Data Relationships, Predictions and Conclusions

Looking for relationships between geographical variables

Geographers often investigate whether two things vary together. For example, does noise level decrease with distance from a busy road? Bivariate data consists of paired values for two variables. Each pair must refer to the same observation: the distance and noise level recorded at one survey site belong together.

A scatter plot displays these pairs. One variable goes on the horizontal axis and the other on the vertical axis. Label both axes with the variable and its unit, choose evenly spaced numerical scales and plot each pair as a separate point. Unlike a line graph showing change over time, the individual points are not joined together.

Recognising the direction and strength of a relationship

Correlation describes how two variables vary together. Read the pattern from left to right:

• Positive correlation: as one variable increases, the other generally increases; the points slope upwards.
• Negative correlation: as one variable increases, the other generally decreases; the points slope downwards.
• No correlation: there is no clear increasing or decreasing pattern.

Direction and strength are different. Points clustered closely around a clear trend show stronger correlation than points scattered widely around it. A steep slope does not necessarily mean strong correlation: strength depends on how closely the points follow the pattern.

Suppose a survey produced the following noise levels at eight sites near a road. The horizontal axis shows distance in kilometres; the vertical axis shows noise level in decibels, written dB.

Data for Distance from a road and noise level

The main pattern is negative correlation: sites farther from the road generally have lower noise levels. At 0.5 km, the noise level is 76 dB; at 4 km, it is 54 dB. However, the site at 3 km has a noise level of 78 dB and lies well above the main pattern. This is an outlier. A nearby noise source or a measurement problem could explain it, but the graph alone cannot tell us which.

Sketching a trend and drawing a line of best fit

A trend line summarises the overall direction of the points. Begin by looking at the main cluster and sketching its general trend. Where the pattern is roughly straight, draw an estimated straight line of best fit with a ruler.

Place it through the centre of the main cluster, with roughly balanced numbers of points and distances on either side. It need not pass through particular points. Do not let a single outlier pull it away from the main pattern, and do not force it through the origin unless the data and context justify that choice.

The line in the noise example represents the overall decrease rather than every individual site's reading. If there is no clear relationship, a straight line will not provide a useful prediction.

Making predictions within and beyond the data

To estimate noise level at a given distance, find the distance on the horizontal axis, move vertically to the line of best fit, then move horizontally to the vertical axis. Read the estimated noise level, including its unit.

For a distance of 2.25 km, the example line gives approximately 66 dB. This is interpolation, because 2.25 km lies within the observed distance range of 0.5–4 km. It estimates the general pattern, not the exact reading guaranteed at a particular site.

Extending the line to 5 km gives approximately 49 dB. This is extrapolation, because 5 km lies beyond the observed range. It is less reliable: the relationship may change farther from the road, or other noise sources may become more important. A larger, appropriately collected sample and a clearer relationship generally provide a firmer basis for predictions, but neither makes them certain.

Checking whether a statistical presentation is trustworthy

Before accepting a graph's message, check its title, labels, units, scale and any key. These tell you what is being compared and how values should be read.

Equal distances along an ordinary numerical axis should represent equal changes in value. For example, labels of 0, 10, 20 and 50 at equal intervals would distort the graph. A missing key on a graph containing two groups prevents you from identifying their results. Missing units make numerical values ambiguous.

An axis starting above zero is not automatically incorrect, but it can make differences appear larger. Read the actual values rather than judging only the visual height or spacing. Likewise, check whether two graphs use the same scale before comparing their appearance.

Also distinguish weaknesses in presentation from limitations in the evidence. A neatly labelled graph can still represent a small sample or measurements made under different conditions. Those limitations affect how confidently its findings can be applied more widely.

Drawing a justified geographical conclusion

A useful conclusion connects a claim to numerical evidence and explains its geographical meaning. For the example, you could conclude: ‘The data generally support a decrease in noise level with distance from the road: readings fall from 76 dB at 0.5 km to 54 dB at 4 km. However, the 78 dB reading at 3 km shows that distance alone does not explain every site's noise level.’

When comparing groups, use appropriate averages and measures of spread. A higher median indicates a higher typical value; a larger range or interquartile range indicates greater variation. Give the figures and explain them in context, rather than simply listing statistics. Comparisons are more convincing when the measurements were taken using comparable procedures and conditions.

Finally, correlation does not establish causation. Two variables may vary together because another factor influences both. Sunflower height and puppy weight, for example, may both increase with time, but one does not cause the other. A scatter plot supports a statement about an observed relationship; establishing its cause requires further evidence.

Describe the relationship

• Positive: both variables generally increase together.
• Negative: one generally decreases as the other increases.
• None: no clear trend.
• Strength depends on clustering around the trend, not steepness.
• Mention both variables and any outliers. Correlation does not prove causation.

Fit and predict

Draw an estimated line through the centre of the main pattern, balancing points and distances on either side.

Read from the known axis value to the line, then across to the other axis.

• Interpolation: within the observed range.