GEOG 3810
Morphological Measurements
of Fossils in Manitoba
Quantitative Research Methods in Geography: Take Home Assignment
Delaney Brooks
7694719
Morphological Measurements of Fossils in Manitoba
Delaney Brooks
Part A: Introduction and Sampling Methods
The excavation of a large number of geological sites in Manitoba have shown a
reoccurring appearance of many specimens of a specific fossil type. The morphological
measurements of the fossils excavated is important in comparing the differences between
Manitoba geological sites. The intention of this project for the Manitoba Government by
AZZOCA Consulting is to determine whether the morphological measurements, in centimeters,
of a specific fossil type that has been excavated from geological Site A is greater than the
morphological measurements (cm) of the same fossil type excavated from geological Site B,
both in Manitoba.
For this study, the target population is all of the fossils of the particular type of fossil. The
target area is all of the geological sites in Manitoba. The study will be on the observations of
only two sites, which is known as the sampling area. Commonly excavated fossils in Manitoba
include: Mosasaurs, Plesiosaurs, sharks, a variety of fish, turtles, birds, and squid (Canadian
Fossil Discovery Centre, 2015). Although there are many geological sites in Manitoba, only two
have been selected for the comparison. The geological sites that will be selected for the study
may have any variety of the ancient animals listed above. The samples collected (the sampling
population) are from specific locations; therefore, a spatial sampling method shall be used. The
most effective sampling method will be a Stratified Point Sample.
To retrieve samples, the sites being used will each be divided into sub-areas, or smaller,
more manageable sections. The number and size of the sub-areas will be dependent on the
sample size needed and the size of the sites, respectively. There may be a difference in sample
size for Site A and Site B. Once the sample sizes have been identified, each site will be divided
into the same number of sub-areas as sample sizes are needed; each sub-area in a site being of
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Morphological Measurements of Fossils in Manitoba
Delaney Brooks
equal size. This creation of sub-areas, or subsections, will ensure that fossils used in the study are
selected from all areas of the geological sites. Next, one fossil will be randomly selected from
each sub-area. This will result in a random sampling of fossils excavated. As well, the population
will be accurately represented from all areas of the two geological sites.
Sample size is important for representing the population. As a general rule, 30 is an ideal
minimum sample size. However, as 30 may be more or less than the necessary number of
samples taken, the actual sample sizes needed for Site A and Site B will be calculated from the
data in Table 1. The sample size must be calculated for both Site A and Site B as a representation
of fossils is needed from both geological sites to fulfill our hypothesis test. Before the sample
sizes can be calculated, the margin of error (E) that the study is willing to accept must be
calculated. The error for Site A and Site B are shown below:
Site A
Site B
𝜎2
𝜎2
𝐸 = 𝑍√ 𝑛
𝐸 = 1.96√
𝐸 = 𝑍√ 𝑛
(0.7729)2
𝐸 = 1.96√
10
𝐸 = 0.4790
(0.7182)2
10
𝐸 = 0.4451
To find the sample size for each site, we will use the margin of error. The calculations for
sample size of Site A and Site B are as follows:
Site A
Site B
𝑍𝑠
𝑍𝑠
𝑛 = ( 𝐸 )2
𝑛= (
𝑛 = ( 𝐸 )2
(1.96)(0.7729) 2
)
0.4790
𝑛= (
𝑛 = 10.002 = 11
(1.96)(0.7182) 2
)
0.4451
𝑛 = 10.002 = 11
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Morphological Measurements of Fossils in Manitoba
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The calculations show, for an accurate representation of the population, a sample size of
eleven will suffice for both Site A and Site B, with a total of twenty two samples. Although the
calculations show that the sample size would be closer to ten, the sample size must be rounded
up to ensure an accurate representation. The minimum necessary sample size for both Site A and
Site B are much smaller than 30. Using the calculations to find the needed sample sizes allows
for a more cost effective experiment. The more samples that are gathered results in a higher cost
and a longer time commitment to the study.
