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positioning sampling units in the landscape
how do we decide where to put
our sample units when we're determining our sampling
designs? These decisions are made with respect to the need for
good interspresion throughout the population
or area of interest, practical constraints of
time and cost and the need for randomization
there are various approaches to locating sampling
units that exist and we're going to review a few of them now
one of the most commonly used approaches
is simple random sampling. With simple random sampling
each sampling unit has an equal probability
of selection aand the selection of
sampling units is independent so there
is no relationship, if one unit is selected
it does not impact whether another unit is selected
simple random sampling
is best done in relatively small and relatively homogeneous
areas especially if the required sample size
is not overly large. The advantages
of this approach are that data are used to analyze
and it meets assumptions of
independence. Disadvantages are that just by chance you could have poor dispersion
of units and potentially it could be very inefficient
if you're dealing with a relatively large area
there are couple of approaches to
randomly allocating or locating
units the first one is the cooordinate method
in this case we have our area of interest
and we superimpose an x,y coordinate system
over the general area of interest
we then select
x and y coordinates randomly
and then examine where they fall. If the x,y coordinates
fall with in the area we keep it and if it falls
outside of the area we would reject it. One of the disadvantages of
the coordinate method especially if we are using transects is it is possible to locate
x,y coordinate that exists
in the area but they would put the transect outside
the area of interest. If we reject those points we've effectively
reduced or shrunk the area
that were studying to accommodate
those lost units. One possible solution
that may be used
is if an x,y coordinate
puts a transect so that it would go outside
the area of interest you would then
bend it back at an angle
so that you would sample in this
area out here
another approach is the grid cell method. In this case
we overlay the area with virtual grid and the grid cell size and shape is
equal to the size and shape the sampling
units so the possible number of sampling units are displayed
in this grid. We
randomly select grid cells without replacement
and essentially what this does is
allows us to use randomization and independence
to locate our sampling units
now you can see by comparing
these three different possible samples
is that we have variation in dispersion
and we can get, one of the disadvantages is that
we can get under-dispersion where some areas are
over-represented and
other areas under-represented
an alternative type of sampling is restricted random sampling
and this is best applied when the number of samples
must be relatively low in this case
we want good interspersion of units and so what we do is we
we divide the area into segments:
and then within a segment we randomly locate
one sampling unit, in another segment
randomly locate another sampling unit if we have the same number of segments
that we have
required sampling units we then end up
with one sample
per segment. The advantage of this
is we get relatively good interspersion although occasionally
you may run into a situation like this where
two sampling units are relatively close to each other
stratified random sampling
is very commonly used in natural resource
measurements in this case we stratify an
area into subtypes that are based on some kind of a classifying characteristic
oftentimes this can be vegetation type, soil type,
ecological sites, landforms,
anything is not the attribute of
interest
we allocate sampling units to the different strata
and the advantages this are that it's very efficient
we can improve quality information
for the different strata in a variable environment
and that data from each of the stratum
may be analyzed either separately or together. Now there are different
approaches to allocating units to the strata and we will examine
two of those now. Proportional allocation
is where we allocate units to strata
proportional to the relative area of
each stratum relative to the area
the entire population or area of
interest for example if we need
a total sample size of twenty
and the loamy uplands is 50 percent
of the total area we would allocate
10 units to loamy uplands.
Granite Hills is 20 percent, it would get four units
and the draw would get 6 representing 30 percent of the total number of
sampling units. Optimum allocation
is an alternative approach that aims to best
get the best information
for a given level of sampling effort the allocation of
units to the strata is weighted by variability of
each strata so we have to have some information
about the variability of each straum. Let's take an example
and assume that we've done some pilot sampling that indicated that the granite
Hills
ecological site has the highest variability
of the three ecological sites it also has the smallest
relative area only 20 percent and if you recall from the proportional
allocation we would have put
four sampling
units in the Granite Hills
site
so based on our pilot sampling we already know the proportion
of areas and we are you able to determine
some measure of variability the standard deviation
in this case for the different sites and we can see that
loamy upland
has less variability than the granite hills we then
calculate, we multiply the proportion of the area
by the standard deviation. That gives us a value that we then solve for the area
and that we take this proportion, this weighted
proportion and divide that by the sum for the area to come up
with a weighted ratio. we then multiply that
by the
number of sampling units that we're going to put in the
area and what this gives us now
is a new allocation of sampling units to the different strata
that's eightedt by both the proportional
area and variability
ofthese areas in this case
the loamy upland which formerly had
10 would be reduced to five, and the Granite Hills which formerly had four
would be increased to11 because the gravelly
Hills area is more variable it would take
more sampling units to estimate the variability
as well as it does for the
other strata
systematic sampling is commonly used
as well this involves the regular placement sampling units
we divide the area into equal segments and
randomly locate the first unit and then systematically place
others at equal distances
subsequently
in another approach we can use
a combination sampling unit that is a transect
we then randomly
locate the first quadrat and then subsequent quadrats on this transect
are located systematically
from that first quadrat we do the same
the next transect locating a new
starting point for the quadrats that are then then systematically placed
after that first one and we do this repeatedly
until we have all over sampling units allocated.
the advantages of systematic sampling is that it does give good dispersion
and it can be far more efficient than random sampling
potential disadvantages are that we can
under- or over-estimate
the actual the variable of interest if there are some regular patterns
in the vegetation and
because these are not randomly located there is the potential for bias
selective sampling is another approach that we can use
this is sometimes called subjective sampling
in this case sampling is restricted to key areas
or critical areas the focus is on providing information
driven by management issues and so
if we know that we want to
sample specifically in targeted areas
we use selective sampling because
the selection of locations is non-random it does have
a potential for bias that most always be considered
cluster sampling is another approach in this case
we're measuring small scale variation within a cluster of
individuals this is best to do when it's difficult to take a random sample
of the element of interest let's see how this works
we'll randomly locate a belt transect
and then we measure the element of interest
on every individual that occurs with in that belt
transect again we have another belt transect and we
measure every individual that occurs
within
that transect double sampling
is an efficient approach to estimate a variable
when it is costly or difficult
to measure. It incorporates
frequent estimation and infrequent measurement
double sampling is commonly used for production
est so in this example what we have is for
quadrat we have estimated
production in 3 of them so that's the frequent estimation and the fourth one
we estimate and then we clip or harvest all of the
vegetation out of that quadrat that's the infrequent measurement we then
repeat this process
of frequent estimation and infrequent measurement so now what we have
is 12 quadrats that we have estimated
and of those three of them have been estimated
and measured the estimated variable
correlates with the measured variable and if you have a good relationship
between those two
you can use that information to estimate the attribute
of interest
so whether we need good dispersion through the population of
interest we have to consider the practical constraints of
time and cost and the need for randomization
all included with our management and sampling
objectives these are criteria that we
use in order to determine how to position
our sampling units in the landscape
