Transcript Sampling Techniques & Sources of Bias

Sampling Techniques
&
Sources of Bias
STT 2820 Reasoning with Statistics
Mr. Caleb Marsh
Types of Studies
 Observational Study – In an observational
study, we observe and measure specific
characteristics, but we don’t attempt to
modify the subjects being studied.
 Experimental Study – In an experiment,
we apply some treatment and then
proceed to observe its effects on the
subjects. Subjects in experiments are
referred to as experimental units.
To ensure a representative
sample…
 Simple Random Sample – Members from
the population are selected in such a way
that each individual member has an equal
chance of being selected.
 Probability Sample – Involves selecting
members from a population in such a way
that each member has a known, but not
necessarily the same, chance of being
selected.
Simple Random Sample
 Population
 Sample
Probability Sample
Procedure - Select Purple twice as
much as Green
 Population
 Sample
Systematic Sampling
 We select some starting point then select
every kth element (such as the 50th) in the
population to sample.
 **Caution** this sampling technique can
cause issues if the selection of k leads to
improper sampling.
Systematic Sampling
Procedure – Select every 4th
Element
 Population
 Sample
Stratified Sampling
 We subdivide the population into at least
two different subgroups (called strata) so
that subjects within the same subgroup
share the same characteristics. Then,
from each subgroup, we select a simple
random sample.
Simple Random Sample
 Population
 Sample
Cluster Sampling
 Divide the population area into sections
(called clusters, usually done
geographically). Randomly select some of
those clusters and then choose all
members from the selected clusters.
Cluster Sampling
 Population
 Sample
Lincoln’s Gettysburg Address
Four score and seven years ago our fathers brought forth on this continent, a new
nation, conceived in Liberty, and dedicated to the proposition that all men are
created equal. Now we are engaged in a great civil war, testing whether that nation,
or any nation so conceived and so dedicated, can long endure. We are met on a
great battle-field of that war. We have come to dedicate a portion of that field, as a
final resting place for those who here gave their lives that that nation might live. It
is altogether fitting and proper that we should do this. But, in a larger sense, we
can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The
brave men, living and dead, who struggled here, have consecrated it, far above our
poor power to add or detract. The world will little note, nor long remember what we
say here, but it can never forget what they did here. It is for us the living, rather, to
be dedicated here to the unfinished work which they who fought here have thus far
so nobly advanced. It is rather for us to be here dedicated to the great task
remaining before us -- that from these honored dead we take increased devotion to
that cause for which they gave the last full measure of devotion -- that we here
highly resolve that these dead shall not have died in vain -- that this nation, under
God, shall have a new birth of freedom -- and that government of the people, by the
people, for the people, shall not perish from the earth.
Experimental Design
 Cross-sectional Study – Data are
observed, measured and collected at one
point in time.
 Retrospective (or case control) Study –
Data are collected from the past by going
back in time (through examination of
records, interviews and so on.)
 Prospective (longitudinal or cohort) Study
– Data are collected in the future from
groups sharing common factors.
More Experimental Design
 Randomization – Subjects are assigned to
different groups through a process of
random selection.
 Replication – The repetition of an
experiment on more than one subject.
 Blinding – A technique in which the subject
does not know whether he or she is
receiving a treatment or a placebo.
Confounding
 Confounding occurs in an experiment
when you are not able to distinguish
among the effects of different factors.
Types of Errors
 Sampling Error – The difference between
a sample result and the true population
result; such an error results from chance
sample fluctuations.
 Non-sampling Error – Occurs when the
sample data are incorrectly collected,
recorded or analyzed.
Bias
 Bias –The tendency of our sample to
misrepresent our population either by
sampling or non-sampling error.
 Our goal in using a variety of sampling
procedures is to reduce bias.
 However, there are certain “abuses” that
can exist within the confines of statistical
research.
1. Voluntary Response Sample
 A sampling procedure in which the respondents
themselves decide on whether or not to be
included in the study.
 Problem – Typically individuals that are highly
motivated to respond, do… those that are not,
do not.
2. Small Samples
 Conclusions cannot be based on samples that
are too small.
 Problem – Small samples put too much
influence on a selected few.
3. Misleading Graphs
KWH
845
840
 INCORRECT
835
830
825
July
August
KWH
 CORRECT
1000
800
600
400
200
0
July
August
4. Loaded Questions
 Example – When asked 97% believe that
the President should be granted line item
veto powers to eliminate waste.
 Example – When asked 57% believe that
the President should be granted line item
veto powers.
5. Non - Response
 Occurs when either a person in
unavailable for a response or refuses to
respond to a survey question.
 Problem – Typically people who refuse to
respond are socialized to do so. These
individuals opinion’s might differ from the
typical respondent.
6. Self Interest Study
 Occasionally an individual or group of
individuals will commission a study with which
the outcomes greatly effect the status quo.
Hey… Do you like m&ms?
Final Issues
 7. Precise Numbers – The total number of
hairs on your head is 1,275,562.
 8. Partial Pictures – Average class size at
ASU is 27 students.
 9. Deliberate Distortions – The Average
American Salary is $75,627 per year.