1. Sampling Fundamentals 2

2. Sampling Process Identify Target Population Determine Sampling Frame
Select Sampling Procedure
Determine Sample Size

3. Determining Sample Size – Ad Hoc Methods
Rule of thumb
Each group should have at least 100 respondents
Each sub-group should have 20 – 50 respondents
Budget constraints
The question then is whether the study can be modified or cancelled
Comparable studies
Find similar studies and use their sample sizes as guides

4. Factors determining sample size
Number of groups and sub-groups in the sample that are to be analyzed
Value of the study and accuracy required
Cost of generating the sample
Variability in the population

5. Sample size determination
In most MR problems we are interested in knowing the mean. (e.g. mean attitude scores, mean sales, etc.).
We want an good estimate of the population mean
Since the population mean is generally unknown, we must select the sample with care so that the sample mean will be the closest approximation to the population mean

6. Sample size determination
We want a sample that is
Selected through random sampling
Is as large as possible

7. 1. Normal Distribution
The entire area under
the curve adds up to 100%

8. 1. Features of normal distributions
68% of responses between  + 1 
95% of responses between  + 2 
99.99% of responses between  + 3 
Bell shaped curve
Mean = Median = Mode

9. 2. Sampling distribution of means
Distribution of mean responses on an item, from every probability sample taken from the same population, the sample being taken an infinite number of times
Smaller sample size = unstable means and greater variability (higher standard error of the mean) and greater sampling error (Recall what is sampling error?)
Larger sample sizes = stable means and lower variability (lower standard error of the mean) and smaller sampling error (Recall what is sampling error?)
Sampling distribution of means with larger sample sizes give a better approximation to the normal distribution
E(X bar) = µ

10. 3. Standard Error of the Mean
Standard deviation of the sampling distribution of means
sxbar = sx / n
I.e. standard error of the mean will equal the standard deviation of the population divided by the square root of the sample size
I.e. the greater the n, the smaller the standard error
Therefore random sampling with a larger sample size gives a more accurate estimate