Add correlation coeeficient to this assignment (Ds to soil temp, air temp or humidity)
Your values for X and Y should come in pairs. First of all calculate Xbar and Ybar: these
are the means of the X's and the Y's respectively, so for Xbar, add up your values for X and
divide by 8. Similarly, for Ybar, add up your values for Y and divide by 8.
Next, we calculate Sx and Sy, the sample standard deviations of X and Y. To calcuate Sx,
we proceed as follows:
for each X value, calcuate
(X - Xbar)^2
(the square of X - Xbar), add all these up and then divide by 7; taking the square root of
your result yields Sx. The procedure for Sy is analagous.
Now we come to the final hurdle. For each pair of X and Y-values, calculate
(X - Xbar).(Y - Ybar)
(ie. multiply (X - Xbar) by (Y - Ybar)), then add up the results you get for all the pairs, and
then divide by
7.Sx.Sy,
(ie. the product of Sx, Sy and (n-1) = 8 -1 = 7). This gives you the correlation coefficient.
Positive correlation: If x and y have a strong positive linear
correlation, r is close
to +1. An r value of exactly +1 indicates a perfect positive fit. Positive
values
indicate a relationship between x and y variables such that as values
for x increases,
values for y also increase.
Negative correlation: If x and y have a strong negative linear
correlation, r is close
to -1. An r value of exactly -1 indicates a perfect negative fit. Negative
values
indicate a relationship between x and y such that as values for x increase,
values
for y decrease.
No correlation: If there is no linear correlation or a weak linear
correlation, r is
close to 0. A value near zero means that there is a random, nonlinear
relationship
between the two variables
Note that r is a dimensionless quantity; that is, it does not depend on the
units
employed.
A perfect correlation of ± 1 occurs only when the data points all lie exactly
on a
straight line. If r = +1, the slope of this line is positive. If r = -1, the slope of
this
line is negative.
A correlation greater than 0.8 is generally described as strong, whereas a
correlation
less than 0.5 is generally described as weak. These values can vary based
upon the
"type" of data being examined. A study utilizing scientific data may require a
stronger
correlation than a study using social science data.
Calculator: http://easycalculation.com/statistics/correlation.php
Correlation Co-efficient :
Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])]
where
N = Number of values or elements
X = First Score
Y = Second Score
ΣXY = Sum of the product of first and Second Scores
ΣX = Sum of First Scores
ΣY = Sum of Second Scores
ΣX2 = Sum of square First Scores
ΣY2 = Sum of square Second Scores
Correlation Co-efficient Example: To find the Correlation of
X Values Y Values
60
3.1
61
3.6
62
3.8
63
4
65
4.1
Step 1: Count the number of values.
N=5
Step 2: Find XY, X2, Y2
See the below table
X
Y
Value Value
60
3.1
61
3.6
62
3.8
63
4
65
4.1
X*Y
60 * 3.1 =
186
61 * 3.6 =
219.6
62 * 3.8 =
235.6
X*X
60 * 60 =
3600
61 * 61 =
3721
62 * 62 =
3844
63 * 63 =
63 * 4 = 252
3969
65 * 4.1 = 65 * 65 =
266.5
4225
Y*Y
3.1 * 3.1 =
9.61
3.6 * 3.6 =
12.96
3.8 * 3.8 =
14.44
4 * 4 = 16
4.1 * 4.1 =
16.81
Step 3: Find ΣX, ΣY, ΣXY, ΣX2, ΣY2.
ΣX = 311
ΣY = 18.6
ΣXY = 1159.7
ΣX2 = 19359
ΣY2 = 69.82
Step 4: Now, Substitute in the above formula given.
Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 (ΣY)2])]
= ((5)*(1159.7)-(311)*(18.6))/sqrt([(5)*(19359)-(311)2]*[(5)*(69.82)(18.6)2])
= (5798.5 - 5784.6)/sqrt([96795 - 96721]*[349.1 - 345.96])
= 13.9/sqrt(74*3.14)
= 13.9/sqrt(232.36)
= 13.9/15.24336
= 0.9119
AP Environmental Science
Wheeler High School
Mr. Walstead
Leaf Litter Biodiversity
(adapted from Dr. Kim Largen’s at George Mason University EVPP 111 lab write up)
________________________________________________________
Background
Species diversity is a
characteristic that is unique to a
community level of biological
organization. The biodiversity in
different communities has been
severely affected by human
activities.
The number of species in a
community is very important.
There seems to be evidence that the
greater the species diversity, the
more stable the community.
When diversity is low, the community
is less stable. A community with low
diversity is less able to rebound from
severe
disturbance such as pollution and
habitat disruption.
The purpose of this lab is to
measure the biodiversity of
organisms found in a sample of leaf
litter collected on campus. A
Berlese funnel apparatus will be
used to separate from the leaf
litter the small organisms dwelling
within it. The organisms will then
be organizing into similar taxonomic
categories and counted. Finally, the
species diversity of the leaf litter
sample will be calculated.
________________________________________________________
Procedure
Day 1
1. Collect a leaf litter sample as
follows:
a. on a patch of the forest floor,
envision a square that is
approximately 30cm on each
side (roughly 1 square foot)
b. from this area, collect all of the
leaf litter to the top layer of
soil-like material (down to a
depth of approximately 1.5cm,
to the extent that you can
remove it with your fingers)
and place into your plastic
collection bag
2. Record the following information
at the site:
a. Soil Temperature
b. Air Temperature
c. Relative humidity
d. Description of the litter (depth,
type, dry/moist, etc)
e. Description of the area (Light
penetration/canopy, types of
vegetation, land features, soil
type, etc.)
f. Sketch the area (from a birdseye view)
3. Return to the lab.
Day 1 (cont)
4. Obtain a Berlese funnel
apparatus. Place a piece of
marking tape on the beaker and
label it with your names.
