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Week05_SamplingII.pdf

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Kong MGM 403

Sampling II

Kong MGM 403

Efficiency of Sampling Method

• Precision of sampling methods: think of it as generating representative sample – Greater precision usually comes with higher

sample collection cost

• Efficiency is similar to a precision-cost ratio – improve efficiency means to obtain higher

precision (a better representative sample) relative to cost

Kong MGM 403

Strengths and Weaknesses of Basic Sampling Techniques

Technique Strengths Weaknesses Nonprobability Sampling Convenience sampling

Least expensive, least time-consuming, most convenient

Selection bias, sample not representative, not recommended for descriptive or causal research

Judgmental sampling Low cost, convenient, not time-consuming

Does not allow generalization, subjective

Quota sampling Sample can be controlled for certain characteristics

Selection bias, no assurance of representativeness

Snowball sampling Can estimate rare characteristics

Time-consuming

Probability sampling Simple random sampling Easily understood,

results projectable

Difficult to construct sampling frame, expensive, lower precision, no assurance of representativeness Can decrease representativeness

Stratified sampling Include all important subpopulations, precision

Difficult to select relevant stratification variables, not feasible to stratify on many variables, expensive

Cluster sampling Easy to implement, cost effective

Imprecise, difficult to compute and interpret results

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Use of Nonprobability and Probability Sampling

Nonprobability sampling

• When projections to population are not needed – Concept test, package

test, copy tests

• Interested in proportion of sample that expresses various attitudes

Probability sampling

• When highly accurate estimates of market share or sales volume for the entire market are needed – National market tracking

studies on product category and brand usage rates (IRI, Nielsen)

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Internet Sampling

• E.g., visitors to a website are intercepted through pop-up window; send email to selected respondents

• Can apply probability sampling as well as nonprobability sampling – Consider website traffic, time constraint

• Pros: convenience for respondents; data collection fast and inexpensive

• Cons: Sample might not be representative of target population

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Internet Sampling

• Amazon.com wants to conduct an Internet survey to determine customer satisfaction. How would you select the sample?

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Sample Size for Probability Sampling

• Budget: costs of samples usually grow linearly with sample size

• Sample size needs to increase with – Traditional statistical methods:

• Desired confidence level

• Dispersion or heterogeneity in responses (S)

– Number of cells, comparison groups, or segments

– Number of variables under investigation

• Rules of thumb – 200 respondents per comparison group (ideal!)

– Absolute minimum > 5 per comparison group

– Look for conventions we can apply

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Compute Sample Size based on Statistical Method

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Basic Statistics (Review)

• Study students restaurant dining expenditure in the past month – Population: senior students at School of

Management

– Sample: simple random sample with size n=100

• Sample statistics: measures computed from the sample data

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Sample Statistics: Mean

• Mean of monthly expenditure

• n is sample size

is each data point (monthly expenditure for each student)

i k

n X 



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Sample Statistics: Standard Deviation

• Standard deviation of monthly expenditure – Measures dispersion of the expenditures we

observe from the sample

is the variance of monthly expenditure

( )

i k

x x S

n 

 





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Sample Statistics: Standard Deviation

Scenario 1 amount percentage

Under $50 0

50-99 0

100-149 20

150-199 40

200-249 30

Above $250 0

Scenario 2 amount percentage

Under $50 5

50-99 10

100-149 20

150-199 30

200-249 25

About $250 10

Kong MGM 403

Sample Statistics: Standard Deviation

Scenario 1: less disperse amount percentage

Under $50 0

50-99 0

100-149 20

150-199 40

200-249 30

Above $250 0

Scenario 2: more disperse amount percentage

Under $50 5

50-99 10

100-149 20

150-199 30

200-249 25

About $250 10

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Confidence Interval Estimate

• Suppose the sample mean of expenditure is $180.5, what would be the best estimate of the population mean (i.e., the average restaurant dining expenditure of all senior students at SOM during the past month)?

• However a point estimate (typically the sample mean) would rarely be the true value

• Less risky to provide a range estimate for the population mean, e.g., “I guess the population average is somewhere $180.5 $10”. A confidence interval estimate would be such a range estimate

Kong MGM 403

Confidence Interval Estimate

• Confidence interval of population mean

= sample mean margin of error

= : sample mean

: Z score corresponding to a chosen confidence level

: standard deviation of expenditure in sample

– n: sample size

• Technical detail: derivation based on central-limit theorem

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Confidence Interval Estimate

• Confidence level (CL) is measured as a percentage

• A 95% confidence level means that “with 95 percent confidence, I think the population mean would fall within that range”

• Technical detail: 95% CL means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.

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Confidence Interval Estimate

Confidence Level

Corresponding Z score

99% 2.576

95% (most common)

1.96

90% 1.645

• Higher confidence level, larger Z score, wider range of confidence interval

• • suppose • 99%

• 95%

• 90%

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Determining Sample Size

• Given 95% confidence level, if we want to narrow down the margin of error (i.e., the +/- difference from the sample mean), we need to increase sample size

• Suppose under 95% confidence, we want ME to be $2, the

required sample size would be ∗ . ∗

round to the next larger integer 217

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Determining Sample Size

• Slightly different formula for proportions – E.g., we are interested in population proportion of students

visited Asian restaurants

– Sample proportion is 35%

• Margin of error for a population proportion is

is the sample proportion; n is sample size

• 95% confidence interval for the population proportion (n=100) is . .

, or

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Determining Sample Size

• Given

• The required sample size is

• Under 95% confidence level, If we want 5% margin of error, the required sample size would be

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Sample Size for Nonprobability Sampling

• Judgment: • Best guess of “experts”

• Draw on your experience to determine sample size

• Conventional: • What have others done?

• See what the sample size has been for similar studies