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Morphological Measurements of Fossils in Manitoba
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Part B: Descriptive Statistics
Table 2 The Descriptive Statistics of the data from Site A and Site B.
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Site_A
10
1.32
3.64
2.0850
.77292
Site_B
10
1.30
3.78
1.8900
.71821
Valid N (listwise)
10
Table 2 (above) exhibits the descriptive statistics from the data provided of
morphological measurements of the selected type of fossil excavated from geological Site A and
Site B. The sample size, denoted as N, is the same for Site A and Site B at 10 samples. It is
shown that the minimum morphological measurements for both sites are very close; Site A with
a minimum measurement of 1.32 and Site B with a minimum measurement of 1.30. The
difference between the maximum morphological measurements of Site A and Site B are greater
at 3.64 and 3.78, respectively. The mean, or average, of the morphological measurements of the
specific fossil type at each site varies greatly. The mean of Site A is slightly larger, at 2.0850,
than the mean of Site B, at 1.8900. The difference between the two means appears to coincide
with the hypothesis stating the morphological measurements of the specific fossil type is larger at
Site A than Site B. However, statistically the mean of Site A and Site B may be equal. Testing
the hypothesis would have to occur to conclude whether the mean of Site A is in fact greater than
the mean of Site B. The standard deviation of Site A and Site B are also fairly close numerically.
The standard deviation is the amount of variation in a data set. Therefore the standard deviation
of Site A, being 0.77292, is more variable that the standard deviation of Site B, at 0.71821.
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Morphological Measurements of Fossils in Manitoba
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Figure 1 The boxplots representing the descriptive statistics from Site A and Site B.
Figure 1 (above) demonstrates visually the descriptive statistics in the form of boxplots.
The boxplot on the left is representing the morphological measurements data of Site A and the
boxplot on the right represents the morphological measurements data of Site B. Although Site B
has a higher maximum value, Site A has a larger range. This is due to the maximum value of Site
B (3.78) being an outlier. An outlier is a value that is outside of the standard deviation of the
dataset. The outlier may be a result of an inaccurate measurement. In a boxplot the median of the
data is shown as a line on the inside of the box. It is seen that the median of Site A is skewed to
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Morphological Measurements of Fossils in Manitoba
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the right, meaning the majority of the dataset points are of a smaller length (in centimeters). Site
B has a median that is roughly centre, making it appear to be normally distributed, or equal to the
mean. It is impossible to know whether Site A or Site B are truly normally distributed by only
observing a boxplot. The interquartile range is the middle fifty percent of the data, making up the
box part of a boxplot. Site A has a much larger interquartile range than Site B. This means the
middle fifty percent of the data in Site A is spread over a much larger range than Site B. The
whiskers of the boxplot represent the lower twenty-five percent and upper twenty-five percent of
the data. It is observed that Site A has the upper twenty-five percent of its data spread over a
wider range, also resulting in a larger range. The upper and lower twenty-five percent of data for
Site B is spread over a smaller range of measurements, contributing to the smaller range.
Overall, by observing the boxplots and the descriptive statistics, some inconclusive
assumptions can be drawn about the morphological measurements of the selected fossil type in
the two geological sites in Manitoba. The boxplots and descriptive analysis show that the data
from Site A is skewed to the right, has a higher mean, and larger range and interquartile range
than the data from Site B. It is also observed that Site B has an outlier which may be due to a
misrepresentation of data. However, to have conclusive evidence to answer the hypothesis of
whether the morphological measurements at Site A are greater than the morphological
measurements at Site B, hypothesis testing will have to occur.
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Morphological Measurements of Fossils in Manitoba
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Part C: Methods and Results
As the intent of this study is to determine if the morphological measurements of a
specific fossil type in Manitoba is greater at Site A than Site B, a Two Sample Difference test
will be used. However, before the hypothesis can be tested, the data for Site A and Site B must
be tested to observe whether it meets the assumptions for a parametric or non-parametric test.
