Sample size

Ch 13 2

Sample Size Formula

• Standard sample size formula for estimating a percentage:

Ch 13 3

Practical Considerations in Sample Size Determination

• How to estimate variability (p times q) in the population– Expect the worst cast (p=50; q=50)– Estimate variability: Previous studies?

Conduct a pilot study?

Ch 13 4

Practical Considerations in Sample Size Determination

• How to determine the amount of desired sample error–Researchers should work with

managers to make this decision. How much error is the manager willing to tolerate?–Convention is + or – 5%– The more important the decision, the

more (smaller number) the sample error.

Ch 13 5

Practical Considerations in Sample Size Determination

• How to decide on the level of confidence desired–Researchers should work with

managers to make this decision. The more confidence, the larger the sample size.–Convention is 95% (z=1.96)– The more important the decision, the

more likely the manager will want more confidence. 99% confidence, z=2.58.

Ch 13 6

ExampleEstimating a Percentage in the Population

• What is the required sample size?– Five years ago a survey showed that 42% of

consumers were aware of the company’s brand (Consumers were either “aware” or “not aware”)

– After an intense ad campaign, management wants to conduct another survey and they want to be 65% confident that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population.

– What is n?

Ch 13 7

Estimating a Percentage: What is n?

• Z=1.96 (95% confidence)• p=42• q=100-p=58• e=5• What is n?

Ch 13 8

Estimating a Percentage: What is n?

• What does this mean?– It means that if we use a sample size of 374,

after the survey, we can say the following of the results: (assume results show that 55% are aware)

– “Our most likely estimate of the percentage of consumers that are ‘aware’ of our brand name is 55%. In addition, we are 95% confident that the true percentage of ‘aware’ customers in the population falls between 50% and 60%.”

N=374

Ch 13 9

Estimating a Mean

• Estimating a mean requires a different formula (See MRI 13.2, p. 378)

• Z is determined the same way (1.96 or 2.58)• E is expressed in terms of the units we are

estimating (i.e., if we are measuring attitudes on a 1-7 scale, we may want error to be no more than ± .5 scale units

• S is a little more difficult to estimate…

Ch 13 10

Estimating s

• 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.

Ch 13 11

Estimating s

• How to estimate s?–Use standard deviation from a previous

study on the target population.–Conduct a pilot study of a few members

of the target population and calculate s.– Estimate the range the value you are

estimating can take on (minimum and maximum value) and divide the range by 6.

Ch 13 12

Estimating s

–Why divide the range by 6?• The range covers the entire distribution and ± 3

(or 6) standard deviations cover 99.9% of the area under the normal curve. Since we are estimating one standard deviation, we divide the range by 6.

Ch 13 13

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).

– Management wants to be 99% confident in the results and they do not wan the allowed error to be more than ±.5 scale points.

– What is n?