Sampling Theory and Methods in Marketing Research

Value of Sampling in Marketing Research

• Definition of Sampling: Selecting a small number of elements from a larger defined group to make accurate judgments about the larger group.
• Purpose of Sampling: Used when a census (data collection from every member of the target population) is not possible.
• Advantages:
  • Quicker and less costly than a census.
  • Important for questionnaire design.

Sampling Theory Basics: Population

• Population: An identifiable group of elements pertinent to the research problem.
• Target Population: The entire set of elements identified for investigation based on research objectives.
• Sampling Units: Elements actually available during sampling.
  • Examples:
  • Mazda: Adult purchasers of automobiles, sampling new Mazda purchasers.
  • Retail Banking: Households with checking accounts within a 10-mile radius of Charlotte, NC.

Sampling Theory Basics: Sampling Frame

• Sampling Frame: A list of all eligible sampling units.
  • Common Sources: Voter lists, magazine subscribers, credit card holders.
• Challenges: Obtaining accurate and current sampling frames can be difficult and costly.

Sampling Theory Basics: Underlying Factors

• Complete Knowledge: Perfect information would eliminate the need for primary research.
• Central Limit Theorem (CLT): Samples derived from a simple random sample will be normally distributed if sample size (n) is sufficiently large (n ≥ 30).
• Mean and Error:
  • Mean (x) fluctuates around the true population mean (μ) with a standard error of \frac{\sigma}{\sqrt{n}}.

Sampling Theory Basics: Tools Used to Assess Sample Quality

• Sampling Error: Bias due to selection mistakes; can be reduced by increasing sample size.
• Nonsampling Error: Errors that occur regardless of sampling or census, affecting data accuracy and quality.

Probability and Nonprobability Sampling

• Probability Sampling: Each unit has a known probability of selection, ensuring unbiased selection.
  • Results can be generalized to the target population.
• Nonprobability Sampling: Selection is based on judgment; probability is unknown.

Probability Sampling Designs

Simple Random Sampling

• Definition: Every unit has an equal chance of selection.
  • Advantages: Generalizable results, valid representation.
  • Disadvantages: Difficult to obtain complete lists.

Systematic Random Sampling

• Method: Target population is ordered; samples drawn at regular intervals.
  • Advantages: Easy to draw samples; time-saving.
  • Disadvantages: Potential bias from hidden patterns.

Stratified Random Sampling

• Method: Population divided into strata; samples taken from each stratum.
  • Variations: Proportionate (larger strata sampled more) vs. disproportionate sampling.
  • Advantages: Assures representativeness, allows cross-stratum comparisons.
  • Disadvantages: Difficulty in determining strata.

Cluster Sampling

• Definition: Divides units into clusters and samples from these.
  • Advantages: Cost-effective and simple to implement.
  • Disadvantages: Clusters may be homogeneous, leading to less precise estimates.

Nonprobability Sampling Designs

Convenience Sampling

• Definition: Samples drawn at the convenience of the researcher.
  • Advantages: Quick data collection.
  • Disadvantages: Difficult to assess representativeness; not generalizable.

Judgment Sampling

• Definition: Respondents chosen based on the researcher’s belief of their representativeness.
  • Advantages: Better than convenience sampling.
  • Disadvantages: Cannot measure representativeness.

Quota Sampling

• Definition: Participants selected according to quotas for certain characteristics.
  • Advantages: Reduces selection bias, ensures subgroup representation.
  • Disadvantages: Reliant on subjective decisions; limits generalization.

Snowball Sampling

• Definition: Existing respondents help identify new ones.
  • Advantages: Useful for hard-to-reach populations.
  • Disadvantages: Potential for bias; limited ability to generalize results.

Determining the Appropriate Sampling Design

• Considerations:
  • Research objectives (qualitative vs. quantitative).
  • Needed accuracy and insights.
  • Availability of resources and timelines.
  • Knowledge of the target population and sampling frame.

Determining Probability Sample Sizes

• Factors:
  • Population variance and standard deviation impact sample size.
  • Desired confidence level correlates with sample size requirement.
  • Precision of estimates affects sample size choices; smaller errors require larger samples.

Determining Probability Sample Sizes: The Formulas

• Estimating Population Mean:
  n = \frac{Z^2 \sigma^2}{e^2}
• Estimating Population Proportion:
  n = \frac{Z^2 P Q}{e^2}
• Correction Factor for Small Populations:
  n = \frac{N}{1 + (N - 1)\frac{e^2}{Z^2}}

Steps in Developing a Sampling Plan

1. Define the target population.
2. Select the data collection method.
3. Identify the necessary sampling frame(s).
4. Select the appropriate sampling method.
5. Determine sample sizes and overall contact rates.
6. Create an operational plan.
7. Execute the operational plan.

Sampling and Secondary Data

• Accuracy: Evaluate how original data were collected, the competence of researchers, documentation quality, timing of original data, and method consistency with standards.
• Multiple Sources: Check for consistency across sources for reliability.