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- Chapter 17
- Sample Size Determination
- Adapted from Andrei Strijnev

Basic Considerations in Determining Sample Size

- Precision the degree of error in a study, or

the size of the estimating interval - How precise should the estimate be?
- More less error, smaller estimation interval
- Less more error, greater estimation interval
- Confidence the degree to which one can feel

confident that an estimate approximates the true

value - These two terms are highly correlated

The Importance of Sample Size

- Too small sample size leads to undesirably large

sampling error. - Too large sample size wastes time and money.

Methods of Determining Sample Size

- Ad Hoc Methods
- Based on budget constraint
- Use of expert guidance
- Use previous sample sizes
- Statistical Method

Sample Size Determination The Intuition

- More accurate information required larger

sample size needed - More diversified population larger sample size

needed - The marginal gain in information accuracy is

diminishing with the increase of sample size

Sample Size DeterminationThe Equation

The relationship between sampling error and

sample size

sampling error for variable x

s estimated standard deviation for variable

x in the population

n sample size

Sampling Error Sample Size

Sampling Error Confidence Interval

- Marketing researchers usually use confidence

intervals to describe sampling error. - Meaning of confidence interval
- If the estimate of a variable is 1000 and it has

a 95 confidence interval of ?100, then - with 95 probability the true value of that

variable is between 900 and 1100.

Sample Size Determination Measures of Interest

in Most Surveys

- Sample Mean, Examples include
- Mean rating on an attitudes measurement scale
- Mean income, age
- Mean number of purchases, monthly expenditure
- Sample Proportion, Examples include
- Proportion of households owning ? 2 cars
- Proportion of households spending more than

400/month on food - Probability of purchase

The Confidence Interval Approach to Sample Size

Estimates of Means

- If a 95 confidence interval of ? I95 is

desired,

.

Example

- A marketing manager of a frozen foods firm wants

to estimate the average dollars that families in

a certain city spend on frozen foods per year. - He wants the estimate to have a 95 confidence

interval of ?10. - He estimates that the standard deviation of

annual family expenditures is about 100. - What is the desired sample size for this study?

In this problem, I9510, s100. Applying

,

we obtain that n(1.96100)2/102385. Thus,

385 families must be chosen for this study.

How to Estimate Standard Deviation (s)

- 1. Subjective judgment
- 2. Use pilot study
- 3. If min and max values in population is known,

choose s (max value - min value) / 6.

The Confidence Interval Approach to Sample Size

Estimates of Proportions

- If a 95 confidence interval of I95 is desired,

,

where p is the estimated proportion in the

population.

Example

- A sporting goods marketer wants to estimate the

proportion of tennis players among college

students. - He wants the estimate to have a 95 confidence

interval of ?0.02. - A pilot study of 50 students showed that 20 of

them played tennis. - What is the required sample size for the final

study?

In this problem, I950.02, p20/500.4.

Applying

,

we obtain that n(1.962)/0.0220.4(1-0.4)2305

. Thus, 2305 students must be sampled.

How to Estimate p

- 1. Subjective judgment
- 2. Use pilot study
- 3. Set p50

More Examples

- PETsMART wants to determine the average number of

cats in each U.S. household. It wants the

estimate to have a 95 confidence interval of ?

0.5 cat. You recall once reading an article that

says the households with the most cats was headed

by an 85 year old woman who owned 35 cats. What

is the desired sample size for this study?

More Examples

- PETsMART wants to determine the proportion of

U.S. households who have dogs. It wants its

estimate to have a 95 confidence interval of ?

0.04. What is the desired sample size for this

study?

Punch-Lines

- The intuition of sample size determination
- Determine sample size for estimating means and

proportions - Three ways of estimating s and p

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