The statistical techniques used in geography (measures of central tendency and dispersion, percentage change, Spearman's rank correlation and significance testing) and how to calculate, apply and critically interpret them in geographical contexts.

What this dot point is asking

OCR embeds statistical skills across all components and the Independent Investigation. You need to calculate, apply and critically interpret measures of central tendency and dispersion, percentage change, Spearman's rank correlation and significance testing, in geographical contexts. These are tested as AO3 in Papers 01 and 02 and are central to analysing fieldwork data.

The answer

Central tendency and dispersion

The choice of measure matters geographically. The mean uses all values but is distorted by outliers (one huge value pulls it up), so for skewed data, incomes, settlement sizes, the median is often more representative. The interquartile range, $IQR = Q_3 - Q_1$, measures the spread of the middle $50\%$ and, like the median, resists outliers. The standard deviation, $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$, measures the average distance of values from the mean: a small $\sigma$ means values cluster tightly (a well-sorted beach, a uniform region), a large $\sigma$ means they are widely spread. Reporting both a central value and a measure of spread gives a fuller picture than either alone.

Percentage change

Percentage change standardises change so that places or times of different sizes can be compared. It is calculated as

A positive result is an increase, a negative result a decrease. The strength of the measure is comparability: a rise of $50\,000$ people means very different things in a town of $100\,000$ ($+50\%$) and a city of $5$ million ($+1\%$). The caution is that percentage change can mislead from a small base (a doubling from $2$ to $4$ is $+100\%$ but trivial in absolute terms), so it should be read alongside absolute figures.

Spearman's rank correlation

Spearman's rank correlation coefficient ($r_s$) tests the strength and direction of the relationship between two variables by ranking them. It is calculated as

where $d$ is the difference between the ranks of each paired observation and $n$ is the number of pairs. The result lies between $+1$ (perfect positive correlation, both rise together), $0$ (no correlation) and $-1$ (perfect negative correlation, one rises as the other falls). It is widely used in geography (for example testing whether pebble size decreases downstream, or whether deprivation correlates with distance from a city centre) because it works on ranked data and does not assume a normal distribution.

Significance testing

A calculated $r_s$ must be checked for statistical significance to judge whether the relationship is real or could be due to chance. The calculated value is compared with a critical value from a significance table for the relevant sample size ($n$) and chosen significance level, commonly $0.05$ (the $95\%$ confidence level, meaning a $5\%$ chance the result is random). If the calculated $r_s$ exceeds the critical value, the result is significant and the null hypothesis (that there is no relationship) is rejected; if it does not, the relationship cannot be distinguished from chance. Significance depends strongly on sample size: the same coefficient is significant in a large sample but not a small one, which is why fieldwork needs an adequate, justified sample.

Examples in context

Example 1. Testing the Bradshaw model with Spearman's rank. A river study might rank measured values of, say, velocity against distance downstream at several sites and compute $r_s$ to test the predicted positive relationship. A strong positive coefficient, checked against the critical value for the sample size, supports the model, while a non-significant result prompts reflection on sample size or confounding factors. This shows statistical testing applied to a physical-geography hypothesis and is a classic Independent Investigation technique.

Example 2. Comparing deprivation with standard deviation. Comparing two cities' neighbourhood deprivation scores, the mean might be similar, but a larger standard deviation in one city reveals greater inequality (deprivation more polarised between rich and poor areas), a difference the mean alone hides. This demonstrates why dispersion matters as much as central tendency in human geography, and links to the Changing Spaces; Making Places analysis of uneven places.

Try this

Q1. State the formula for percentage change. [2 marks]

• Cue. $\frac{\text{new value} - \text{original value}}{\text{original value}} \times 100$.

Q2. A Spearman's rank coefficient is $-0.85$ and exceeds the critical value at the $0.05$ level. Interpret this result. [3 marks]

• Cue. A strong negative correlation (as one variable rises, the other falls) that is statistically significant at the $95\%$ confidence level, so the null hypothesis of no relationship is rejected; note that correlation does not prove causation.