Ecology
Lab (BIO357)
Lab
One (Part Two)
Sampling Design
In
this lab we are going to further define the measurements we are going to make
based upon the hypotheses we stated in the previous lab.
Variable
A variable
is a measured feature of the natural world.
We use a variety of tools to help us measure variables.
It is useful to think of variables as one of two types: either continuous
or discrete. Continuous variables show gradual and incremental variation
and are assumed to have an infinite number of values. Many of the variables we study in biology are continuous.
Measures such as length, area, volume, weights or temperature are all
examples. Discrete variables that
have only certain fixed numerical values, with no intermediate values possible
in between and can be recorded as integers.
Measures such as the number of bristles on the leg of a flea, or the
number of leaves on a stem, or the number of plants or animals in a given area
are all examples. The type of
variable will become important when we start thinking about what statistical
tests to perform.
In
Part One, we generated a number of null and alternative hypotheses.
I have listed them below, along with a few others that were mentioned but
not written down. For each one,
circle whether it is a continuous or discrete variable.
Null
hypotheses: there is no difference between forest and grassy areas in:
H0:
Air temperature
Continuous or
Discrete
H0:
Soil temperature
Continuous or
Discrete
H0:
Soil Moisture
Continuous or
Discrete
H0:
Soil texture
Continuous or
Discrete
H0:
Soil composition
A:
pH
Continuous or
Discrete
B.
Nitrate
Continuous or
Discrete
C.
Phosphate
Continuous or
Discrete
D.
Potassium
Continuous or
Discrete
E.
Organic Material (Humus)
Continuous or
Discrete
H0:
Amount of sunlight
Continuous or
Discrete
H0:
Amount of bare space
Continuous or
Discrete
H0:
Number of plants (abundance)
Continuous or
Discrete
H0:
Number of different plants (diversity)
Continuous or
Discrete
H0:
Number of animals (abundance)
Continuous or
Discrete
H0:
Number of different animals (diversity)
Continuous or
Discrete
Accuracy
and Significant Figures
Accuracy
is how close a measurement is to the actual value of the variable being
measured. Precision
is not a synonymous term, but refers to the closeness to each other of repeated
measurements of the same quantity. Particularly
when dealing with continuous variables, but also sometimes with discrete
variables, we need to be aware of the accuracy of our measurements.
The number of significant figures
denotes this. I am assuming you all
remember how to work with significant figures, so, will not bore you here. But, I will make an important note to bear in mind.
Calculators and computers typically yield results with more significant
figures than are justified by the data. A
good practice to avoid rounding errors would be to retain all significant
figures for all steps until the last in a series of calculations.
On obtaining the final result to round off to the appropriate significant
figure. Again, here are the null
hypotheses we are working with. For
each, write the measurement we are going to make.
Null
hypotheses: there is no difference between forest and grassy areas in:
H0:
Air temperature
Measure: ______________________
H0:
Soil temperature
Measure: ______________________
H0:
Soil Moisture
Measure: ______________________
H0:
Soil texture
Measure: ______________________
H0:
Soil composition
A:
pH
Measure: ______________________
B.
Nitrate
Measure: ______________________
C.
Phosphate
Measure: ______________________
D.
Potassium
Measure: ______________________
E.
Organic Material (Humus)
Measure: ______________________
H0:
Amount of sunlight
Measure: ______________________
H0:
Amount of bare space
Measure: ______________________
H0:
Number of plants (abundance)
Measure: ______________________
H0:
Number of different plants (diversity)
Measure: ______________________
H0:
Number of animals (abundance)
Measure: ______________________
H0:
Number of different animals (diversity)
Measure: ______________________
Frequency
Distributions
The more samples we take, the
more we may find our measurements cluster together.
Frequency Distribution shows us how the data cluster together.
There are a number of standard frequency distributions.
The most commonly used one is the Normal
Distribution. In a normal
distribution, most of the measurements will cluster around the mean.
As you move away from the mean (either higher or lower) the number of
measurements gets smaller and smaller. In
fact, if our data is distributed such as we see in a normal distribution (i.e.
normally distributed) then we can specify how probable our measurement is to the
actual value. Also, if we assume a
normal distribution we can specify how likely we are to make that measurement.
A lot of the statistics we are going to use in this class makes use of a
normal distribution. More on that
later.
Populations
and Samples
Our ultimate goal is to test hypotheses about our
observations. Therefore, we need to
make as many observations or measurements as possible.
The Population (universe)
represents the entire collection of measurements about which one wishes to draw
conclusions. In most situations, it
is not practical to measure the entire population, so we typically take a sample,
or subset, of the population. Ideally,
our samples should be an unbiased set of observations from the universe and we
should sample in such a way that all portions of the universe have an equal
chance of being represented. This
will allow us to make valid inferences about the natural world.
Such a strategy of unbiased sampling is called Random Sampling. This
is often done by assigning each measurement or member of a population a unique
number, and then drawing a sample by choosing a set of numbers at random.
The table at the back of this lab provides 10,000 random digits.
Each digit from 0 to 9 has an equal and independent chance of appearing
anywhere in the table. Likewise,
each combination of two digits, from 00 to 99, is found at random as is any
number from 000 to 999. In
addition, there are a number of websites dedicated to random numbers and their
generation. Two very good ones are:
www.random.org and www.randomizer.org.
There are a number of different
ways to make random measurements. Probably
the most affective way is to lay out a grid and randomly choose locations within
the grid in which to take samples. Here
are the steps we are going to take in the field:
1.
Lay out two 10-meter tape measures at right angles to each other.
2.
Each meter on the two tapes, starting from where they cross will be
represented by a number 0 to 9. This
will make a grid.
3.
Choose ten pairs of random numbers.
The first number will represent the distance on one tape measure and the
second will represent the distance on the second tape measure
4.
In the field, we will use flags to identify each square within the grid
that we will take measurements and samples from.
For the last part of today’s
exercise, we will break into two groups. One
group will be in charge of choosing numbers for the forested area, and the other
group for the grassy area. Make
sure you record the random number pairs from the other group.
Also, bring this with you on the field trip.
Grassy Area Forested Area
Random
Numbers
Random Numbers
1.
_____ , ______
1. _____ , ______
2.
_____ , ______
2. _____ , ______
3.
_____ , ______
3. _____ , ______
4.
_____ , ______
4. _____ , ______
5.
_____ , ______
5. _____ , ______
6.
_____ , ______
6. _____ , ______
7.
_____ , ______
7. _____ , ______
8.
_____ , ______
8. _____ , ______
9.
_____ , ______
9. _____ , ______
10.
_____ , ______
10. _____ ,
______
Sample
Design for Field trip