coefficient weaker. It shows direction only.

Perfect correlations

A perfect positive correlation is:

$$r_s=+1$$

or:

$$r=+1$$

A perfect negative correlation is:

$$r_s=-1$$

or:

$$r=-1$$

A coefficient cannot be greater than \(+1\) or less than \(-1\).

For example:

$$r=1.24$$

is not a valid correlation coefficient.

Statistical significance

Observed values

The coefficient calculated from the research data is the observed value.

For example:

$$r_{s,\text{observed}}=0.72$$

or:

$$r_{\text{observed}}=-0.81$$

The observed value is compared with a critical value obtained from the appropriate statistical table.

Critical values

The critical value depends on information such as:

• the number of paired scores;

• the chosen significance level;

• whether the hypothesis is directional or non-directional;

• the statistical test being used.

A directional hypothesis requires a one-tailed critical value.

A non-directional hypothesis requires a two-tailed critical value.

The selection of critical values is covered in probability and significance.

Comparing observed and critical values

For Spearman’s rho and Pearson’s \(r\), the observed coefficient must be equal to or greater than the critical value in magnitude for the result to be statistically significant.

When the observed coefficient is negative, compare its absolute value with the critical value.

For example:

$$r_{s,\text{observed}}=-0.74$$

The magnitude is:

$$|-0.74|=0.74$$

Suppose the critical value is:

$$r_{s,\text{critical}}=0.62$$

Compare the magnitudes:

$$0.74\geq0.62$$

The result is statistically significant.

The negative sign must still be retained when reporting the direction of the correlation.

Worked significance example: Spearman’s rho

A researcher obtains:

$$r_{s,\text{observed}}=+0.68$$

The critical value is:

$$r_{s,\text{critical}}=0.60$$

Compare the values:

$$0.68\geq0.60$$

The result is statistically significant.

A suitable conclusion is:

The observed Spearman’s rho value of \(0.68\) was greater than the critical value of \(0.60\). The result was statistically significant, so the null hypothesis was rejected. There was a statistically significant positive correlation between the two ranked co-variables.

Worked significance example: Pearson’s \(r\)

A researcher obtains:

$$r_{\text{observed}}=-0.58$$

The critical value is:

$$r_{\text{critical}}=0.65$$

Compare the magnitude:

$$|-0.58|=0.58$$

$$0.58<0.65$$

The result is not statistically significant.

A suitable conclusion is:

The magnitude of the observed Pearson’s \(r\) value was lower than the critical value. The result was not statistically significant, so the null hypothesis was retained.

Significance and causal conclusions

Even when a correlation is statistically significant, it does not show causation.

A suitable conclusion is:

There was a statistically significant negative correlation between stress and sleep quality.

An unsuitable conclusion is:

Stress caused participants’ sleep quality to decrease.

The statistical test shows a relationship, not cause and effect.

Writing a complete test justification

Spearman’s rho justification

A complete justification might state:

Spearman’s rho is appropriate because the researcher is investigating a correlation between two co-variables and both co-variables have been measured using ordinal ranks.

Pearson’s \(r\) justification

A complete justification might state:

Pearson’s \(r\) is appropriate because the researcher is investigating a correlation between two co-variables and both variables have been measured at the interval level.

What not to include

Do not justify Spearman’s rho only by stating:

The data are ordinal.

This identifies the level of measurement but not the research purpose.

Do not justify Pearson’s \(r\) only by stating:

The results are numbers.

Numbers may represent nominal codes or ordinal ratings.

A full explanation must show that:

• the study investigates a correlation;

• the co-variable data are at the correct level of measurement.

Key Words 🔑

Key word	Student-friendly definition	How it may be used in an exam
Spearman’s rho	An inferential test used to investigate a correlation between ordinal co-variables.	You may identify or justify it from ranked or ordered data.
Pearson’s \(r\)	An inferential test used to investigate a correlation between interval co-variables.	You may identify or justify it from numerical data measured using equal units.
Correlation	A relationship between two measured co-variables.	Both Spearman’s rho and Pearson’s \(r\) are tests of correlation.
Co-variable	One of the two variables measured in a correlational investigation.	Every participant or case provides a score for both co-variables.
Paired scores	Two corresponding scores obtained from the same participant or case.	Each pair is used when analysing the correlation.
Ordinal data	Data that can be ranked or ordered but do not necessarily have equal intervals.	Ordinal co-variables indicate Spearman’s rho.
Interval data	Numerical data measured using equal intervals.	Interval co-variables indicate Pearson’s \(r\).
Rank	A position within an ordered sequence.	Ranked co-variable scores may be analysed using Spearman’s rho.
Correlation coefficient	A value between \(-1\) and \(+1\) showing the direction and strength of a relationship.	Both tests produce a correlation coefficient.
Positive correlation	A relationship in which both co-variables tend to increase together.	It is shown by a positive coefficient.
Negative correlation	A relationship in which one co-variable tends to decrease as the other increases.	It is shown by a negative coefficient.
Zero correlation	An absence of a consistent relationship between the co-variables.	It is indicated by a coefficient close to zero.
Observed value	The coefficient calculated from the research data.	It is compared with a critical value.
Critical value	The statistical-table threshold used to determine significance.	The observed coefficient must meet or exceed it in magnitude.
Statistical significance	A judgement that the result meets the selected probability criterion.	A significant result leads to rejection of the null hypothesis.
Causation	A relationship in which one factor directly produces a change in another.	Neither correlation test can demonstrate causation.

Hints from the Examiner Reports 💡

No lesson-specific examiner guidance was identified in the provided reports.

