The sign test | AQA A-Level Psychology Revision
- Revision Notes
- Aug 5
- 17 min read
Updated: 7 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 60 minutes
This sign test A-Level Psychology revision page explains how to calculate and interpret one of the inferential statistical tests required for AQA Research Methods. You will learn when the sign test is appropriate, how to convert paired results into positive and negative signs, and how to calculate the observed value. You will then compare this with a critical value to determine statistical significance. The lesson builds directly on introduction to statistical testing and your understanding of nominal data.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Identify when the sign test is an appropriate inferential statistical test.
Explain why the sign test requires related data and nominal signs.
Convert paired scores into positive, negative and zero signs.
Calculate the sign-test observed value.
Use a statistical table to identify the appropriate critical value.
Determine whether a sign-test result is statistically significant.
Write a contextual conclusion and make an appropriate decision about the null hypothesis.
Revision Notes 📚
The sign test in A-Level Psychology
The sign test is an inferential statistical test used to investigate a difference between two sets of related data.
It allows a researcher to decide whether the direction of the differences between paired scores is sufficiently consistent for the result to be considered statistically significant.
The sign test is appropriate when:
The researcher is testing for a difference.
The two sets of scores are related.
The differences between paired scores can be converted into nominal data, represented by positive and negative signs.
A useful summary is:
$$\text{Difference}+\text{Related data}+\text{Nominal signs}=\text{Sign test}$$
The sign test does not use the size of each difference. It uses only the direction of the difference.
Purpose of the sign test
A descriptive comparison may show that scores changed between two conditions.
For example, a psychologist may measure anxiety:
before a relaxation activity;
after the relaxation activity.
The researcher may find that most anxiety scores are lower after the activity. However, this apparent pattern might have occurred through chance variation.
The sign test helps the researcher decide whether the direction of the changes is statistically significant.
It does this by examining how many paired scores:
increased;
decreased;
stayed the same.
When should the sign test be used?
Three decisions must be made before selecting the sign test.
The study must investigate a difference
The sign test is a test of difference.
It is used when a researcher compares:
two conditions;
two occasions;
two treatments;
paired or matched scores.
For example:
Is there a difference in anxiety scores before and after relaxation training?
This is a test of difference because two sets of scores are being compared.
The sign test is not used to test:
a correlation between two co-variables;
an association between two independent categorical variables;
a difference between unrelated groups.
The broader process of deciding which test to use is covered in choosing an inferential test.
The scores must be related
The sign test requires related data.
Related data are produced when there is a meaningful link between each score in one condition and a score in the other condition.
This occurs in:
repeated measures designs;
matched pairs designs.
Repeated measures design
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 silence is paired with their own score in background noise.
Matched pairs design
In a matched pairs design, each participant in one condition is paired with a similar participant in another condition.
The participants may be matched on a relevant characteristic, such as age or an initial test score.
Each matched pair produces two related scores.
These designs are explained in experimental designs.
The data must be converted into nominal signs
The sign test converts the direction of each paired difference into one of three categories:
positive;
negative;
zero.
These categories are usually written as:
$$+$$
$$-$$
$$0$$
Once converted, the data are nominal because each pair is placed into a category based on the direction of change.
The original measurements may have been numerical scores. However, the sign test does not use the precise size of the difference.
For example:
Change between conditions | Sign |
Increase of \(1\) point | \(+\) |
Increase of \(8\) points | \(+\) |
Decrease of \(2\) points | \(-\) |
Decrease of \(10\) points | \(-\) |
No change | \(0\) |
An increase of \(8\) receives the same positive sign as an increase of \(1\) because only the direction is used.
The distinction between nominal, ordinal and interval data is covered in levels of measurement.
When the sign test is not appropriate
The sign test would not be appropriate when:
the study investigates a correlation;
the study investigates an association between unrelated categories;
the scores come from two unrelated groups;
there are more than two conditions being compared;
the researcher needs a test that uses the magnitude or rank of the differences.
For example, a researcher compares memory scores from:
one group tested in silence;
a different group tested in noise.
The data are unrelated because different participants take part in each condition. The sign test would not be suitable.
The stages of the sign test
A sign test can be completed using the following stages:
Arrange the results into pairs.
Decide how the difference will be calculated.
Assign a positive, negative or zero sign to each pair.
Remove zero differences from the sign-test calculation.
Count the remaining positive and negative signs.
Calculate the value of \(N\).
Identify the less frequent sign.
Record its frequency as the observed value, \(S\).