5. Place a small volume of methanol
in the bottom of the beaker
6. Place the funnel in the top of the
plastic container and place the
screen plug in the base of the
funnel.
7. Place the leaf litter that you
collected in the woods into the top
of the funnel. As the leaf litter
dries, from the top down, the
organisms in the leaf litter will
migrate downward (trying to stay
in the moist litter) and will
eventually fall into the methanol
which will preserve them for later
observation.
Day 2
1. Discard the leaf litter from the
funnel of your Berlese apparatus.
PLEASE BE SURE
THAT YOU DO NOT THROW
AWAY THE SCREEN PLUG
FROM THE BOTTOM OF THE
FUNNEL!!!!!!!!!!!
2. Obtain a dissecting microscope
3. Pour the methanol from the
bottom of the container, which
now contains the organisms from
the leaf litter, into one or more
petri dishes (depending on how
many in your group will be
assisting with identification).
4. Observe the organisms in the petri
dish under a microscope.
a. Separate the sample into piles
of like organisms within the
petri dish.
b. Determine the total number of
each type of organism
identified in your group's
sample. Record this data in
Table 1 in the column headed
“absolute abundance”
________________________________________________________
Data Analysis
1. Determine the relative
abundance of each individual
species and record in Table 1
(you determined the absolute
abundance of each species by
counting the number of individuals
of each different species).
Relative abundance compares the
number of organisms of a
particular species with the total
number of organisms found in the
sample. Relative abundance of a
species in a sample is calculated
by dividing the number of
individuals of that species by the
total number of individuals in the
entire sample. An example
calculation follows:
Relative abundance = ni / N
ni = actual number of individuals of
species i
N = the total number of individuals of
all types collected in sample
Example data and calculations for
relative abundance:
2. Determine the diversity of your
sample using Simpson’s Index
of Diversity and record in Table
1. The following example
illustrates how to calculate
Simpson's Index of Diversity:
Ds = 1 - {50(49) + 25(24) + 10(9)}
85(84)
Ds = 1 - (Σni(ni-1) / N(N-1))
Ds values closer to 0 = low
diversity
Ds = closer to 1 = greater diversity
Ds = 1 - 3140 / 7140
Ds = 1 - 0.44
Ds = 0.56
Record your group's value for
Simpson's Index of Diversity in Table
2 and on the transparency (or
blackboard) Record other groups'
values for Simpson's Index of
Diversity and location information in
your Table 2.
________________________________________________________
Sample Table 1
Sample Table 2
This is a formal lab report. Be sure you include the following:
Introduction (10pts) – 1-2 Paragraphs discussing types of biodiversity, why we should
care about it, and factors that influence it. (A hypothesis is not necessary)
Materials and Method (5pts) – Describe the procedure in paragraph form.
Results (10pts) –
 Site description and sketch
 3 Scatter Plots and Correlation
 Properly labeled tables 1 & 2
Coefficients for (air temp. vs. Ds,
 Information summarized in a
soil temp vs. Ds, & humidity vs. Ds)
paragraph.
Discussion (10pts) - 1-2 paragraphs that explain the “WHY" of your results. Is their a
correlation of Ds to Air temp, soil temp. or humidity?
References (5 pts) – Any source used in the introduction or to clarify an explanation in
the discussion (minimum 2)
Layout/Neatness (5pts)
Conventions of writing (5 pts)
**See the Formal Lab Report Guide for Complete Guidelines**
Identifying Arthropods
Major External Characteristics
1. Exoskeleton containing chitin
2. Body bilaterally symmetrical
3. Body segments grouped into specialized regions (= tagmata, plural)
4. Jointed appendages
5. These jointed appendages variously specialized for feeding, locomotion,
sensing
Key to the Adults of the Common Classes of Arthropoda
1a. Two pairs of antennae (one pair may be reduced, difficult to see);
Number of legs variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Class Crustacea, go to 2
1b. One pair of antennae or none. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2a. Two distinct body regions (cephlothorax and abdomen);
Five pairs of thoracic legs. . . . . . . . . . . . .. . . crayfish, lobsters, shrimp; Order Decapoda
2b. Three distinct body regions (head, thorax, abdomen);
Seven pairs of thoracic legs . . . . . . . . . . . . sowbugs, pillbugs, roly-polys; Order Isopoda
3a. No antennae; Two distinct body regions (cephlothorax and abdomen);
Four pairs of legs;. . . . . . . . . . . . . . . . . . spiders, ticks, scorpions, etc; Class Arachnida
3b. One pair of antennae. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4a. Three distinct body regions (head, thorax, abdomen);
Three pairs of thoracic legs. Wings present or absent. . . . . . . . . . . . . . Class Insecta
4b. Two distinct body regions (head and trunk). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
5a. One pair of legs per trunk segment. . . . . . . . . . . . . . . . . . . . . . centipedes; Class Chilopoda
5b. Two pairs of legs per trunk segment. . . . . . . . . . . . . . . . millipedes; Class Diplopoda
Arachnida
Isopoda
Chilopoda
Diplopoda
Insecta