chapter13 determining the size of a sample. sample accuracy sample accuracy: refers to how close a...
Post on 20-Dec-2015
225 views
TRANSCRIPT
Chapter 13
Determining the Size of
a Sample
Sample Accuracy
• Sample accuracy: refers to how close a random sample’s statistic ( mean, S.D. ) is to the true population’s value ( µ, š ) it represents
• Important points:• Sample size is not related to
representativeness• Sample size is related to accuracy
Sample Size Axioms
• The only perfectly accurate sample is a census.• A probability sample will always have some
inaccuracy (sample error).• The larger a probability sample is, the more
accurate it is (less sample error).• Probability sample accuracy (error) can be
calculated with a simple formula, and expressed as a ± % number.
Sample Size Axioms…cont.
• You can take any finding in the survey, replicate the survey with the same probability sample size, and you will be “very likely” to find the same finding within the +- range of the original finding.
• In almost all cases, the accuracy (sample error) of a probability sample is independent of the size of the population.
Sample Size Axioms…cont.
• A probability sample can be a very tiny percentage of the population size and still be very accurate (have little sample error). (e.g., consumer confidence panel– 5,000 )
• The size of the probability sample depends on the client’s desired accuracy (acceptable sample error) balanced against the cost of data collection for that sample size.
The Confidence Interval Method of Determining Sample Size
• Confidence interval approach: applies the concepts of accuracy, variability, and confidence interval to create a “correct” sample size
• Two types of error:• Nonsampling error: pertains to all sources of error
other than sample selection method and sample size• Sampling error: involves sample selection and
sample size• Sample error formula:
The Confidence Interval Method of Determining Sample Size
• The relationship between sample size and sample error:
The Confidence Interval Method of Determining Sample Size
Variability
• Variability: refers to how similar or dissimilar responses are to a given question
• P: percent• Q: 100%-P
The Confidence Interval Method of Determining Sample Size
Normal Distribution
The Confidence Interval Method of Determining Sample SizeNotion of Confidence Interval
• Confidence interval: range whose endpoints define a certain percentage of the responses to a question
• Central limit theorem: a theory that underlies many statistical concepts and holds that a bar chart of all repeated samples of a survey within a population would look like a normal curve
Sample Size Formula
• To calculate the proper sample size for a survey, only three factors need to be considered:• The amount of variability believed to be in the
population• The desired accuracy• The level of confidence required in your
estimates of the population values
Sample Size Formula…cont.
• Standard sample size formula:
Examples
• At 95% confidence level: e = ± 10
1.962 (50x50) 102
At 99% confidence level: e = ± 5 2.582 (50x50) 52
n = = 96
n2
= = 665.6
Practical Considerations in Sample Size Determination
• How to estimate variability in the population• Expect the worst case.• Estimate the actual variability.
• How to determine the amount of desired sample size
• How to decide on the level of confidence desired• How to balance sample size with the cost of data
collection
Other Methods of Sample Size Determination
• Arbitrary “percentage rule of thumb” sample size:• Arbitrary sample size approaches rely on
erroneous rules of thumb.• Arbitrary sample sizes are simple and easy to
apply, but they are neither efficient nor economical.
Other Methods of Sample Size Determination…cont.
• Conventional sample size specification• Conventional approach follows some
“convention” or number believed somehow to be the right sample size.
• Using conventional sample size can result in a sample that may be too large or too small.
• Conventional sample sizes ignore the special circumstances of the survey at hand.
Other Methods of Sample Size Determination…cont.
• Statistical analysis requirements of sample size specification• Sometimes the researcher’s desire to use
particular statistical technique influences sample size.
• Cost basis of sample size specification• “All you can afford” method• Instead of the value of the information to be gained
from the survey being a primary consideration in the sample size, the sample size is determined by budget factors that usually ignore the value of the survey’s results to management.
Special Sample Size Determination Situations
Sampling from Small Populations
• Small population: sample exceeds 5% of total population size
• Finite multiplier: adjustment factor for sample size formula
• Appropriate use of the finite multiplier formula will reduce a calculated sample size and save money when performing research on small populations
Finite Multiplier
k1 = (N - n)/(N – 1)
Where:
N = Population size
n = sample size
Special Sample Size Determination Situations
Sample Size Using Nonprobability Sampling
• When using nonprobability sampling, sample size is unrelated to accuracy, so cost-benefit considerations must be used
Case 13.1 Peaceful Lake Subdivision
• Please read Case 13.1 in pp. 396-397.
• Analyze the case and answer questions 1, 2.
Case 13.1
( pq )
e2
=384
n1 = 384 x Finite Multiplier
= 384 x 0.60
= 230
n = z2