Use a statistical table to find the critical value.
Compare the observed and critical values.
Decide whether the result is statistically significant.
Reject or retain the null hypothesis.
Write a conclusion in the context of the study.
Step 1: Arrange the results into pairs
Each score in the first condition must be matched with its corresponding score in the second condition.
For a repeated measures design, the pair consists of two scores from the same participant.
For example:
Participant | Before treatment | After treatment |
A | \(18\) | \(14\) |
B | \(15\) | \(12\) |
C | \(20\) | \(17\) |
Participant A’s scores form one pair:
$$(18,14)$$
Participant B’s scores form another pair:
$$(15,12)$$
The pairing must be preserved. Do not reorder each condition independently before calculating the signs.
Step 2: Decide the direction of subtraction
The direction of subtraction must be consistent for every pair.
For example, the researcher might calculate:
$$\text{After score}-\text{Before score}$$
Using this rule:
a positive result means the after score is higher;
a negative result means the after score is lower;
zero means there is no change.
For Participant A:
$$14-18=-4$$
The sign is therefore:
$$-$$
For Participant B:
$$12-15=-3$$
The sign is:
$$-$$
The exact size of each difference is not used when calculating the sign-test statistic. Only the signs are counted.
An alternative sign rule
Instead of showing subtraction, a question may ask you to assign a sign based directly on the direction of change.
For example:
use \(+\) when the score is higher after treatment;
use \(-\) when the score is lower after treatment;
use \(0\) when the scores are equal.
Either method is acceptable if the rule is applied consistently.
Step 3: Assign the signs
Suppose a participant scores:
$$12$$
before an activity and:
$$16$$
after the activity.
Using:
$$\text{After}-\text{Before}$$
the difference is:
$$16-12=+4$$
The sign is:
$$+$$
Suppose another participant scores:
$$17$$
before and:
$$13$$
after.
The difference is:
$$13-17=-4$$
The sign is:
$$-$$
If the scores are:
$$14\text{ and }14$$
the difference is:
$$14-14=0$$
The sign is:
$$0$$
Step 4: Remove zero differences
A zero difference, sometimes called a tie, occurs when the two scores in a pair are equal.
For example:
$$15-15=0$$
Zero differences are not counted as positive or negative signs.
They must be excluded when calculating:
$$N$$
This means that \(N\) is not always the same as the original number of participants or pairs.
Use:
$$N=\text{Number of positive signs}+\text{Number of negative signs}$$
Zero signs are omitted.
Worked example: calculating \(N\)
Suppose a study produces:
\(7\) positive signs;
\(3\) negative signs;
\(2\) zero signs.
The original sample contained:
$$7+3+2=12$$
paired scores.
However:
$$N=7+3=10$$
Therefore:
$$\boxed{N=10}$$
The two ties are excluded from \(N\).
Step 5: Count the positive and negative signs
After removing zero signs, count the number of:
$$+$$
and:
$$-$$
For example:
Sign | Frequency |
\(+\) | \(8\) |
\(-\) | \(2\) |
The total number of non-zero signs is:
$$N=8+2=10$$
Step 6: Find the observed value
The observed value for the sign test is represented by:
$$S$$
The observed value is the frequency of the less common sign.
Use:
$$S=\text{Frequency of the less common sign}$$
In the previous example:
positive signs: \(8\);
negative signs: \(2\).
The less common sign is negative, so:
$$\boxed{S=2}$$
Do not calculate the difference between the sign frequencies.
The observed value is not:
$$8-2=6$$
It is:
$$S=2$$
What if the signs occur equally often?
Suppose there are:
\(5\) positive signs;
\(5\) negative signs.
The observed value is:
$$S=5$$
There is no clear tendency for scores to change in one direction.
Such a result is unlikely to meet the critical-value requirement for statistical significance.
Complete worked example: calculating the sign test
A psychologist investigates whether anxiety scores differ before and after a relaxation activity.
The null hypothesis is:
There will be no difference in participants’ anxiety scores before and after the relaxation activity.
The researcher calculates:
$$\text{After score}-\text{Before score}$$
The results are shown below.
