sampling.... Quota Sampling..
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Transcript of sampling.... Quota Sampling..
Sampling
Dr. Mary Wolfinbarger
Marketing Research
Sample vs. Census
Census -- every population member included
With sampling, researcher infers population characteristics from a sample
Why sample?
Saves money Saves time A sample can be more accurate; it has fewer
“nonsampling” errors than a census
Sampling terms Population (or Universe): a complete listing
of a set of elements having a given characteristic(s) of interest
An example of population definition: Americans Registered Voters Voters Swing voters
(Which is more relevant to politicians?)
Sampling terms
Element: Unit about which information is sought
Most common units in marketing: individuals households Sudman and Blair suggest a conceptual
sample: sales dollars or potential sales dollars
Sampling terms
Sample Frame: A list of population members May get a complete listing of population,
but often population and sample frame are different
Example: “American recreational tennis players?”
Differences between the sample frame and population: “sample frame error”
Sampling terms
Parameter: The actual characteristic of the population, the true value of which can only be known by taking an error-free census
Statistic: The estimate of a characteristic obtained from the sample
Sampling terms
Non-response error: error created when chosen sample members who do not participate
Non-response creates two problems: Need a larger initial sample size to allow
for non-response More seriously, non-respondents may differ
from respondents (“questionnaire freaks?”)
Sample Types
Two broad categories: Probability: each population element has a
known, non-zero chance of being included in the sample
Non-probability: cannot mathematically estimate the probability of a population element being included in the sample
Sample Types
Statistician’s opinion: all N-P samples are worthless because you cannot estimate the degree to which your results are generalizable
So, why are N-P samples ever used?
Non-probability Samples
Convenience Judgment Quota
Convenience Samples
“Accidental samples” -- those in sample are where the data is being collected
One major form in marketing: “Mall Intercept”
What do statisticians think? “Rarely do samples selected on a convenience sample basis, regardless of size, prove representative, and are not recommended for descriptive or causal research.”
Convenience Samples
I agree, but….
Minimizing drawbacks of convenience samples:
compare sample characteristics and findings to those collected on a census/random sample basis
speculate intelligently about bias, and how it is likely to have affected results
Convenience Samples
When possible, collect the sample where your population is likely to be (retailers collecting in-store surveys)
Cultivate diversity in the sample (e.g. mall intercept using multiple locations)
May be better at understanding relationships between variables than at making descriptive estimates
Judgment Samples
Also called purposive sampling Sample elements are hand picked because it
is felt that they are representative of some population of interest
Typically a small sample (maybe as small as 10) in which the researcher tries to represent all groups or segments from the population
Judgment Samples
Snowball design: a special form of judgment sample
Appropriate for small specialized populations
Each respondent is asked to identify one or more other population members
Judgment Samples
Drawbacks? Those with more ties to sample members
are selected Similar people are more likely to be named
Quota Sampling
Attempt to be representative by selecting sample elements in proportion to their known incidence in the population
Quota Sampling
Example: Surveying undergraduate students about campus food services
Step 1: Identify attributes researcher believes is important, e. g. sex and class level
Step 2: Look at incidence of sex and class level in population
Quota Sampling
Class Level
Freshmen 3200
Sophomores 2600
Juniors 2200
Seniors 2000
Sex
Males 4500
Females 5500
If I sample 100, how many of each type do I select?
Quota Sampling
Don’t be fooled -- relies on personal, subjective selection of quota attributes
The sample can still be non-representative with respect to some other characteristic (e.g. in this example, perhaps race)
I plead guilty -- I have sinned -- and will do so again -- …….so shoot me………….
Probability Sampling
Does not guarantee representativeness, but does allow for the assessment of sampling error
Sampling error: error that occurs because a sample rather than a census is used
Simple Random Sampling (SRS)
Each sample element has a known, non-zero, equal chance of being selected
Example: Lottery numbers Or, put everyone’s name in a hat Major polling firms use random digit dialing
to approximate random samples Or, use a random numbers table (actually
pseudo-random I’m told)
Systematic Sampling
Systematically spreads sample through a list of population members
Example: If a population contained 10,000 people, and need a size of 1000, select every 10th list name
In nearly all practical examples, the procedure results in a sample equivalent to SRS
Systematic Sampling
Only exception: when there are “regularities” in the list
Systematic Sampling
Another application of systematic sampling: select a number of millimeters or inches
down a page or column that will be selected (it’s easier than counting!)
Stratified Sampling
Information about subgroups in the sample frame is used to improve the efficiency of the sample plan
Stratified Sampling
Three major reasons to use
Some subgroups are more homogenous than others so fewer numbers are needed for those groups to obtain the same level of precision
Group comparison is the purpose of the study (disproportionate stratified sampling)
Some elements are more important in determining outcome of research interest than are others
How is this different from quota sampling? Within strata, selection of sample elements
is random, not first available
Bad Uses of Stratification
To satisfy people distrustful that random sampling will not be representative
To correct for MAJOR problems with survey cooperation
Poststratification is OK
Is done after sampling Corrects for MINOR differences between
sample and population produced by non-cooperation
Area (or Cluster) Sampling
Elements are geographically grouped into relatively homogenous clusters (e.g. a city is divided into 40 areas)
From these areas, 10 are randomly selected From these larger areas, blocks within areas
will be randomly selected Within each block, attempt to survey each
household
Area (or Cluster) Sampling
Especially useful for door-to-door personal surveys (significantly reduces costs)
However, clustering increases sampling errors (people who live close together tend to be more similar)
Statistics formula suggests in marketing research 20-25 clusters is appropriate with 20-25 observations per site
Determining Sample Size
Ad Hoc Methods (non-statistical)
Rules of thumb: Collect sample size large enough so that when divided into groups, each group will have a minimum sample of 100 or so (Sudman)
Budget constraints: calculate the cost of interview and data analysis per respondent. Divide total budget by this amount to get maximum sample size.
Ad Hoc Methods (non-statistical)
Comparable studies: Find similar studies which are successful and getting sufficiently reliable results
Most general formula
Total sampling error=
desired confidence level (Z)*standard deviation of sample (SD)/sample size (N)
Sampling error: the standard deviation of the distribution of sample means
Sampling error is expressed as an absolute, and is not a percentage: it is the amount your measurement is from the true value
Re-arranging Algebraically
N=Z22/(sampling error )2
Where N=sample size
Z=z score from normal curve table (1.96 for a confidence interval of 95%)
=standard deviation (obtained from previous survey or estimated, e. g. 95% of responses fall between 3 and 5, so 1 SD=.5)
Example:
For example, if allowable sampling error = .20 (on a 7 point scale), SD=1.34, and a confidence interval of .05 is being used,
N=1.962*1.342/.202
N=172
What this formula suggests
If the sample is more varied, a larger sample is required
If more precision is required, a larger sample is necessary
If a small confidence interval is desired, a larger sample is necessary
The increase required to achieve ever more precision and confidence increases at an increasing rate!