Summaryofconcepts
•Wehavefocusedonlyonpopulationunits
–Targetpopulation
–Samplingframe
–Selectingaprobabilitysample
•Wehavenotdiscussedanycharacteristicsofa
populationelement
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Survery Error - Survey Sampling Techniques - Lecture Slides, Slides of Survey Sampling Techniques
Survey Sampling Techniques course is one of important courses in Statisitics. Major poiuts of this course are: probability sampling, confidence intervals, Two-stage cluster sampling, Two-stage cluster sampling, estimation for mean, choosing strata, allocation across strata, ratio estimation, domain estimation, Two-stage cluster sampling. Keywords in these slides are: Survery Error, Target Population, Sampling Frame, Probability Sample, Population Parameters, Histogram, Population Distribution o
Typology: Slides
2012/2013
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Summary
of
concepts
We
have
focused
only
on
population
units
Target population
Sampling frame - Selecting a probability sample
We
have
not
discussed
any
characteristics
of
a
population
element
Characteristics of the target population
We
are
really
interested
in
making
statements
that
summarize
characteristics
of
the
target
population,
i.e.
population
parameters
The average school loan debt owed by currently enrolled
ISU
students
The total surface area of county parks in the
US
The fraction of Des Moines households that fall below the poverty line
Data value for a target population element
A
data value is y i^
the value of characteristic for element i
Examples - Element = county in US y i^ = - Element = student enrolled at ISU y i^ = - Element = Des Moines household y i^ =
Population
distribution
of
y
y
is
often
referred
to
as
the
Variable of interest
There
are
N
data
values
for
y
There is one value of y for each of the
N
elements in the target population There may be fewer than
N
unique values
So y has a
DISCRETE
distribution
How
do
we
summarize
discrete
distributions?
Population
distribution
of
y
Histogram for y i^
number of courses a 2003 Stat
student i was registered for
N
Histogram 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 Number of courses y c(y) Number of students Number of courses y Number of students c(y) 1 0 2 2 3 7 4 6 5 3 6 6
Population
distribution
of
y
Discrete probability distribution of y
Horizontal axis = all UNIQUE values of y - Vertical axis = RELATIVE frequency of elements with a specific value of y , called P( y ) - Like a histogram with the frequencies (vertical axis) divided by
N
Usually start by making a table of
Unique values of the variable , y - Relative frequency of the unique values of y , P( y )
Population
distribution
of
y
Histogram
Probability
distribution
Can
also
describe
distribution
of
y
through
summary
descriptions
called
parameters
(more
later)
Total for y
courses for all students)
Mean of y
courses per student)
Population
distribution
of
y
The population distribution of y is what we are trying to describe when we draw a sample, collect data, and calculate an estimate for a summary parameter
The population distribution of y is
FIXED
No matter what sample design we choose - Regardless of the sample we draw from a given design - We do not assume a parametric distribution - Forget normal distributions assumed in other classes (for now)
Response
process
The
process
of
collecting
data
from
sampled
units,
e.g.,
via
a
questionnaire
or
observation
form
Response
process
Assume we have selected a probability sample from a frame
The next step is to collect data from each sampled element - This will lead to values for y i^ for each element in the sample - We will act like we only collect one characteristic from each sampled element, but usually, we are collecting dozens or even 100s of different characteristics from each element
Problems
in
Response
process
Outcomes for a sample selected from a frame
Can not locate/contact a sampled unit (e.g., household)
- unreachable - Locate/contact a unit, but can’t get any data - Sampled person refuses to participate ‐ nonrespond - Sampled person is unable to participate (illness) ‐ incapable - Collect data on some, but not all characteristics - Respondent doesn’t answer all questions - Data collector forgets to record a variable
Response
process
and
eligibility
Recall that the frame (and thus sample) may contain units that do not belong in the target population
In this case, we need to “screen” the unit to determine if the unit is eligible to be included in the survey - Eligible means that the unit belongs to the target population - In practice, there are cases where we can not determine if a unit is eligible or not to participate in study
Sampled
population
The
sampled
population
is
the
collection
of
all
possible
units
that
would
be
the
outcome
of
the
sampling
and
response
process
Could have been chosen in a sample, and
Would have provided data during the response process if sampled
Sampled
population
Sample
process:
includes
only
those
units
that
were
in
the
sampling
frame
Response
process:
includes
only
those
that
would
have
responded
Were available during interview period,
Were willing to be interviewed, and - Were physically/mentally capable of providing responses