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BIOL208 Study Guide - Final Guide: Carbon Cycle, Sympatry, Density Estimation

Biology (Biological Sciences)
Course Code
Jessamyn Manson
Study Guide

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LAB 1: Statistical analyses of sampling data
Intro: The Scientific Method
Systematic method of inquiry
Involves observations, development of hypotheses, collection of empirical data,
and the testing of hypotheses.
Hypothesis development
Hypothesis: supposition to explain an observed phenomenon.
Must be falsifiable (can be refuted).
Different types of hypotheses
Working hypothesis: used as part of the scientific method to execute experiments
and then examine the results. It is provisionally accepted that is used for further
Null hypothesis (AKA Statistical hypothesis): the statement that the phenomenons
that you were examining are NOT related; results may be the product of random
chance events.
Make a prediction and then test it.
Your degree of confidence about the difference between control and treated
groups depends on the: 1. Magnitude of difference between groups
2. Variability of the measurements within each group
Experimental and statistical design
Samples: subsets of populations (statistical, not necessarily biological
populations) for which a generalization about some attribute is desired.
Catch a fraction of the population, selected at random from all available
individuals, and extrapolate the measurements to the population as a whole.
Measures of central tendency and spread
Frequency distribution can be graphed into a histogram.
Mean (average)
Mode (most common observation)
Median (middle observation)
* If data fit perfect normal distribution, mean=mode=median
Range (largest value – smallest value)
Variance (s2)
* Samples from diff. populations ma have the same central tendencies,
but different variances.
Standard Deviation (s)
Parametric statistics and the normal distribution
Parametric statistics assumes that the frequency distribution of the
population/sample conforms to a bell-shaped (Gaussian) distribution
68.3% of observations are within 1 SD of the mean, 95.4% are within 2 SD, and
99.7% are within 3 SD of the mean.
This is assumed if it has a single mode, relatively symmetrical, and mean

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Skewed distribution if it has one tail longer than the other; the mean moves away
from the median towards the long tail.
Standard error of the mean and confidence limits
Confidence interval: the interval in which the true population lies
CI = mean ± t * sx
Standard error of the mean (sx)
Degrees of freedom = n-1
t comes from the t-table
α = 1 – degree of certainty (usually 0.95) so is usually 0.05.α
The t-test:
Used to test whether or not the difference between two populations is real (statistically
significant) or due to sampling (sampling error)
Null hypothesis: there is no real difference between two populations
P-value: the probability of obtaining your results due to chance alone if H0 is true.
Display results using bar graph (standard error balls represent standard error of
the mean)
ANOVA (single factor) – Analysis of variance
Used to test null hypothesis that two or more samples are drawn from the same
population (each sample would be equal).
F statistic: ratio of the variation between a group of means relative to the variation
within the groups
Sampling data types
Measurement data: quantifies characteristics of a population (individual members
will possess). Can be continuous or discrete.
Enumeration data: involves classifying the state of individuals in a population,
often require analysis of statistical techniques.
Chi-square goodness of fit test
Used to compare a given distribution of enumeration data with a theoretical/expected
If calculated value is larger than critical value = reject H0.
Used to see if two factors are related to each other (whether or not they are correlated).
Relationships can be cause-and-effect but we never know this or can assume this.
Both variables may be responding to a common cause.
The product-moment Correlation Coefficient (r) shows the strength of a linear
association. -1 < r < +1
r = 0, no correlation
r = -1 perfect negative correlation
r = +1 perfect positive correlation
Linear regression
Use to establish the form and significance of a functional relationship between two
variables. Objectively gives us a line that best fits the data.

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The coefficient of determination (r2) measures the strength of the relationship
(whether the data points fit closely to the line or if they deviate). 0 < r2 < 1. 1 =
strong linear relationship.
The reliability of the equation is expressed by the probability of obtaining this
linear relationship if H0 were true.
Collecting data
Data loggers for light and temperature
Vernier calipers
LAB 2: Sampling, density estimation, and spatial relations
In order to generalize from a sample population, it must be representative:
1. Must be unbiased
2. Must be adequate in size
Choosing samples
Random sample: every member of the population (every individual organism or
every point of ground) has an EQUAL and INDEPENDENT probability of being
* Ensure randomness (avoid subconscious bias) – let chance
determine samples. Can use random numbers generated on a
calculator, computer, or a random numbers table.
Systematic sample: some sort of systematic/regular arrangement when taking
samples. Usually simpler than random. Bias is only present if there is some sort of
pattern in the population.
Selected samples: if you try to select only “representative” samples – may leave
out extreme conditions
Random sampling > systematic sampling.
Adequacy of sampling
Number and size of samples => accuracy and precision of the estimates.
The larger the sampling size, the more likely it is to be adequate.
A large number of small or medium sized samples > a small number of large size
Simple, homogeneous area will require less sampling than a complex,
heterogeneous one.
Judging sampling adequacy:
1. Performance curves
Plots the cumulative mean value of some trait against the number of samples.
Cumulative mean: dividing the total number of objects encountered at a given
number of plots.
Once the change in the mean becomes very small with the addition of another
sample, we assume that our sample mean = true population mean.
2. Two-step sampling
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