Participant | Before relaxation | After relaxation | Difference | Sign |
A | \(18\) | \(14\) | \(14-18=-4\) | \(-\) |
B | \(15\) | \(12\) | \(12-15=-3\) | \(-\) |
C | \(20\) | \(17\) | \(17-20=-3\) | \(-\) |
D | \(16\) | \(13\) | \(13-16=-3\) | \(-\) |
E | \(14\) | \(15\) | \(15-14=+1\) | \(+\) |
F | \(17\) | \(13\) | \(13-17=-4\) | \(-\) |
G | \(19\) | \(16\) | \(16-19=-3\) | \(-\) |
H | \(13\) | \(11\) | \(11-13=-2\) | \(-\) |
I | \(16\) | \(16\) | \(16-16=0\) | \(0\) |
J | \(21\) | \(17\) | \(17-21=-4\) | \(-\) |
K | \(18\) | \(15\) | \(15-18=-3\) | \(-\) |
L | \(15\) | \(11\) | \(11-15=-4\) | \(-\) |
Count the signs:
$$+=1$$
$$-=10$$
$$0=1$$
Exclude the zero sign:
$$N=1+10=11$$
The less frequent non-zero sign is positive:
$$\boxed{S=1}$$
This is the observed value.
Why the smaller sign frequency is used
Under the null hypothesis, increases and decreases would be expected to occur with similar frequency.
A very unbalanced result, such as:
$$10\text{ negative signs and }1\text{ positive sign}$$
is less likely to occur through chance than a balanced result such as:
$$6\text{ negative signs and }5\text{ positive signs}$$
The observed value records the frequency of the less common sign.
A very small value of \(S\) indicates that the signs are strongly concentrated in one direction.
This is why a smaller observed value provides stronger evidence against the null hypothesis in the sign test.
Using a statistical table
Once \(S\) and \(N\) have been calculated, the observed value must be compared with a critical value.
The critical value is found in a sign-test statistical table.
To identify the correct critical value, you need:
the value of \(N\);
the significance level;
whether the hypothesis is directional or non-directional.
Directional and non-directional hypotheses
A directional hypothesis predicts the direction of the difference.
For example:
Participants will have lower anxiety scores after the relaxation activity than before it.
A directional hypothesis requires the one-tailed column of the statistical table.
A non-directional hypothesis predicts a difference but does not state its direction.
For example:
There will be a difference in anxiety scores before and after the relaxation activity.
A non-directional hypothesis requires the two-tailed column.
The construction of hypotheses is covered in aims and hypotheses.
Example sign-test table
The following is an example extract from a critical-values table for the sign test at:
$$p\leq0.05$$
\(N\) | One-tailed critical value | Two-tailed critical value |
\(8\) | \(1\) | \(0\) |
\(9\) | \(1\) | \(1\) |
\(10\) | \(1\) | \(1\) |
\(11\) | \(2\) | \(1\) |
\(12\) | \(2\) | \(2\) |
\(13\) | \(3\) | \(2\) |
In the worked anxiety example:
$$N=11$$
The hypothesis is non-directional, so use the two-tailed column.
The critical value is:
$$\boxed{S_{\text{critical}}=1}$$
The sign-test significance rule
For the sign test, the result is statistically significant when:
$$S_{\text{observed}}\leq S_{\text{critical}}$$
This is sometimes remembered as:
The observed value must be equal to or smaller than the critical value.
In the worked example:
$$S_{\text{observed}}=1$$
and:
$$S_{\text{critical}}=1$$
Compare the values:
$$1\leq1$$
The observed value has met the critical value.
Therefore:
$$\boxed{\text{The result is statistically significant}}$$
The null hypothesis should be rejected.
Equality counts as significant
The observed value does not need to be smaller than the critical value. It can be equal to it.
For example:
$$S_{\text{observed}}=2$$
$$S_{\text{critical}}=2$$
Because:
$$2\leq2$$
the result is statistically significant.
Worked conclusion
The anxiety study produced:
$$S=1$$
with:
$$N=11$$
The two-tailed critical value at:
$$p\leq0.05$$
was:
$$1$$
A complete conclusion would be:
The observed value of \(S=1\) was equal to the critical value of \(1\). The result was therefore statistically significant at \(p\leq0.05\). The null hypothesis was rejected. There was a statistically significant difference in anxiety scores before and after the relaxation activity.
The scores mainly decreased after relaxation, but because the hypothesis was non-directional, the formal conclusion should focus on the predicted difference.
A non-significant example
Suppose a sign test produces:
$$S_{\text{observed}}=3$$
The critical value is:
$$S_{\text{critical}}=1$$
For significance:
$$S_{\text{observed}}\leq S_{\text{critical}}$$
However:
$$3>1$$
The result is therefore not statistically significant.
The null hypothesis should be retained.