The data for both Site A and Site B must be tested for normal distribution. This was done by
applying a Kolmogorov-Smirnov test to both datasets. In the test, a significance level of 95%
(0.05) is used, meaning we are 95% confident that the sample mean falls within two standard
deviations of the true mean. The results are shown below in Table 3 and Table 4.
Table 3 The Kolmogorov-Smirnov Test results from the fossil data of Site A.
Tests of Normality
Kolmogorov-Smirnova
Statistic
Site_A
df
.244
Sig.
10
Shapiro-Wilk
Statistic
.094
df
.850
Sig.
10
.058
Table 4 The Kolmogorov-Smirnov Test results from the fossil data of Site B.
Tests of Normality
Kolmogorov-Smirnova
Statistic
Site_B
.306
df
Sig.
10
.008
Shapiro-Wilk
Statistic
.725
df
Sig.
10
.002
The p-value for Site A is 0.094 which is larger than the significance level (0.05) meaning
the data from Site A is normally distributed. Therefore Site A meets all the assumptions of a
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Morphological Measurements of Fossils in Manitoba
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parametric test; the data is normally distributed, randomly sampled, and is interval/ratio data.
The p-value for Site B is 0.008 which is much smaller than the significance level of 0.05 and
therefore there will be less than a 5% chance of making a type one error. This results in the data
from Site B being non-parametric; the data is not normally distributed, it is randomly sampled,
and is interval/ratio data. Due to Site A being parametric and Site B being non-parametric, a nonparametric test will be run to test the hypothesis.
The null hypothesis of the study is stated as the morphological measurements of the fossil
type at geological Site A in Manitoba is equal to the morphological measurements of the fossil
type at geological Site B in Manitoba. The alternative hypothesis is stated as the morphological
measurements of the fossil type at geological Site A in Manitoba is greater than the
morphological measurements of the fossil type at geological Site B in Manitoba. A MannWhitney test is performed to determine whether the null hypothesis will be rejected or not
rejected. The Mann-Whitney test has its own set of assumptions; the samples must have a similar
shape of distribution, the data must be ordinal, and the two samples being used must be
independent of one another and be randomly sampled. The datasets meet these assumptions and
therefore the test can be run. This significant level for the test is 0.05 and the confidence interval
will be set at 1.65 due to the alternative hypothesis being a one-tailed test (greater than). The
outcome of the test is below in Table 5:
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Morphological Measurements of Fossils in Manitoba
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Table 5 The Mann-Whitney Test results for the difference test of Site A and Site B.
Table 5 clearly states that the null hypothesis will not be rejected. This is due to the pvalue (0.631) being larger than the significance level (0.05). Therefore, the Mann-Whitney Two
Sample Difference test proves the null hypothesis. The Mann-Whitney Two Sample Difference
test can also be calculated. The calculations use the critical value and coincides with the p-value.
When the calculations are done for the datasets of Site A and Site B, the test statistic is -0.5291
which is smaller than the significance level of ±1.65.
The Mann-Whitney Two Sample Difference Test and the Kolmogorov-Smirnov Test may
be inaccurately depicting the population of the fossils excavated. The sample sizes used in the
tests is ten which is lower than the minimum ideal sample size of eleven. As well, the boxplots
made it appear as though the shape of the distribution is drastically different between Site A and
Site B. The study was limited by the low number of sample sizes for both Site A and Site B.
In conclusion, and as an answer to the Minister, AZOCCA Consulting has confirmed the
fossils excavated at the geological Site A in Manitoba are not greater in morphological
measurement than the fossils excavated in the geological Site B in Manitoba. This is only true
when using the dataset that was available and may differ if there was fewer limitations.
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References
Canadian Fossil Discovery Centre. (2015). General Information. Retrieved from Canadian Fossil
Discovery Centre: www.discoverfossils.com
Quanititative Research Methods in Geography. (2015). Lecture Notes. John Iacozza. Winnipeg,
Manitoba. (University of Manitoba).
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