4.2.3.3 - The sign test
Inferential tests help decide whether an observed pattern is unlikely to have arisen by chance under a null hypothesis. This lesson introduces the logic through the sign test, where paired differences are reduced to plus and minus signs and ties are removed. You will calculate the test statistic, identify the effective sample size and connect the result to a cautious statistical conclusion.
Why statistical testing is needed
Psychologists often collect data from a sample and then want to make a careful conclusion about a wider population. A difference in sample data can look convincing, but it might still be a chance pattern. Statistical testing asks how unusual the observed pattern would be if the null hypothesis were true. An unusual result may justify rejecting that hypothesis; it does not prove that a finding is real or representative.
Statistical testing
Statistical testing uses a formal procedure to assess how likely the observed result, or a more extreme result, would be if the null hypothesis were true.
In A-level Psychology, these tests are usually described as inferential because the researcher is moving from sample data toward a wider conclusion.
Inferential test
An inferential test is a statistical test used to make an inference from sample data about whether a difference or association is likely to exist in the wider population.
A research methods answer should keep two ideas separate:
| Descriptive statistics | Inferential statistics |
|---|---|
| Summarise what was found in the sample. | Test whether the sample pattern is likely to reflect something beyond chance. |
| Examples: mean, median, range, standard deviation, graph. | Example in this lesson: the sign test. |
| "This group scored higher in our sample." | "Is the difference large/consistent enough to reject the null hypothesis?" |
This connects to the hypothesis language from earlier research methods.
Null hypothesis
A null hypothesis states that there is no population difference or association of the kind being tested; observed sample differences can arise through chance variation.
This lesson introduces the simplest AQA inferential test: the sign test. You need to know when to use it and how to calculate its value, called S or sometimes s in AQA materials.
We are not yet making the final significance decision. That belongs mainly to the next lesson. For now, the target is clean calculation: choose the sign test correctly, turn paired data into plus and minus signs, ignore no-change scores, and find S.
When to use the sign test
The sign test compares the directions of change within meaningful pairs of observations. The pairs must be independent of other pairs: one person should not contribute several changes that are treated as separate independent participants.
Sign test
The sign test is an inferential statistical test used to test for a difference between two related sets of scores after each pair has been classified as a positive change, a negative change or no change.
The sign test is useful because it works with very simple categories. Instead of using the size of each difference, it asks only: did the score go up, go down or stay the same?
Use the sign test when all three conditions fit the scenario.
| Condition | What it means | Scenario clue |
|---|---|---|
| The study tests a difference | The researcher compares two conditions, times or treatments. | "Before and after", "condition A compared with condition B". |
| The data are related | The scores can be paired meaningfully. | Same participants in both conditions, or matched pairs. |
| The data are nominal/categorical, or can be converted to signs | The analysis uses categories: +, - or 0/no change. | "Improved, deteriorated or no change", or raw scores converted into signs. |
Related design
A related design is one where scores are paired, either because the same participants are tested in both conditions or because participants have been matched in pairs.
The other key term is about the level of measurement used after the scores have been converted into signs.
Nominal data
Nominal data classify observations into categories; the analysis counts category membership rather than measuring how much a score changes. The sign test uses frequencies of plus and minus categories, even when the original scores contained richer information.
AO2 example: A researcher measures 14 students' anxiety scores before and after a breathing exercise. Each student's after-score can be compared with their own before-score, so the design is related. The researcher is testing for a difference, not a correlation. Each student can be categorised as lower anxiety, higher anxiety or no change, so the sign test could be used.
Do not use the sign test if the question is about an association between two co-variables, such as hours slept and test score. Do not use it for an independent groups design where different participants are in each condition and cannot be paired.
How to calculate S
The calculation is deliberately simple, but exam marks are often lost through small handling errors. Use the same routine every time.
Continue this lesson.
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