A suitable conclusion would be:
The observed value of \(S=3\) was greater than the critical value of \(1\). The result was not statistically significant, so the null hypothesis was retained.
Interpreting a directional result
Suppose the researcher predicts that scores will decrease after treatment.
The majority of signs must show the predicted decrease before the alternative hypothesis can be supported.
For example, if the sign rule is:
$$\text{After}-\text{Before}$$
then a decrease produces:
$$-$$
A result containing mainly negative signs supports the predicted direction.
If the signs are mainly positive, the scores changed in the opposite direction. The researcher cannot claim support for the directional hypothesis, even if the signs are highly unbalanced.
Selecting the correct table column
Use the hypothesis to select the table column.
Hypothesis | Table column |
Predicts a specific direction | One-tailed |
Predicts a difference without a direction | Two-tailed |
Null hypothesis only is provided | Use the information in the question to identify the research hypothesis or required tail |
Do not decide whether the test is one-tailed or two-tailed by looking at the results. The decision comes from the hypothesis established before the data were analysed.
Significance levels
The statistical table may provide critical values for different significance levels.
Common examples include:
$$p\leq0.05$$
and:
$$p\leq0.01$$
A result significant at:
$$p\leq0.05$$
is judged to have a probability of no more than \(5\%\) of occurring through chance if the null hypothesis is true.
A result significant at:
$$p\leq0.01$$
must meet a stricter criterion.
The detailed interpretation of significance levels is covered in probability and significance.
Understanding the sign-test table
When reading a table, check:
You are using the sign-test table.
You have removed all zero differences from \(N\).
You have selected the correct row for \(N\).
You have selected the correct significance level.
You have selected the correct tail.
You have copied the critical value accurately.
You apply the sign-test comparison rule.
The rule is:
$$S_{\text{observed}}\leq S_{\text{critical}}$$
Complete sign-test checklist
Before calculating:
Is the study testing a difference?
Are the scores related?
Can each paired difference be coded as \(+\), \(-\) or \(0\)?
During the calculation:
Have the scores been paired correctly?
Is the same subtraction rule used for every pair?
Have all signs been assigned correctly?
Have zero differences been removed?
Is \(N\) based only on positive and negative signs?
Is \(S\) the frequency of the less common sign?
When using the table:
Is the hypothesis directional or non-directional?
What is the required significance level?
What is the correct critical value for \(N\)?
Is the observed value equal to or smaller than the critical value?
When concluding:
Is the result significant?
Should the null hypothesis be rejected or retained?
Has the conclusion been written in the context of the study?
Sign test and experimental design
The sign test can be used with:
repeated measures data;
matched pairs data.
It cannot be used with an independent groups design because there is no direct pairing between the scores.
Repeated measures example
Each participant completes the same task before and after sleep deprivation.
The before and after scores are paired for each participant.
Matched pairs example
Participants are matched according to an initial memory score. One member of each pair completes Condition A and the other completes Condition B.
The two scores within each matched pair are compared.
Sign test and level of measurement
The sign test uses nominal data because each difference is placed into a sign category.
These categories are:
$$+,\ -,\ 0$$
The precise size of the original difference is discarded.
For example:
$$+1$$
and:
$$+12$$
both become:
$$+$$
This is a limitation of the information retained by the test, but evaluation of statistical tests is not required within this calculation lesson unless a question asks you to explain the consequences of converting data into signs.
Sign test compared with other tests of difference
Statistical test | Purpose | Data relationship | Level used for test selection |
Sign test | Difference | Related | Nominal |
Wilcoxon | Difference | Related | Ordinal |
Mann-Whitney | Difference | Unrelated | Ordinal |
Related \(t\)-test | Difference | Related | Interval |
Unrelated \(t\)-test | Difference | Unrelated | Interval |
The sign test is selected when the data meet the lowest level of measurement required for these tests of difference.
The other tests are covered in Wilcoxon and Mann-Whitney tests and related and unrelated t-tests.
Writing a complete test justification
A question may ask why the sign test is appropriate.
A complete justification should include three elements:
It is a test of difference.
The data are related.
The data used in the test are nominal.
For example:
The sign test is appropriate because the researcher is testing for a difference between two conditions, the same participants take part in both conditions, and the direction of each difference is converted into nominal positive and negative signs.
Do not justify the sign test only by saying that it uses signs. This does not address the purpose or design of the study.
Writing a complete statistical conclusion
A complete conclusion should include:
The observed value.
The critical value.
The significance level.
