Download - MARK202 Spring 2012 Lectures Lecture 4
Sampling & Field Work
Instructor & Tutor: Kathy Ning Shen, PhD
Sampling techniques and sampling error Sample size determination Field work and data collection
Agenda
What are available sampling techniques?
What are the rationale for each technique? Sampling error? And how to deal with it?
Sampling techniques
The Sampling Design Process
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process
Probability sampling: Elements in the
population have a known probability of being selected as samples. Major type: simple random sampling. Used when generalizeability is important.
Non-probability sampling: Used when generalizeability is NOT important. Major type: Convenience sample.
Types of sampling
A researcher has the task of estimating how many
units of a new, revolutionary photocopy machine (it does not require ink cartridges and is guaranteed not to jam) will be purchased by business firms in Cleveland, Ohio for the upcoming annual sales forecast. She is going to ask about their likelihood of purchasing the new device, and for those “very likely” to purchase, she wants respondents to estimate how many machines their company will buy. She has data that will allow her to divide the companies into small, medium, and large firms based on number of employees at the Cleveland office.
– Nonsampling error: pertains to all sources
of error other than sample selection method and sample size
– Sampling error: involves sample selection and sample size
Sampling Error
Sample Accuracy
Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents
Important points:
Sample size is not related to representativeness
Sample size is related to accuracy
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-8
Sample Size and Accuracy
Intuition: Which is more accurate: a large probability sample or a small probability sample?
The larger a probability sample is, the more accurate it is (less sample error).
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-9
How to Interpret Sample Accuracy
From a report…
The sample is accurate ± 7% at the 95% level of confidence…
From a news article
The accuracy of this survey is ± 7%…
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-10
How to Interpret Sample Accuracy
Interpretation
Finding: 60% are aware of our brand
So… between 53% (60%-7%) and 67% (60%+7%) of the entire population is aware of our brand
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-11
Does the population size directly affect the
size the of sample? The larger the sample size, the higher the
confidence (smaller values of p) The larger the variance (difference
amongst subjects), the lower the confidence.
Larger variance requires a larger sample size to achieve the same level of confidence.
Sample Size (Non-technical)
In almost all cases, the accuracy (sampling
error) of a probability sample is independent of the size of the population.
A probability sample can be a very tiny percentage of the population size and still be very accurate (have little sample error).
The size of a random sample depends on the client's desired accuracy balanced against the cost of data collection for that sample size.
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-13
Sample Size Axioms
Population Size
e=±3% Sample Size
e=±4% Sample Size
10,000 ____ ____
100,000 ____ ____
1,000,000 ____ ____
100,000,000 ____ ____
Where is N (size of the population) in the sample size determination formula?
Sample Size and Population Size
1,067 600
1,067 600
1,067 600
1,067 600
In almost all cases, the accuracy (sample error) of a probability sample is independent of the size of the population.
Population Size
e=±3% Sample Size
Sample as % of Population
10,000 1,067 1%
100,000 1,067 0.1%
1,000,000 1,067 0.01%
100,000,000 1,067 0.0001%
Does the size of the population, N, affect sample size or sample error?
13-15
A probability sample size can be a very tiny percentage of the population size and still be very accurate (have little sample error).
MR – What level of accuracy do you want? MM – I don’t have a clue. MR – National opinion polls use ±3.5%. MM – Sounds good to me. MR – Okay, that means we need a sample
of 1,200. MM – Gee Whiz. That small? MR – Yup, and at a cost of $20 per
completion, it will be $24,000. MM – Holy Cow! That much? MR – I could do 500 for $10,000, and that
would be ±4.4% accurate, or 300 for $6,000 at ±5.7%.
MM – 500 sounds good to me.13-16
Putting It All Together
The size of a probability sample depends on the client’s desired accuracy (acceptable sample error) balanced against the cost of data collection for that sample size.
Putting It All Together
There is only one method of determining sample size that allows the researcher to PREDETERMINE the accuracy of the sample results…
The Confidence Interval Method of Determining
Sample Size
Assuming a confidence level of 95%, precision
level of 10$ and a standard deviation of $100, what should be the sample size to determine the average monthly household expenditure on product X?
Typical Scenario:
Sample error formula:
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-19
Computations Help Page
n
pqze
Let’s try 3 n’s
1000
500
100
1.96 50 times 50
Answers this way…
Computations Help Page
n
pqze
Let’s try 3 n’s
1000 ±3.1%
500 ±4.4%
100 ±9.8%
1.9650 times 50
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-21
Review: What does sample accuracy
mean? 95% Accuracy
Calculate your sample’s finding, p%
Calculate your sample’s accuracy, ± e%
You will be 95% confident that the population percentage (π) lies between p% ± e%Copyright © 2010 Pearson Education, Inc.
publishing as Prentice Hall 13-22
Review: What does sample accuracy
mean? Example
Sample size of 1,000 Finding: 40% of respondents like
our brand Sample accuracy is ± 3% (via
our formula) So 37% - 43% like our brand
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-23
Sample Size Formula
Standard sample size formula for estimating a percentage:
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-24
Practice Examples
We will do some examples from the questions and exercises at the end of the chapter on sample size…question 5 on page 396.
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-25
Practical Considerations in Sample Size Determination
How to: Estimate variability (p times q) in the
population Determine the amount of desired
sample error Determine the amount of desired
sample error Decide on the level of confidence
desired13-26
Estimating a Mean
Estimating a mean requires a different formula (See MRI 13.1, p. 412.)
Z is determined the same way (1.96 or 2.58) S: variability indicated by an estimated standard deviation Since we are estimating a mean, we can assume that our
data are either interval or ratio. When we have interval or ratio data, the standard deviation, s, may be used as a measure of variance.
How to estimate s Estimate the range the value you are estimating can
take on (minimum and maximum value) and divide the range by 6.
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ExampleEstimating the Mean of a Population
What is the required sample size? Management wants to know
customers’ level of satisfaction with their service. They propose conducting a survey and asking for satisfaction on a scale from 1 to 10. (since there are 10 possible answers, the range=10).
13-28
ExampleEstimating the Mean of a Population
Management wants to be 99% confident in the results and they do not want the allowed error to be more than ±.5 scale points.
What is n?
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 13-29
Estimating a Mean: What is n?
S=10/6 or 1.7 Z=2.58 (99% confidence) e=.5 scale points What is n?
13-30
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
See the formula on page 419.
13-31
Field Work
Nonsampling Error in Marketing Research
Nonsampling error includes: All types of nonresponse error Data gathering errors Data handling errors Data analysis errors Interpretation errors
14-33
Data Collection Errors
14-35
Nonresponse Error
Nonresponse: failure on the part of a prospective respondent to take part in a survey or to answer specific questions on the survey
Response rate enumerates the percentage of the total sample with which the interviews were completed
CASRO response rate formula:
14-36
Nonresponse Error
CASRO response rate formula:
14-37
Unreliable Responses
Unreliable responses are found when conducting questionnaire screening, and an inconsistent or unreliable respondent may need to be eliminated from the sample.
Copyright © 2010 Pearson Education, Inc. publishing as Prentice Hall 14-38
Exercise on sample size determination Share focus group results Work on the questionnaire
Tutorial Activities