Lesson 2...STATISTICS.ppt Data collection

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 1.1
Lesson 2:
STATISTICS
Data Collection and Sampling

Recall…
Statistics is a tool for converting data into information:
Data
Statistics
Information
• But where then does data come from?
• How is it gathered?
• How do we ensure its accurate?
• Is the data reliable?
• Is it representative of the population from which it was drawn?

Methods of Collecting Data…
There are many methods used to collect or obtain data
for statistical analysis. Three of the most popular
methods are:
• Direct Observation
• Experiments, and
• Surveys.

Surveys…
A survey solicits information from people;
examples: polls; pre-election polls; marketing surveys.
Surveys may be administered in a variety of ways.
Example given:
• Personal Interview,
• Telephone Interview,
• Internet, and
• Self Administered Questionnaire

Questionnaire Design…
Over the years, a lot of thought has been put into the science of the design
of survey questions. Key design principles:
1. Keep the questionnaire as short as possible.
2. Ask short, simple, and clearly worded questions.
3. Start with demographic questions to help respondents get started
comfortably.
4. Use dichotomous (yes|no) and multiple choice questions.
5. Use open-ended questions cautiously.
6. Avoid using leading-questions.
7. Pretest a questionnaire on a small number of people.
8. Think about the way you intend to use the collected data when preparing
the questionnaire.

Sampling Plans…
A sampling plan is just a method or procedure for specifying how a
sample will be taken from a population.
We will focus our attention on these three methods:
• Simple Random Sampling,
• Stratified Random Sampling, and
• Cluster Sampling.
• Random sampling, by far, is the most common one used.

Simple Random Sampling…
A simple random sample is a sample selected in such a way that
every possible sample of the same size is equally likely to be
chosen.
Drawing three names from a hat containing all the names of the
students in the class is an example of a simple random sample: any
group of three names is as equally likely as picking any other group
of three names.
VERY EASY TO DEFINE!
VERY, VERY DIFFICULT TO DO!

Simple Random Sampling…
A government income tax auditor must choose a sample of 5 of 11
returns to audit…[Can do many different ways]
Person
baker 0.87487
george 0.89068
ralph 0.11597
mary 0.58635
sally 0.34346
joe 0.24662
andrea 0.47609
mark 0.08350
greg 0.53542
aaron 0.37239
kim 0.73809
Generate
Random # Person
1 mark 0.08350
2 ralph 0.11597
3 joe 0.24662
4 sally 0.34346
5 aaron 0.37239
andrea 0.47609
greg 0.53542
mary 0.58635
kim 0.73809
baker 0.87487
george 0.89068
Sorted
Random #

Stratified Random Sampling…
A stratified random sample is obtained by separating the population
into mutually exclusive sets, or strata, and then drawing simple
random samples from each stratum.
Strata 1 : Gender
Male
Female
Strata 2 : Age
< 20
20-30
31-40
41-50
51-60
> 60
Strata 3 : Occupation
professional
clerical
blue collar
other
We can acquire about the total population, make inferences
within a stratum or make comparisons across strata

Stratified Random Sampling…
After the population has been stratified, we can use simple random
sampling to generate the complete sample:
If we only have sufficient resources to sample 400 people total,
we would draw 100 of them from the low income group…
…if we are sampling 1000 people, we’d draw
50 of them from the high income group.

Cluster Sampling…
A cluster sample is a simple random sample of groups or clusters of
elements (vs. a simple random sample of individual objects).
This method is useful when it is difficult or costly to develop a
complete list of the population members or when the population
elements are widely dispersed geographically. Used more in the
“old days”.
Cluster sampling may increase sampling error due to similarities
among cluster members.

Sample Size…
Numerical techniques for determining sample sizes
will be described later, but suffice it to say that the
larger the sample size is, the more accurate we
can expect the sample estimates to be.

Sampling and Non-Sampling Errors…
Two major types of error can arise when a sample of observations is
taken from a population:
sampling error and nonsampling error.
 Sampling error refers to differences between the sample and the
population that exist only because of the observations that happened to
be selected for the sample. Random and we have no control over.
 Nonsampling errors are more serious and are due to mistakes made in
the acquisition of data or due to the sample observations being selected
improperly. Most likely caused be poor planning, sloppy work, act of
the Goddess of Statistics, etc.

Sampling Error…
Sampling error refers to differences between the sample and the
population that exist only because of the observations that
happened to be selected for the sample.
Increasing the sample size will reduce this type of error.

Nonsampling Error…
Nonsampling errors are more serious and are due to mistakes made
in the acquisition of data or due to the sample observations being
selected improperly. Three types of nonsampling errors:
Errors in data acquisition,
Nonresponse errors, and
Selection bias.
Note: increasing the sample size will not reduce this type of error.

Errors in data acquisition…
…arises from the recording of incorrect responses, due to:
— incorrect measurements being taken because of faulty equipment,
— mistakes made during transcription from primary sources,
— inaccurate recording of data due to misinterpretation of terms, or
— inaccurate responses to questions concerning sensitive issues.

Nonresponse Error…
…refers to error (or bias) introduced when responses are not
obtained from some members of the sample, i.e. the sample
observations that are collected may not be representative of the
target population.
As mentioned earlier, the Response Rate (i.e. the proportion of all
people selected who complete the survey) is a key survey parameter
and helps in the understanding in the validity of the survey and
sources of nonresponse error.

Selection Bias…
…occurs when the sampling plan is such that some members of the
target population cannot possibly be selected for inclusion in the
sample.

Lesson 2...STATISTICS.ppt Data collection

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