The correct comparison.
Whether the result is significant.
Whether the null hypothesis is rejected or retained.
A contextual statement about the variables or conditions.
For example:
The observed value of \(S=1\) was equal to the critical value of \(1\) at \(p\leq0.05\). As the observed value was equal to or less than the critical value, the result was statistically significant. The null hypothesis was rejected. There was a statistically significant difference in memory scores between the two conditions.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Sign test | An inferential test used to investigate a difference between two sets of related nominal data. | You may identify when it should be used, calculate it or interpret its result. |
Test of difference | A statistical analysis comparing two conditions or groups. | The sign test is used when a researcher investigates a difference. |
Related data | Scores connected through the same participants or matched pairs. | The sign test requires related scores. |
Repeated measures | An experimental design in which the same participants take part in both conditions. | The paired scores may be analysed using the sign test. |
Matched pairs | A design in which participants in different conditions are matched on relevant characteristics. | Each matched pair produces related scores. |
Nominal data | Data consisting of separate, unordered categories. | Sign-test differences are coded into positive and negative categories. |
Positive sign | A sign showing that a paired score changed in the designated positive direction. | Positive signs are counted when calculating \(N\) and \(S\). |
Negative sign | A sign showing that a paired score changed in the designated negative direction. | Negative signs are counted and compared with positive signs. |
Zero difference | A pair in which both scores are equal. | Zero differences are removed before calculating \(N\). |
Tie | Another term for a zero difference between paired scores. | Ties are excluded from the sign-test calculation. |
\(N\) | The number of non-zero paired differences included in the sign test. | It determines the row selected from the critical-values table. |
Observed value | The sign-test statistic calculated from the data. | For the sign test, it is the frequency of the less common sign. |
\(S\) | The symbol commonly used for the sign-test observed value. | You may calculate and compare it with a critical value. |
Critical value | The threshold obtained from a statistical table for determining significance. | It is selected using \(N\), the significance level and the hypothesis direction. |
One-tailed test | A test used with a directional alternative hypothesis. | It determines which critical-value column should be used. |
Two-tailed test | A test used with a non-directional alternative hypothesis. | It uses the two-tailed critical-value column. |
Statistical significance | A judgement that the result meets the selected probability criterion. | For the sign test, the observed value must be equal to or smaller than the critical value. |
Null hypothesis | A prediction that there is no difference and that any apparent result is due to chance. | It is rejected when the sign-test result is significant. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Selecting the sign test for unrelated groups.
Why this is incorrect:
The sign test requires paired scores from the same participants or matched pairs.
How to improve:
Check the experimental design before selecting the test. Look for repeated measures or matched pairs.
Mistake: Selecting the sign test for a correlation.
Why this is incorrect:
The sign test investigates a difference between two related conditions. It does not analyse a relationship between two co-variables.
How to improve:
Identify whether the research is testing a difference, correlation or association before considering the level of measurement.
Mistake: Applying different subtraction rules to different pairs.
Why this is incorrect:
Inconsistent subtraction may reverse some signs and change the result.
How to improve:
Write the rule above the table before beginning:
$$\text{Condition B}-\text{Condition A}$$
Apply it to every pair.
Mistake: Counting the size of the differences rather than their direction.
Why this is incorrect:
The sign test uses only positive and negative categories.
How to improve:
After finding the sign, ignore the magnitude of the difference.
Mistake: Including zero differences in \(N\).
Why this is incorrect:
Ties do not support either direction and must be excluded from the sign-test calculation.
How to improve:
Use:
$$N=+\text{ signs}+-\text{ signs}$$
Do not include zero signs.
Mistake: Using the original sample size as \(N\) when ties are present.
Why this is incorrect:
The table row must be based on the number of non-zero differences.
How to improve:
Count the positive and negative signs after removing ties.
Mistake: Calculating \(S\) by subtracting the sign frequencies.
Why this is incorrect:
The observed value is the number of occurrences of the less frequent sign.
For example, if:
$$+=9$$
and:
$$-=2$$
then:
$$S=2$$
not:
$$S=9-2=7$$
How to improve:
Circle the smaller sign frequency and record it as \(S\).
Mistake: Using the larger sign frequency as the observed value.
Why this is incorrect:
The sign-test observed value is the less frequent sign.
How to improve:
Remember:
$$S=\text{smaller sign frequency}$$
Mistake: Selecting the tail from the direction of the results.
Why this is incorrect:
The use of a one-tailed or two-tailed critical value depends on the hypothesis, not the pattern obtained.
