CRIM 220 Lecture Notes - Lecture 8: Uptodate, Statistical Parameter, Confidence Interval
7 Jun 2018
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Lecture 8, Week 9: Chapter 8 Tuesday 13th March
Crim 220: Ethics and Criminal Justice Research
• Much of the value of research depends on how the data is collected
Reasons for sampling:
1. Often not possible to collect information from all the persons or other units we wish
to study
2. Often not necessary to collect information from all persons or other units
•Probability sampling techniques enables relative few observations and then
generalizing to a much wider population
• Probability sampling is central to criminal justice research, it can not always be used
•Non probability sampling can be used as an alternative, these have their own logic
and provide useful samples
Important goal:
• Reduce, or understand, potential biases that may be at work when selecting
subjects
The Logic of Probability Sampling
Samples serve to:
Represent some larger population of people or other things
Generalize from it to an unobserved population— the one it is intended to
represent
• If members of a population are identical in all aspects then there is no need to carry
careful sampling procedure
In extreme cases of homogeneity, one case might be representative of the
whole population
Human beings of any population are heterogenous
Conscious and Unconscious Sampling Bias
• Refers to the idea that those selected are not representative of the population
• Bias is inevitable when researchers pick subjects casually
• Polls linked to blogs, text messages or emails cannot be trusted to represent the
general population
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Sampling- process of selecting observations— selecting some units of a larger
population for study
Probability Sampling- method of sampling in which each member of a
population has a known chance or probability of being selected. Can allow
accurate predictions of the samples representation.
•THE MORE SELF-SELECTION IS INVOLVED, THE MORE BIAS WILL BE INTRODUCED INTO
THE SAMPLE
Representativeness and Probability of a Selection
• A sample is representative of the population from which it is selected if the
aggregate characteristics of the sample closely approximate the characteristics in
the population
• Samples don’t always have to be representative on all respects, only to those
relevant characteristics
• Sample will be representative if all members of the population have an equal
chance of being selected
Equal probability of selection method (EPSEM)
Advantages of probability sampling:
1. Tend to be more representative that other types of samples because they avoid
biases
2. Permits to establish the accuracy of representativeness of the sample
Can provide accurate estimate of success or failure
Probability Theory and Sampling Distribution
• Probability theory permits inferences about how sampled data are distributed
around the value found in a larger population
Sample elements: unit about which information is collected and that provides the basis
of analysis. In surveys, these are typically people. In CJ research they can be
correctional facilities, street blocks, etc. Elements and units of analysis are often the
same in a given study.
Population: the theoretically specified grouping of study elements. Turns abstract
concepts into workable populations.
EXAMPLE: Delinquents → person’s charged with delinquent offences in the
previous six months
Population parameter: value for a given variable in a population. An important
proportion of CJ research involves estimating population parameters on the basis of
sample observations.
Sample statistics: the summary description of a given variable in the sample. Used to
make estimates of population parameters.
• Ultimate purpose of sampling is to select a set of elements from a population in such
a way that descriptions of those elements accurately portray the parameters of the
total population from which elements are selected.
Probability sampling gives increases the likelihood of this
Provides methods for estimating the degree of probable success
Key is random selection
Reasons to use random selection:
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Confidence levels- estimated probability that a population parameter is
within a specific confidence interval
Confidence interval- range of values that include a population parameter
• Procedure serves as a check on conscious and unconscious bias on the part of the
researcher
• Allows to estimate population parameters and to estimate how accurate our
statistics are likely to be
The Sampling Distribution
• Increasing sample size improves estimations
From Sampling Distribution to Parameter Estimates
• Quasi- as even though the list might not exist, samples can still be drawn
• By increasing the number of samples selected and interviewed, the range of
estimates provided by the sampling operation also increases
Increase in dilemma in attempting to find the parameter in the population
Estimating Sampling Error
• Probability theory can help solve our dilemmas with basic statistical concepts
• If many random samples are selected from a population, sample statistics provided
by those samples will be distributed around the population parameter in a known
way
• Probability theory tells us where the true value is approximately, by evaluating at
where the majority of values are in the graph
Formula for estimating how closely sample statistics are clustered around the true value:
S- standard error
P and Q- population parameters for the
binomial
n- number of cases in each sample
•Value indicates how closely the sample
estimates will be distributed around the population parameters
• Tells us how much sample statistics will be dispersed or clustered around a
population parameter
• Probability theory states that ≈34% of sample estimates will fall within one standard
error increment above the population parameter, and another 34% will fall within
one standard error below the population parameter
• Standard error is also a function of sample size— an inverse function
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Sampling Distribution- Range of sample statistics obtained if many samples
are selected.
Sampling frame- list or quasi-list of elements in a population that is used to
select a sample
Document Summary
Tuesday 13th march: much of the value of research depends on how the data is collected. Sampling- process of selecting observations selecting some units of a larger population for study. Important goal: reduce, or understand, potential biases that may be at work when selecting subjects. Probability sampling- method of sampling in which each member of a population has a known chance or probability of being selected. Can allow accurate predictions of the samples representation. Represent some larger population of people or other things. Generalize from it to an unobserved population the one it is intended to represent: if members of a population are identical in all aspects then there is no need to carry careful sampling procedure. In extreme cases of homogeneity, one case might be representative of the whole population. !42: the more self-selection is involved, the more bias will be introduced into.
