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

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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).

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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%…

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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?

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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:

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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

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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

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Sample Size Formula

Standard sample size formula for estimating a percentage:

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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.

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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).

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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?

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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.

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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

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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:

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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.

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Exercise on sample size determination Share focus group results Work on the questionnaire

Tutorial Activities