Sampling Techniques

• Sampling gathers useful information about a population in business.
• Data are gathered from samples and used to draw conclusions about the population via inferential statistics.
• Samples provide a method for gathering useful decision-making information that might be otherwise impossible to obtain.

Reasons for Sampling

• Sampling saves money, time, and broadens study scope given the resources.
• Sampling doesn't destroy all products when the research process is destructive.
• Sampling is the only option when accessing the population is impossible.

Random Sampling Methods

• Random sampling includes simple, stratified, cluster, systematic, and multistage sampling.

Simple Random Sampling

• Entire sample is drawn from the sampling frame.
• Each sampling unit has an equal probability (n/N) of being selected, where n is the number of units to be selected, and N is the total number of units.
• Selected units may be "clumped" together, resulting in a less representative sample.

Stratified Sampling

• Divides population elements into homogeneous groups called strata.
• Simple random sampling is then used within each stratum.
• Each group is called a stratum.
• Strata should be relatively homogenous within, while contrasting with each other.
• Dividing heterogeneous populations into relatively homogenous groups is called stratification.
• Demographic variables are often used as the basis for stratification.

Cluster Sampling

• Divides the population into non-overlapping areas or clusters.
• Stratified sampling uses homogenous strata, cluster sampling uses internally heterogeneous clusters.
• Clusters contain a wide range of elements that are good representatives of the population.
• To survey individual consumers, cities can be divided into clusters of blocks, selecting consumers randomly from the blocks, if surveying individuals in a city is too large.
• Two-stage sampling divides the original cluster into a second set of clusters.

Systematic Sampling

• Used for its convenience and ease of administration, not to reduce sampling error.

Multistage Sampling

• Selection occurs in two or more steps and can also be called cluster sampling.
• A three-stage random sample might randomly select 10 of 50 states, five counties in each state, and 100 households in each county, totaling 5,000 households.
• Multistage sampling overcomes limitations on the availability of a full sampling frame
• It is impossible to use single-stage sampling because no sampling frame covers the entire population of interest.
• Multistage sampling ensures that the sample is well distributed across certain categories.
• Multistage sampling ensures the sample is clustered to reduce data collection costs.

Non-Random Sampling Methods

• Non-random sampling involves quota, convenience, judgment, and snowball sampling.

Quota Sampling

• Uses population subclasses (age, gender, region) as strata.
• Employs nonrandom sampling to gather data from each stratum until the desired quota is filled.
• Quota controls set the sample sizes obtained from subgroups, typically based on population proportions.

Convenience Sampling

• Elements are selected based on the researcher's convenience.
• The researcher chooses readily available, nearby and willing participants.
• Samples tend to be less variable, with fewer extreme elements.

Judgment Sampling

• Judgment of the researcher chooses elements selected for the sample.
• Researchers use sound judgement to save time and money believing they can find a more representative sample.
• Random sampling methods can outperform judgment sampling in estimating the population means.
• It's impossible to calculate the probability of element selection, so the sampling error cannot be objectively determined.

Snowball Sampling

• Survey subjects are selected based on a referral from other survey respondents.
• Researchers asks these people for other names/locations of potential candidates.
• It's cost-effective and efficient when subjects are difficult to locate.

Sampling Distribution and the Central Limit Theorem

• The central limit theorem states:
  • As sample size (n) increases, the sampling distribution of means approximates a normal distribution
  • The mean of the sampling distribution of means equals the population mean (μ).
  • The standard deviation equals σ/√n.
• Even if the shape of the population isn't normal, the sampling distribution will be normal if n ≥ 60.
• The mean of the sampling distribution of means, is called the expected value, equals μ
• Sample means are unbiased estimates of the population mean
• Standard error (σM) is the standard deviation of the sampling distribution of means.
• While a sample mean is expected to be close to the population mean, it will likely vary due to chance or random sampling error.
• The standard error (σM) represents the expected variation of a sample mean (M) from the population mean (μ).
• Formula for the standard error of the mean: σM = σ/√n.
• As sample size increases, standard error decreases.

Probabilities, Proportions, and Percentages of Sample Means

• The sampling distribution of means can determine probabilities, proportions, and percentages associated with sample means.
• Formulas are modified because of using sample means rather than raw scores.
• Formulas:
  • z = (M - μ) / σM
  • M = μ + (z × σM)
• In the sampling distribution of means, sample means run along the baseline, and z-scores are in standard error units.