Common Mistakes ⚠️

Mistake: Selecting Spearman’s rho for every study containing ordinal data.

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 considering the measurement level.

Mistake: Selecting Pearson’s \(r\) whenever the results are numerical.

Why this is incorrect:

Numbers may represent ranks, ordered ratings or category codes.

Pearson’s \(r\) requires a correlation using interval data.

How to improve:

Check what the numbers represent and whether the intervals are equal.

Mistake: Using a correlation test to compare two conditions.

Why this is incorrect:

Spearman’s rho and Pearson’s \(r\) investigate relationships between co-variables, not differences between conditions.

How to improve:

Look for paired measurements of two co-variables rather than two experimental conditions.

Mistake: Confusing Spearman’s rho with Pearson’s \(r\).

Why this is incorrect:

The tests have the same purpose but require different levels of measurement.

How to improve:

Remember:

$$\text{Spearman's rho}=\text{Ordinal correlation}$$

$$\text{Pearson's }r=\text{Interval correlation}$$

Mistake: Referring to an independent variable and dependent variable in a correlation.

Why this is incorrect:

A correlational study measures two co-variables rather than manipulating an independent variable.

How to improve:

Name the two measured variables as co-variables.

Mistake: Treating paired co-variable scores as a repeated measures design.

Why this is incorrect:

A correlation measures two co-variables for each participant. A repeated measures design compares the same participants across conditions.

How to improve:

Decide whether the researcher is measuring a relationship or testing a difference.

Mistake: Saying that a negative coefficient is weaker than a positive coefficient.

Why this is incorrect:

The sign indicates direction rather than strength.

For example:

$$r_s=-0.85$$

is stronger than:

$$r_s=+0.42$$

How to improve:

Compare the distance of each value from zero.

Mistake: Reporting an impossible coefficient.

Why this is incorrect:

Both coefficients must lie within:

$$-1\leq r\leq+1$$

How to improve:

Check that the value is not greater than \(+1\) or lower than \(-1\).

Mistake: Ignoring the negative sign when interpreting direction.

Why this is incorrect:

The negative sign shows that one co-variable tends to decrease as the other increases.

How to improve:

Retain the sign when reporting the coefficient and describe the negative relationship.

Mistake: Comparing a negative observed coefficient directly with a positive critical value.

Why this is incorrect:

The magnitude of the observed coefficient should be used when determining whether it reaches the critical value.

How to improve:

For example:

$$|-0.76|=0.76$$

Then compare:

$$0.76$$

with the critical value.

Mistake: Claiming that a significant correlation proves causation.

Why this is incorrect:

A correlation shows an association between co-variables but cannot establish which variable influences the other or whether another variable affects both.

How to improve:

Use phrases such as:

• related to;

• correlated with;

• associated with;

• tends to increase or decrease.

Mistake: Justifying the test using only the level of measurement.

Why this is incorrect:

A complete justification must also identify that the study investigates a correlation.

How to improve:

State both the research purpose and measurement level.

Exam-Style Questions ✍️

Question 1

State when Spearman’s rho should be used.[2 marks]

Question 2

State when Pearson’s \(r\) should be used.[2 marks]

Question 3

Explain one similarity and one difference between Spearman’s rho and Pearson’s \(r\).[4 marks]

Question 4

A psychologist investigates whether participants’ ranked stress scores are related to their ranked sleep-quality scores.

Identify an appropriate inferential statistical test. Explain your answer.[3 marks]

Question 5

A researcher investigates whether the number of hours slept is related to the number of words correctly recalled.

Both measures are recorded using equal numerical units.

Identify an appropriate inferential statistical test. Explain your answer.[3 marks]

Question 6

A psychologist asks participants to rate:

• anxiety from very low to very high;

• confidence from very low to very high.

The psychologist wants to investigate whether the two ratings are related.

a) Identify the level of measurement.[1 mark]

b) Identify an appropriate inferential statistical test.[1 mark]

c) Explain why the test is appropriate.[2 marks]

Question 7

A researcher records:

• participants’ response times in milliseconds;

• their numerical concentration scores measured using equal units.

The researcher investigates whether the two co-variables are related.

Identify and justify the appropriate inferential statistical test.[3 marks]

Question 8

A researcher obtains:

$$r_s=-0.82$$

a) State the direction of the correlation.[1 mark]

b) Describe the strength of the correlation.[1 mark]

c) Explain why the negative sign does not mean that the correlation is weak.[2 marks]

Question 9

A Spearman’s rho test produces:

$$r_{s,\text{observed}}=-0.71$$

The critical value is:

$$r_{s,\text{critical}}=0.64$$

The observed value must be equal to or greater than the critical value in magnitude.

a) Determine whether the result is statistically significant.[1 mark]

b) Explain your answer.[2 marks]

c) State what should happen to the null hypothesis.[1 mark]

Question 10

A Pearson’s \(r\) test produces:

$$r_{\text{observed}}=+0.49$$

The critical value is:

$$r_{\text{critical}}=0.57$$

a) Determine whether the result is statistically significant.[1 mark]

b) Explain your answer.[2 marks]

c) State an appropriate probability conclusion at the \(0.05\) significance level.[1 mark]

Question 11

The same participants complete an anxiety rating before and after therapy. The ratings are ordinal.

A student selects Spearman’s rho.

Explain why Spearman’s rho is inappropriate and identify the correct statistical test.[4 marks]

Question 12

A researcher finds a statistically significant positive Pearson’s \(r\) correlation between sleep duration and memory performance.

Explain why the researcher cannot conclude that longer sleep caused improved memory performance.[3 marks]