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BIOL 300
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Michael Whitlock
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Chapter 1

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Biology

BIOL 300

Michael Whitlock

Fall

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Chapter 1: Statistics and Samples
1.1- What is Statistics?
- Biologists study properties of living things
- Measuring properties of living things is a challenge because:
o No two individuals of a population are exactly alike
o Can’t measure everyone in a population due to time constraint and
limited funding
- Measuring properties of living things are done through a sample of
individuals drawn from the population
- Sampling brings uncertainty to the measurements because properties of the
sample are not the same as the true values in the population
- Statistics- technology that describes and measures aspects of nature from
samples; makes it possible to quantify the uncertainty in measures
- Estimation- process of inferring an unknown quantity of a target population
using only sample data
o Estimation allows us to assess differences between groups and
relationship between variables
- Parameter- quantity describing a population; “the truth”; ex. averages,
proportions, measures of variation, measures of relationship…etc
- Estimate- related quantity calculated from a sample; “approximation of the
truth, subject to error”
- Statistics tells us how best to estimate these parameters using our
measurements of a sample
- By measuring every possible member of the population, we could know the
parameter without error, but that is rarely possible
- Instead, we use estimates based on incomplete data to approximate the true
value
- Hypothesis testing- process of determining how well a “null” hypothesis
about a population quantity fits a sample of data
o Null hypothesis- specific claim regarding the population quantity;
made for the purposes of argument and often embodies the skeptical
point of view
1.2- Sampling Populations
- Our ability to obtain reliable measures of population characteristics and to
assess the uncertainty of these measures depends on how we sample
populations
Populations and Samples
- Population- entire collection of individuals or units of interest; composed of
large number of individuals; ex. all cats that have fallen from buildings in NYC
- Sample- subset of individuals or units taken from the population; smaller set
of individuals; used to draw conclusions that apply to whole population; ex.
fall cats brought to one veterinary in NYC o Sometimes a basic unit of sampling is literally a single individual or a
group of individuals
o Scientists use several terms to indicate the sampling unit, such as
“unit”, “individual”, “subject”, or “replicate”
Properties of Good Samples
- Estimates based on samples typically depart somewhat from the true
population characteristic
- Sampling error- chance different between an estimate and the population
parameter being estimated
o Larger samples are less affected by chance than smaller samples
therefore will have lower sampling error and higher precision
- Precision- indicated by spread of estimates resulting from sampling error
- Accuracy (Unbiased)- indicated by distance from the true mean value
- Bias- systematic discrepancy between estimates and the true population
characteristics
- Major goal of sampling is to minimize sampling error and bias in estimates
- Ideally, all the estimates are tightly grouped, indicating low sampling error,
and they are centered on the bull’s-eye, indicating low bias
o Estimates are precise if they are tightly grouped and highly repeatable
o Estimates are imprecise if they are spread out and not repeatable
o Estimates are accurate (unbiased) if they are centered on the bull’s-
eye
o Estimates are inaccurate (biased) if they are displaced systematically
to one side of the bull’s-eye
- Both precision and accuracy are important because lack of either means that
an estimate is likely to differ greatly from the truth
- Final goal of sampling is to allow the precision of an estimate to be quantified
Random Sampling
- Random sample- sample in which each member of the population has an
equal and independent chance of being selected
- For a random sample, every unit in the population must have an equal
chance of being included in the sample
o Hard-to-sample individuals must be included in the sample, otherwise
it would lead to bias due to their differences in characteristics from
the rest of the population
- For a random sample, the selection of units must be independent – the
selection of any one member of the population must in no way influence the
selection of any other member
o Individuals from the same household cannot be included in the
sample because it makes the sample effectively smaller and causes the
data to be skewed
- Random sampling minimizes bias and makes it possible to measure the
amount of sampling error
- How to take a random sample (Method 1): o Create a list of every unit in the population of interest and give each
unit a number between 1 and the total population size
o Decide on the number of units to be sampled (call this number n)
o Using a random-number generator, generate n random integers
between 1 and the total number of units in the population
o Sample the units who numbers match those produced by the random
number generator
- How to take a random sample (Method 2):
o Make the basic unit of sampling a group instead of a single individual
o Take the average of the measurements of all the individuals within a
unit (group) as the single independent observation for that unit
(group)
o Create a list of every unit (group) in the population of interest and
give each unit (group) a number between 1 and the total population
size
o Decide on the number of units (groups) to be sampled (call this
number n)
o Using a random-number generator, generate n random integers
between 1 and the total number of units (groups) in the population
o Sample the units (groups) who numbers match those produced by the
random number generator
Sample of Convenience
- Sample of convenience- collection of individuals that are easily available to
the researcher
- Researcher must assume that a sample of convenience is unbiased and
independent like a random sample, but there is no way to guarantee it
- Sample of convenience may be biased because it doesn’t accurately represent
that entire population of interest due to leaving out specific groups of
individuals
- Sample of convenience might also violate the assumption of independence if
individuals in the sample are more similar to one another than individuals
chosen randomly from the population
Volunteer Bias
- Volunteer bias- bias resulting from a systematic difference between the
pool of volunteer (the volunteer sample) and the population to which they
belong
- Volunteer bias arises

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