Square sample areas marked out with a frame Repeatedly place a quadrat at random positions in a habitat Record number of organisms present each time Quadrats Random numbers generated to create coordinates where the quadrat is placed in an area reduces bias ID: 543687
Download Presentation The PPT/PDF document "Quadrats" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1Slide2Slide3
Quadrats
Square sample areas marked out with a frame.
Repeatedly place a quadrat at random positions in a habitat
Record number of organisms present each timeSlide4
Quadrats
Random numbers generated to create coordinates where the quadrat is placed in an area (reduces bias)Slide5
There are two main kinds of data that we can gather for the daisies in
a
field:
Qual
itative: ‘there are
lots of
daisies in the field’
Quant
itative: ‘there are 5087 daisies in the field’
Counting daisiesSlide6
How many daisies in the field?
You have 15 seconds…Slide7
How did you estimate the number of daisies?
Did you try to count them all?
Or did you use another method?
We need a
quantitative
estimate for the number of daisies – it doesn’t have to be perfect but it should be as close as possible to the real number.
Write your first estimate down, then try again, seeing if this will help…
How many did you count?Slide8Slide9
How did you use the grid to estimate the number of daisies? Did it help?
There are 78 daisies
If you were asked to count the number of daisies in the school field, it would be impractical to count each one.
How could you use the grid method to get an accurate, reproducible estimate?
Use the following steps:
Select at least three quadrats and count how many daisies are in each
(
eg
4, 8, 3)
Then find the mean number per quadrat
(4 + 8 + 3 = 15. 15/3 = 5 daisies per quadrat)
Multiply the mean by the number of quadrats that would fit into the field to get your estimated total number of daisies. (5 x 20 = 100 daisies estimated in the field)Is your estimate the same?Slide10Slide11
There were 103 daisies in the field.
How close were you?
How many daisies were there? Slide12
They only work for immobile/slow moving populations.
The more data you collect, the more reproducible your result…the more samples the better!
Quadrats should be placed randomly to avoid bias.
Quadrats: Top TipsSlide13
Chi-squared testSlide14
Chi Squared Test (stats test)
Test for an association between the species
If species always are in the same quadrat (positive)
If species are never in the same quadrate (negative)Slide15
Hypotheses
H
0
= null hypothesis = two species are distributed independently (there is no association)
H
1
= two species associated (either positively or negatively)Slide16
My results
Species
Frequency
Heather only
9
Moss Only
7
Both species
57
Neither species
27
Total samples100Slide17
Heather
absent
Heather
present
Total
Moss
absent
27
9
36
Moss present
75764
Total
34
66
100
Start with a contingency tableSlide18
Expected values
Expected =
row total x column total
grand total
Heather
absent
Heather
present
Total
Moss
absent(34x36)/100 = (66x36)/100
=
36
Moss present
(34x64)x100
=
(66x64)/100
=
64
Total
34
66
100Slide19
Expected values
Expected =
row total x column total
grand total
Heather
absent
Heather
present
Total
Moss
absent(34x36)/100 = 12(66x36)/100
= 24
36
Moss present
(34x64)x100
= 22
(66x64)/100
= 42
64
Total
34
66
100Slide20
Degrees of Freedom
(m – 1) x (n – 1)
m
= number of rows
n
= number of columns
(measure of how many values can vary)Slide21
Degrees of Freedom
(m – 1) x (n – 1)
m
= number of rows = 2
n
= number of columns = 2
(2 – 1) x (2 – 1)
= 1 x 1
Degrees of freedom for this test = 1Slide22
Critical region
Find critical region from a table of chi-squared values
How sure you can be about your
results
Significance level of 5% (0.05
) is the maximum to be regarded as significant.Slide23Slide24
Critical region
Find critical region from a table of chi-squared values
Significance level of 5% (0.05)
For this test = 3.841Slide25
Chi Squared Test
χ
2
=
(O – E)
2
E
(O – E)
2
E
(O – E)
2
E
(O – E)
2
E
(O – E)
2
ESlide26
Chi Squared Test
χ
2
=
(O – E)
2
E
(27
–
12)
2
12
(7
–
22)
2
22
(9
–
24)
2
24
(57
–
42)
2
42Slide27
Chi Squared value
18.75 + 10.23 + 9.38 + 5.36
Chi squared
value =
43.72
Slide28
Which hypothesis
Chi squared
value =
43.72
Critical region = 3.841
Compare calculated chi squared value to critical region
Higher than critical region = reject null hypothesis (there is an association)
Equal to or lower than critical region = keep null hypothesis (there is no association)Slide29
Since the x
2
value of
43.72
is greater than critical value of 3.841,
the null hypothesis is
rejected
.
Therefore, we can be 95% sure that there is a relationship between the heather and moss.Slide30
In pairs complete the random sampling.
Choose 2 of the plants to see if there is an association.
Do 100 throws and record your results.
Work through the sheet to complete the chi squared stats test.
This
powerpoint
is on my website if you need to refer back to it!
Your turn!