Lesson 9: Sampling and Confidence Intervals for Proportions
Some commonly used probability sampling methods:
1.
Simple random sampling
:
Every combination of n individuals within the population has an equal chance to be the sample. A
simple random sample is usually picked by "lottery" methods.
2.
Stratified sampling
:
The population is divided into important subgroups (e.g. East and West) which are groups of individuals or
subjects that are similar in a way that may affect their response.
3.
Cluster sampling
: The population is divided into several subgroups by geographic proximity or closeness of individuals to each
other on a list. In stratified sampling we create the subgroups based on some criteria – ethnicity, geographic region, and then
random sampling of individuals or subjects is done. In Cluster sampling, clusters of individuals or subjects are randomly sampled.
Some methods often used that are NOT probability sampling methods:
1.
Selfselected sample
: volunteer sample with no random selection process imposed by the researcher. Examples are polls done at
web sites and television polls in which viewers are asked to phone in their opinion.
2.
Haphazard sampling
: The pollster wanders around an area (like the Hub or a downtown street) and haphazardly asking people to
participate.
3.
Convenience sampling:
The sample is an available group (say, our Stat 200 class) and no probability methods are used for
selection.
Other Survey Biases
Response bias
:
(false answers biased toward the most "acceptable" answer)
Nonresponse bias
:
(systematic refusal of some people to answer certain types of
questions)
Wording of questions
:
(making one answer seem the most reasonable to give)
Selection bias
:
results when the sample selected does not represent the population of interest.
Chapter 10: Confidence Intervals for Proportions
Confidence Interval and Confidence Level
A confidence
interval
: is an interval, computed using sample information, that estimates the value of a population parameter.
A confidence level
: is the probability (often expressed as a percent) that the procedure used to determine a confidence interval gives an
interval that actually includes the (unknown) value of the population parameter. In other words, a confidence level is the fraction of times the
procedure works by "capturing" the population value.
Calculating a general confidence interval: Sample statistic ± multiplier × Standard Error.
•
Sample
statistic
is a summary value for an observed statistic.
•
The
standard
error
is the estimated standard deviation of the sampling distribution of the statistic.
•
The
multiplier
controls the confidence level and is determined using either a standard normal curve or a tdistribution. We’ll cover
the tdistribution at a later time.
•
The multiplier times the standard error is referred to as the margin of error
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 Spring '08
 BARROSO,JOAOR
 Statistics, Probability, Sampling Methods, Standard Error, Statistical hypothesis testing

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