Probability Sampling and Marketing Research

Census Versus Sampling

• A census means measuring every member of a population or target population. It provides a tabulation of all members of a population.

• The study of statistics has taught us that cost effective estimates of population parameters can be achieved through careful sampling.

• Through a census, population parameters are known. With sampling, parameters are estimated and inferences are drawn about the population.

• Statistical inferences: the act of passing from statistical sample data to generalizations about a population.

• Permits statements to be made concerning population parameters:– "Thirty percent of all households in Rogers with

children out-shop for groceries.– "Younger households tend to regard retailers in Rogers

as ‘less friendly.’– "As the level of education for the head of household

increases, the number of cities shopped increases."

Sampling• A sample saves money and time.– Compare a sample versus a census:– Far greater speed in completing a 5% randomly

selected sample, as opposed to increasingly larger surveys (10%, 20%, etc.)

– Few census designs would satisfy the value of information constraint in marketing research.

• Sample size is directly related to the cost of a study, the more representative the sample, the lower the sample size needed.

Sampling

• A sample may be more accurate than a census.– A census requires enormous numbers of interviewers,

supervisors of interviewers, and people for data entry. There is limited supply of qualified labor available for any research purpose, which minimize sampling error.

• A sample is better in the event that the study results in the destruction or contamination of the element sampled.– You don't want to risk the potential disadvantages of

introducing a unpopular marketing action (advertisement, product, or price) to an entire market.

Sampling Purposes

• Survey research• Descriptive research (focus groups)• Subjects for causal research (experiments)• Syndicated suppliers– Household panels– Nielsen households – Retailer panels

Target Population

• Understanding the population is important, since all generalizations about behavior and preferences will be made toward that end, the target population.– Geography: households in the city of Rogers, or

households in Benton County with a Rogers zipcode.

– Behavior: registered voters versus likely voters.– Decision role: cola drinkers versus cola

purchasers.

Sampling Units• What will form the sampling units, or elements,

which become units of analysis--the basic level of investigation?– Consumers

• Users of the product• Purchasers of the product

– Households (on issues of joint decision making).– "Firms" or executives within the firm (on issues of the

firm's marketing strategy).– Employees of a single firm or employees of several firms

(on issues of motivation and compensation).

Sampling Frame

• The sampling frame is the working or operational population, from which the sample is drawn.

• The closer the sampling frame to the target population, the more accurate the inferences to that population.

• Example: When you rely on published directories in phone surveys, there are problems with unlisted numbers. The question becomes, is the population those households with telephones, or those at home on evenings with published phone numbers?

• Internet listings:– Yellow pages– “Dealer locaters”

• Directories:– Published phone listings– Trade associations– Employees– Students– "Reverse” directories

• Voter registration records• Mailing lists– Magazine subscribers - target market populations– City maps of neighborhoods, provide blocks for

random selection.

Probability Sampling

• In a probability sampling design, each element (or sampling unit) has a known probability of being selected.

• Given an adequate sampling frame, ability of sample to permit generalization becomes a function of only sample size.

• Without the ability to state that all elements of the sampling frame had an equal, nonzero probability of selection, severely limits generalizations to trivial populations

The Sampling Frame Decision:

• Drawing an inference to a target population?

• Permitting random sampling?

• Conducting survey research—would respondents have sufficient interest?

• Simple random sampling: – Combines random number generation with a

numbered sampling frame, such as random number table, computer generated selection, or blind selection.

• Systematic sampling:– Sampling every nth element in a sampling frame.

• Cluster, or multi-stage cluster sampling:– The entire sampling frame is first divided into

"clusters," or sampling unit aggregates, such as cities, or city blocks.

– Clusters are numbered and randomly selected.– Sampling units are selected within the cluster by an

additional probability sampling technique

Stratified Sampling• Problems with random sampling:– Few populations have “normal distributions.”– Identifiable subgroups within the population have

different variances in their responses.– Not all elements in the sampling frame are of equal

importance to marketers.– Not all elements in a sampling frame cooperate equally

in survey research.• Stratified sampling permits more accurate

estimates for the population by separate sampling within the subgroups.

• Proportionate stratified sampling: assures larger segments in population are represented proportionally in the overall sample. The final sample should bear closely resemble the strata overall population.

• Disproportionate stratified sampling:– Consumption levels are not normally distributed, and

the needs of heavier users should be measured more accurately (and more heavily sampled).

– Optimal allocation: some strata have higher variance in their responses, and need to be over-sampled to determine the true population parameters.

Example: Company seeks to broaden demand for a mature or maturing brand.

• Existing marketing strategy has developed a strong attachment of brand to segment of the market of heavier users.

• Current volume with this segment is inadequate, and company is faced with either broadening demand for the existing brand, or creating a new brand.

Group A

Group B

Group CHeavy users

Overallpurchases

Heavy Infrequent

Group A Group B

Group CHigh dispersion, Larger sample

OverallOpinion

Like ad Dislike ad

Stratified Sampling

• Group C: Heavy Users, have mixed, and highly variable opinions about the ad to reposition the brand.

• Group C should be sampled disproportionately to learn the effect of the ad on sales.

• What are the demographics or sampling frame that would give Group C accurate representation?

DEVELOPING A SAMPLING PLAN

Define the Target Population (Relevant Population)

Obtain a “Listing” of the Population

Design the Sample Plan: Size, Method

Access the Population

Draw the Sample

Drop-Down Substitution

Sampling/Resampling

Validate the Sample

Resample if Necessary

What Goes "Wrong" With Intentions to Follow Probability Sampling Designs?

• Limited resources force the marketing researcher to focus use only a very small sample size and very specific target population.

• No acceptable sampling frame exists.• Attempting to identify qualified respondents through

screening questions is a costly process.• The value of information for the research question

simply does not merit the expenses of simple random sampling.

Sampling Distribution of the Mean

• Approach symmetric, “bell-shaped” functions as sample size increases and is assumed to be normal for purposes of hypothesis testing and confidence intervals.

• Mean of this distribution is the population mean.• The standard deviation is the standard error of

the mean.

nss

x

Sample Size Determination for a Mean:Interval or Ratio Questionnaire Items

Where…

n = the sample size

z = standard error associated with the chosen level of confidence

s = variability indicated by an estimated standard deviation

e = acceptable error

2

22

e

zsn

32or ,2.3215

96.144.432

22

2

22

n

e

zsn

A researcher wants to know the average amount eachfairgoer spends on him/herself. A small sample has a standard deviation of $43.44. The researcher wants to know the amount within +/-$15 at the 95% confidence level.

Size and Sample Proportions• Proportions are appropriate with dichotomous

survey items, such as voting preferences.• Where p is a proportion of interest and q is 1-p.

95

95

n

qpzp

szp p

• What is the 95% confidence interval for the population proportion if the sample proportion is 60% and the sample size was 400.

• Error or Acceptable error is +/-0.048 or +/-5%

648,.552.

)0245(.96.160.400

4.6.1.96 , 96.160.

95

n

qp

szp p

Sample Size Determination for a ProportionAppropriate for Categorical or Nominally Coded

Questionnaire Items

Where…

n = the sample size

z = standard error associated with the chosen level of confidence

p = estimated proportion in the population

q = (100-p)

e = acceptable error

2

2 q)*(p

e

zn

600or ,84.59704.

.47)*(.5396.1

q)*(p

2

2

2

2

n

e

zn

A member of the county fair board has heard claims thatthe carnival rides are the single most popular attraction of thefair, more popular than all other attractions combined. A smallsample of fairgoers has indicated 53% for this proportion. Howlarge of a sample would be needed to state the true proportion within +/-4%?