How to improve:
Read the alternative hypothesis before consulting the statistical table.
Mistake: Using the wrong significance rule.
Why this is incorrect:
For the sign test, a smaller observed value provides stronger evidence against the null hypothesis.
How to improve:
Remember:
$$S_{\text{observed}}\leq S_{\text{critical}}$$
means the result is significant.
Mistake: Treating equal observed and critical values as non-significant.
Why this is incorrect:
Equality means the observed value has reached the critical threshold.
How to improve:
Include the equality symbol:
$$\leq$$
Mistake: Giving a conclusion without referring to the study.
Why this is incorrect:
A complete answer should explain what the statistical decision means for the variables or conditions being investigated.
How to improve:
Name the measure and both conditions in the conclusion.
Exam-Style Questions ✍️
Question 1
State the three features of a study that indicate the sign test should be used.[3 marks]
Question 2
A psychologist measures the same participants’ concentration scores before and after a mindfulness activity.
Explain why the data are related.[2 marks]
Question 3
A researcher uses the following rule:
$$\text{Score after treatment}-\text{Score before treatment}$$
Assign a positive, negative or zero sign to each pair.
Participant | Before treatment | After treatment |
A | \(12\) | \(15\) |
B | \(16\) | \(14\) |
C | \(11\) | \(11\) |
D | \(18\) | \(13\) |
E | \(14\) | \(17\) |
[3 marks]
Question 4
A sign-test calculation produces:
\(8\) positive signs;
\(3\) negative signs;
\(2\) zero signs.
Calculate:
a) \(N\).[1 mark]
b) The observed value, \(S\).[1 mark]
Question 5
A researcher measures participants’ memory scores before and after a sleep intervention.
Participant | Before intervention | After intervention |
A | \(9\) | \(12\) |
B | \(11\) | \(14\) |
C | \(13\) | \(13\) |
D | \(10\) | \(15\) |
E | \(12\) | \(14\) |
F | \(15\) | \(14\) |
G | \(8\) | \(11\) |
H | \(14\) | \(17\) |
I | \(10\) | \(13\) |
J | \(12\) | \(16\) |
Using:
$$\text{After score}-\text{Before score}$$
a) Assign a sign to each pair of scores.[3 marks]
b) Calculate \(N\).[1 mark]
c) Calculate the observed value, \(S\).[1 mark]
Question 6
The table below shows critical values for a sign test at:
$$p\leq0.05$$
\(N\) | One-tailed critical value | Two-tailed critical value |
\(8\) | \(1\) | \(0\) |
\(9\) | \(1\) | \(1\) |
\(10\) | \(1\) | \(1\) |
\(11\) | \(2\) | \(1\) |
\(12\) | \(2\) | \(2\) |
\(13\) | \(3\) | \(2\) |
A researcher uses a non-directional hypothesis and obtains:
$$N=11$$
$$S_{\text{observed}}=2$$
a) Identify the critical value.[1 mark]
b) Determine whether the result is statistically significant.[1 mark]
c) Explain your decision.[2 marks]
Question 7
A psychologist predicts that participants will make fewer errors after receiving training.
The study produces:
$$N=11$$
$$S_{\text{observed}}=2$$
Using the table in Question 6:
a) State whether a one-tailed or two-tailed critical value should be used.[1 mark]
b) Identify the critical value.[1 mark]
c) Determine whether the result is statistically significant. Explain your answer.[2 marks]
Question 8
A sign test produces:
$$S_{\text{observed}}=1$$
The critical value is:
$$S_{\text{critical}}=1$$
A student concludes that the result is not significant because the observed value is not smaller than the critical value.
Explain why the student’s conclusion is incorrect.[3 marks]
Question 9
A researcher compares anxiety ratings from two different groups of participants. One group completes a breathing exercise and the other group does not.
The researcher plans to analyse the results using the sign test.
Explain why the sign test is not appropriate.[3 marks]
Question 10
A psychologist investigates whether a relaxation activity changes stress scores. The same participants provide scores before and after the activity.
The researcher obtains:
$$N=12$$
$$S_{\text{observed}}=2$$
The hypothesis is non-directional. The two-tailed critical value at:
$$p\leq0.05$$
is:
$$2$$
Write a complete conclusion for the study. Your answer should:
compare the observed and critical values;
state whether the result is statistically significant;
state whether the null hypothesis should be rejected or retained;
refer to participants’ stress scores.
[4 marks]
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