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Stage 4: Data analysis

Stage 4: Data presentation | Statistics

Data presentation

The meres of North Shropshire are thought to have been formed as kettle-hole lakes at the end of the last glacial period approximately ten thousand years ago. With the retreat of the ice sheets that previously covered the area, huge blocks of ice were deposited, and became buried by glacial deposits and pushed down into the sediment. When these blocks eventually melted a series of lakes were formed. Crosemere is one such lake believed to have been formed in this way. In the years since, a gradual infilling of the lake has occurred due to the build up of soil and the presence of vegetation. This has changed the shape of the lake and its surroundings, and enabled a diverse flora to develop.

The lake margins provide excellent examples of the different seral stages of succession that occur within a hydrosere. A transect can be undertaken running from the current water’s edge inland across the old lake bed. The distribution and abundance of vegetation can be sampled systematically along this transect, along with several abiotic factors (including light, wind, humidity, soil pH and soil moisture). At the water’s edge pioneer algal species can be seen on the pebbles that lie just beneath the surface. Moving inland, as the water gets shallower and the soil deeper, a band of common reed (Juncus spp.) and reed mace (Typha latifolia) thrive. Further away from the lake examples of species associated with a wet meadow community can be found, such as water mint (Mentha aquatica), soft Rrush (Juncus effusus) and brooklime (Veronica beccabunga). Buttercup (Ranunculusspp.) and clover (Trifolium repens) appear in the drier grassland areas, and alder carr (Alnus glutinosa) can also be found at various points around the lake.

The kite diagram below shows vegetation changes along an interrupted belt transect at Crosemere:

 

Statistics

Chi-squared test for association

The chi squared test can be used to test the strength of association between two species. Need more information about this test?

Worked example

A continuous belt transect was taken from the edge of the open water to 25m inland. The belt was 5 frame quadrats in width, making a total sample of 100 quadrats. A species list was made for each frame quadrat.

Bottle sedge is a swamp plant which is found at an early seral stage. Marsh bedstraw is a plant of ditches and wet meadows. Within the 100 quadrats, 12 contained both bottle sedge and marsh bedstraw, 3 contained only marsh bedstraw, 29 contained only bottle sedge, and 56 contained neither species. Is there an association between the two species? This quadrat results are summarised in the table below.

	Bottle sedge	No bottle sedge	TOTAL
Marsh bedstraw	12	3	15
No marsh bedstraw	29	56	85
TOTAL	41	59	100

The null hypothesis is that there is no significant association between marsh bedstraw and bottle sedge.

First calculate expected values.

Expected values = (row total x column total) ÷ (grand total)

	Bottle sedge		Marsh bedstraw		TOTAL
	OBSERVED	EXPECTED	OBSERVED	EXPECTED
Marsh bedstraw	12	6.15	3	8.85	15
No marsh bedstraw	29	34.85	56	50.15	85
TOTAL	41	41	59	59	100

Now calculate the sum of (observed - expected)2 ÷ (expected)

chi squared = (12-6.15)2 ÷ 6.15 + (3-8.85)2 ÷ 8.85 + (29-34.85)2 ÷ 34.85 + (56-50.15)2 ÷ 50.15

chi squared = 5.56 + 3.87 + 0.98 + 0.68

chi squared = 11.09

Now compare the calculated value of chi squared against the critical values for (columns of observed values - 1) x (rows of observed values-1) degrees of freedom.

In our example, at the p=0.05 probability level where degrees of freedom = 1, the critical value of chi squared = 3.84.

Since 11.09 > 3.84, the null hypothesis is rejected at the p=0.05 level.

Therefore, we are 95% certain that there is an association between bottle sedge and marsh bedstraw.

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