You are here: Home >> Geographical enquiry >> Stage 4

Stage 4: Data analysis

Stage 4: Data presentation | Statistics

Data presentation

It is easy to collect data. In your results section, you should aim to summarise every piece of data clearly and help to spot trends in the data. Some useful types of graph are shown below.

1. Bar chart

The x-axis has labels, the y-axis may have numbers. There needs to be a gap between the bars. The example below, from a saltmarsh investigation, shows the Simpson Yule Diversity Index for 12 sites in a saltmarsh. See investigation page.

2. Percentage bar charts

The x-axis has labels, the y-axis has percentages. There needs to be a gap between the bars. Each bar is divided up into coloured or shaded sections based on percentages. The example below, from a downstream changes in a river investigation, shows the percentage of stones in each roundness category at 3 sites. See investigation page.

3. Divided bar charts

The x-axis has labels, the y-axis has numbers. There needs to be a gap between each of the bars. The size of each bar shows the total number. Each bar is divided up into coloured or shaded sections based on percentages. The example below, from a counter-urbanisation investigation, shows the results of a traffic survey carried out at four times of the day. See investigation page.

4. Histogram

The x-axis and y-axis both have numbers. The x-axis is divided into intervals. There are no gaps between bars. The example below, from a glaciation investigation, shows the number of stones in each interval of the Cailleux Index. See investigation page.

5. Pie chart

These show the percentage of the total represented in each category. To work out the angle (in degrees) for each category, calculate percentage x 360. The example below shows employment data, derived from the census, for a rural ward in south-east England.

6. Scattergraph

Use the x-axis for the independent variable and the y-axis for the dependent variable. The example below, from a rural settlement hierarchy investigation, shows the total population size of each settlement (the independent variable) on the x-axis, and the number of services in each settlement (the dependent variable) on the y-axis. See investigation page.

7. Kite diagram

These show the change of a percentage over distance. They are most commonly used to show changes in the percentage cover of plant species along an environmental gradient. The example below, from a sand dunes investigation, shows changes in the percentage cover of a number of species with distance inland in a sand dune system in south Wales. See investigation page.

Statistics

The null hypothesis

Technically all statistical tests involve testing a null hypothesis against an alternative hypothesis

These two terms have specialised meanings, and are not the same as your research question or hypothesis. But the null hypothesis and alternative hypothesis can be constructed from the research hypothesis.

Research hypothesis	Hydraulic radius increases with distance from source in the River Onny
Null hypothesis	There is no significant correlation between hydraulic radius and distance from source in the River Onny
Alternative hypothesis	There is a significant correlation between hydraulic radius and distance from source in the River Onny

A useful idea is innocent until proven guilty. When you carry out a geographical investigation, you must assume that the null hypothesis is true, and only change your mind (and reject the null hypothesis) if there is strong enough evidence to show otherwise.

So for the river investigation, you must start by assuming that distance from source is 'innocent' of causing any change in hydraulic radius, and only change your mind if there is strong enough evidence to show that distance from source is 'guilty'.

Significance testing

How do you decide that the evidence is strong enough - that the distance from source is 'guilty'?

If you roll a dice, the chance of rolling a six is 1/6. If you roll a dice two times, the chance of rolling two sixes is 1/6 x 1/6 = 1/36. If you roll a dice three times, the chance of rolling three sixes is 1/6 x 1/6 x 1/6 = 1/216. If you roll a dice ten times, the chance of rolling ten sixes is 1/60466176 - a very small number! Ten sixes in a row could happen by chance, but is unlikely. If it did happen you might suspect that the dice has been loaded so that it always falls on one side.

Fieldwork results can always be due to chance. The significance level is a measure of how strong the evidence needs to be before the null hypothesis is rejected. Throughout this site, we have used the 5% significance level. For each test we are 95% certain that the result is significant.

Statisical tests

This section summarises the ways in which the different statistcial tests can be used in Geography. For more information on the different statistical tests, see The Seashore. For more information an excellent source developed in FSC Field Centres is Statistics for Geographers.

Mann Whitney U test

• Needs at least 6 replicates per data set
• Tests for the difference between the medians of two sets of data
• The null hypothesis is always
  
  There is no significant difference between the medians of the two sets of data

For detailed instructions see The Seashore.

Theme	Example
Coast: high-energy coasts	Difference in cliff gradient between sites with a beach and sites without a beach
Ice: fluvio-glacial environments	Difference in pebble roundness between two different deposits
Urban: urban inequalities	Difference in deprivation levels between two areas of the same town

Chi-squared test

• Requires the calculation of expected values
• Can be used as a test for differences or as a test for association

For detailed instructions see The Seashore.

Theme	Example
Ecosystem: hydrosere	Testing for an association between two species of plant
Rural: counter-urbanisation	Difference in building age between two villages
Water: flooding	Testing for an association between flood risk and land-use

Spearman's Rank Correlation Coeffiecient test

• Tests the strength of correlation between two variables
• Needs at least 12-15 pairs of data

For detailed instructions see The Seashore.

Theme	Example
Urban: urban rebranding	Correlation between deprivation scores and degree of cloning
Water: downstream changes	Correlation between cross-sectional area and gradient

GO TO NEXT SECTION: Review