A Statistical Analysis of Phosphates and Landuse History

1
A Statistical Analysis of Phosphates and Land-use
History A E Austin
Purpose This experiment was designed to test
the correlation between phosphate levels in the
soil and previous land-use history. Such
information is extremely valuable for
archaeology, as it is a non-intrusive method that
could be extremely cost productive in what is
already a tight- budgeted discipline. Our goal
was to determine how useful phosphate analysis
could be to future archaeological survey to save
both time and effort while gaining valuable
knowledge about the previous land-use history of
a site.
Are cultivated and improved pasture land-use
types statistically different?
The Two-sample t Significance test with Unequal
Variance
Background Information The site chosen for our
experiment was historic Pierce Farm, located at
Harvard Forest in Petersham, MA. Pierce Farm was
originally abandoned ca 1850, and has
subsequently gone through a 150 year period of
reforestation. This site is ideal for our
experimental purposes because of the extended
historic knowledge and resources available
regarding its land-use history. Maps have been
made at continuous intervals since its use
displaying areas of known land-use type, and
original farm walls and modern day differences in
forest vegetation allowed us to clearly see the
boundaries between areas of differing
land-use. David Foster, director of Harvard
Forest, features a discussion of the influence
19th century farming had on phosphorous levels in
his book Forests in Time. The process of
farming itself depletes phosphorous levels in the
soil, as it incorporates the rapid removal of
much of the available organic matter. As the
forest regrows, phosphorous levels are quickly
replaced and are, in result, higher than in areas
where no farming previously occurred. Therefore,
we expect the more intensely used land (i.e.
cultivated) to have higher phosphate values than
areas of minimal land-use intensity (i.e.
woodlot) We differentiated between 5 areas of
land-use type Cultivated, Improved Pasture,
Unimproved Pasture, Woodlot, and the Farm House.
This is based on their original differentiation
in available maps of the area, and were chosen
for expected differences in phosphorous levels
between groups.
Ho µ1 µ2 Ha µ1 ? µ2
Ho µ1 µ2 Ha µ1 ? µ2
Ho µ1 µ2 Ha µ1 ? µ2
t (µ1-µ2) v (s12/ n1 s22/ n2)
t (µ1-µ2) v (s12/ n1 s22/ n2)
t (µ1-µ2) v (s12/ n1 s22/ n2)
t -.074 P 94
t .482 P 65
t .216 P 83
The two-sample t Significance test with Unequal
Variance tests to see if two variables have
different means by chance, or because they
represent two different populations. Here, we
are testing the null hypothesis, Ho which states
that cultivated and improved pasture are
statistically the same. In all three cases, the
null hypothesis was supported, which means we
cannot statistically differentiate between the
means of the cultivated and improved pasture
land-use types.
An original farm wall and extreme vegetation
differences demonstrate a sharp divide between
two different land-use types on Pierce Farm.
Does the fact that variability increases as
land-use intensity increases hurt our ability to
discern land-use type based on phosphate value?
Methods and Data We differentiated between 5
areas of land-use type Cultivated, Improved
Pasture, Unimproved Pasture, Woodlot, and the
Farm area itself. Using vegetation and historic
land-use maps, we were able to identify 5
different core areas for each of these land-use
types. We ran a transect through the center of
each of these land-use territories, and took core
samples in 20 meter intervals off of the
transect. One soil core consisted of up to 1
meter of soil which compacted as 40 cm or less.
In the laboratory, soil cores were separated in
5-10 cm intervals in order to test phosphorous
levels at varying depths. For this experiment,
we have phosphorous levels for the first 10 cm of
the core, 15-25 cm, and 30-40 cm where
applicable. By way of an extractant, we were
able to measure presence of phosphate for each
soil sample. Therefore, our raw data reflects
the measurement of the extractants reaction to
the presence of phosphate.
Analysis Of Variance (ANOVA) Discriminant
Analysis
The discriminant analysis is a statistical
procedure whereby we attempt to ascertain where
the line should be drawn between different
categories (this is represented by the shaded
areas). This process looks at variance and takes
into consideration any outlier present. As you
can see, for the extreme ends (House and
Woodlot), the discriminant analysis works well
and allows us to ignore random outliers.
However, both improved and unimproved pasture
demonstrate the difficulty we would have
classifying these groups without prior knowledge
of their land-use history. For the entire data
set, the discriminant analysis correctly
classified 61 of the x-values. Therefore, even
when using ANOVA, we have great difficulty
creating clear boundaries between groups.
The Tuross Group hard at work in the Lab.
Analysis
Why does the house reflect such a large mean and
standard deviation? How does this either
validate or invalidate our claim that phosphate
values are an indicator of land-use type?
Lurking Variables The house phosphate levels
present another problem with using phosphate
analysis to evaluate prior land-use history
lurking variables. In this case, we analyzed the
phosphate levels on mortar and ceramic found
during test pit excavations in and around the
house. Phosphate levels were up to 15 times
greater by weight in the mortar than in our soil
samples.
Conclusion How helpful is using phosphate
analysis toward determining the differences
between previous land-use types?

• The above graphs of our data imply the following
  
• Mean phosphate values increase as land intensity
  increases
• Phosphate levels, in the case of Pierce Farm,
  appear to increase with depth. However, this may
  be misleading as we have a smaller sample size
  for 30-40 cm samples, and so outliers have a
  greater control over the mean.
• The cultivated and improved pasture land-use
  types have similar means and medians, though
  their standard deviations are slightly different.
  It is difficult at this point to determine if
  they are statistically different
• As land-use intensity increases, so does
  variation
• The farm house area reflects a much higher mean,
  median, and standard deviation than any other
  land-use type. This is surprising as land-use
  intensity (i.e. yard maintenance, gardening) in
  the farm area seems both, in the past, less
  intensive and, in the present, less reforested
  than the cultivated areas.

• Phosphate values have several inherent problems
• - They require a significant sample size to be
  properly interpreted
• - They are affected by both past and CURRENT
  land-use history (ie artifact deposits)
• The data often has outliers
• Analysis of Variance can only discriminate
  between extreme land-use differences
• Extreme differences in phosphate levels are
  often also indicated in differences in
• vegetation or through man-made boundaries such
  as walls

Any value lying between .35 and .90 is applicable
as part of the 95 confidence interval for up to
three different land-use types. Only unusually
high values (over 1.95) can be confidently
categorized for one variable.

• Based on the above conclusions, we need to
  address the following problems
• Are cultivated and improved pasture land-use
  types statistically different?
• Does the fact that variability increases as
  land-use intensity increases hurt or help our
  ability to discern land-use type based on
  phosphate value?
• Why does the house reflect such a large mean and
  standard deviation? How does this either
  validate or invalidate our claim that phosphate
  values are an indicator of land-use type?
• Conclusion How helpful is using phosphate
  analysis toward determining the differences
  between previous land-use types?

• We conclude that Phosphate Analysis is too
  limited in the information it provides and the
  accuracy of information given to be useful in
  determining the difference between unknown
  land-use types.