How do you use Spearman's rank and Pearson's correlation in Advanced Higher Geography?
Correlation tests: Spearman's rank correlation for ranked data and Pearson's product moment correlation coefficient for interval data, interpreting the coefficient and its significance.
How to use the two correlation tests in SQA Advanced Higher Geography: Spearman's rank correlation coefficient for ranked data and Pearson's product moment correlation coefficient for interval data, including interpreting the coefficient between minus 1 and plus 1 and judging significance.
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What this key area is asking
Correlation tests measure whether two variables are related. The spec names two: Spearman's rank correlation coefficient (for ranked data) and Pearson's product moment correlation coefficient (for interval data). For each you should know the data it requires, how to interpret the coefficient between minus 1 and plus 1, and how to check significance. The choice between them follows directly from the data type.
Spearman's rank and Pearson's correlation
The two tests answer the same question but suit different data. Spearman is robust to outliers and works on ranked data; Pearson is more powerful but assumes interval, roughly normal data.
- Spearman's rank. Ranked data; monotonic relationship; robust to outliers.
- Pearson's PMCC. Interval data, roughly normal; linear relationship; more powerful.
Interpreting the coefficient
Reading the coefficient is the first interpretation, but it is not the last. A coefficient describes the sample; whether the relationship is real in the wider population depends on significance, checked against a critical-values table for the sample size and a chosen probability level.
A routine for a correlation test
- Check the data type. Ranked data points to Spearman; interval data to Pearson.
- Calculate the coefficient. Compute the value between minus 1 and plus 1.
- Interpret size and sign. State the strength and direction of the relationship.
- Test significance. Compare against the critical value for the sample size before concluding.
Examples in context
Try this
Q1. What does a correlation coefficient of minus 1 indicate? [1 mark]
- Cue. A perfect negative correlation: as one variable rises, the other falls exactly.
Q2. Which correlation test suits ranked (ordinal) data? [1 mark]
- Cue. Spearman's rank correlation coefficient.
Exam-style practice questions
Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
SQA AH data5 marksExplain when you would use Spearman's rank correlation coefficient and how you would interpret the result.Show worked answer →
Spearman's rank correlation tests the strength and direction of a relationship between two variables using their ranks, so it suits ordinal data or interval data converted to ranks. The coefficient runs from minus 1 (perfect negative) through 0 (no correlation) to plus 1 (perfect positive).
A full answer states the data requirement (ranked data, or data that can be ranked), explains the scale from minus 1 to plus 1, and interprets a result (for example plus 0.8 means a strong positive relationship). The strongest answers check significance against a critical-values table for the sample size before concluding, because a coefficient that looks strong may not be statistically significant in a small sample.
SQA AH data4 marksExplain the difference between Spearman's rank and Pearson's correlation and the data each requires.Show worked answer →
Both measure the strength and direction of a relationship between two variables on a scale from minus 1 to plus 1, but they differ in data requirements. Spearman's rank uses the ranks of the data, so it suits ordinal data or data with outliers, and it detects monotonic relationships. Pearson's product moment correlation uses the actual interval values and detects linear relationships, so it needs interval data that is roughly normally distributed.
Strong answers state the data requirement of each (Spearman: ranked; Pearson: interval), note that Pearson is more powerful when its assumptions hold while Spearman is more robust to outliers and ordinal data, and stress checking significance for both. They link the choice back to the data type.
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Sources & how we know this
- Advanced Higher Geography Course Specification — SQA (2019)
- Advanced Higher Geography Specimen Question Paper — SQA (2019)