Quadrat sampling

1

• Quadrat sampling
• Quadrat shape
• Quadrat size
• Lab

2
Quadrat shape
1. Edge effects
?
best
worst
3
Quadrat shape
2. Variance
4
5
4
1
best
4
Quadrat size
1. Edge effects
?
?
?
?
?
?
3/5 on edge
3/8 on edge
best
worst
5
Quadrat size
1. Edge effects
Density
Quadrat size
6
Quadrat size
2. Variance
Low variance
High variance
7
Quadrat size
So should we always use as large a quadrat as
possible?
Tradeoff with cost (bigger quadrats take longer
to sample)
8
Quadrat lab What is better quadrat shape? Square
or rectangle? What is better quadrat size? 4, 9
,16, 25 cm2 ? Does your answer differ with tree
species (distribution differs)?
22cm
16 cm
9

• Quadrat lab
• Use a cost (time is money) benefit (low
  variance) approach to determine the optimal
  quadrat size for 10 tree species.
• Hendricks method
• Wiegerts method
• Cost
• total time time to locate quadrat time to
  census quadrat
• Benefit
• Variance

10
Quadrat lab Quadrats can also be used to
determine spatial pattern! We will analyze our
data for spatial pattern (only) in the computer
lab next week (1-2pm).
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Quadrat lab points for discussion 1. You need
to establish if any species shows a density
gradient. How will you do this? 2. You will have
a bit of time to do something extra what would
be useful? Group work fine here. 3. Rules -if
quadrat doesnt fit on map -if leaves are one
edge of quadrat
12
Regression

• Problem to draw a straight line through the
  points that best explains the variance

13
Regression

• Problem to draw a straight line through the
  points that best explains the variance

14
Regression

• Problem to draw a straight line through the
  points that best explains the variance

15
Regression

• Test with F, just like ANOVA
• Variance explained by x-variable / df
• Variance still unexplained / df

Variance explained (change in line lengths2)
Variance unexplained (residual line lengths2)
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Regression

• Test with F, just like ANOVA
• Variance explained by x-variable / df
• Variance still unexplained / df

In regression, each x-variable will normally have
1 df
17
Regression

• Test with F, just like ANOVA
• Variance explained by x-variable / df
• Variance still unexplained / df

Essentially a cost benefit analysis Is the
benefit in variance explained worth the cost in
using up degrees of freedom?
18
Regression example

• Total variance for 32 data points is 300 units.
• An x-variable is then regressed against the data,
  accounting for 150 units of variance.
• What is the R2?
• What is the F ratio?

19
Regression example

• Total variance for 32 data points is 300 units.
• An x-variable is then regressed against the data,
  accounting for 150 units of variance.
• What is the R2?
• What is the F ratio?

R2 150/300 0.5 F 1,30 150/1 15
300/30
Why is df error 30?