Sampling Fundamentals 1Sampling Fundamentals 1

Sampling Fundamentals

• Population

• Sample

• Census

• Parameter

• Statistic

The One and Only Goal in Sampling!!

Select a sample that is as representative as possible.

So that an accurate inference about the population can be made – goal of marketing research

Sampling Fundamentals

• When Is Census Appropriate?

• When Is Sample Appropriate?

Error in Sampling• Total Error

• Sampling Error

• Non-sampling Error (dealt with in chapter 4)

Sampling Process: Identify Population

• Question: For a toy store in RH

• Question: For a small bookstore in RH specializing in romance novels

Sampling Process: Determine sampling frame• List and contact information of population

members used to obtain the sample from• Example – to address a population of all

advertising agencies in the US, the sampling frame would be the Standard Directory of Advertising Agencies

• Availability of lists is limited, lists may be obsolete and incomplete

Problems with sampling frames

• Subset problem– The sampling frame is smaller than the

population

• Superset problem– Sampling frame is larger than the population

• Intersection problem– A combination of the subset and superset

problem

Problems with sampling frames

Sampling Process: Sampling ProcedureProbability Sampling

Nonprobability Sampling

Sampling Procedure

Sampling Procedures

Non-Probability Sampling

Probability Sampling

-Simple Random Sampling-Systematic Sampling-Stratified Sampling-Cluster Sampling

-Convenience Sampling-Judgmental Sampling-Snowball Sampling-Quota Sampling

Here’s the difference!

Probability Sampling: Each subject has the same non-zero probability of getting into the sample!

Probability Sampling TechniquesSimple Random Sampling

• Each population member has equal, non-zero probability of being selected

• Equivalent to choosing with replacement

Probability Sampling Techniques

• Accuracy – cost trade off

• Sampling Efficiency = Accuracy/Cost

– Sampling efficiency can be increased by either reducing the cost, increasing the accuracy or doing both

– This has led to modifying simple random sampling procedures

Probability Sampling Techniques

Stratified Sampling• The chosen sample is forced to contain units from

each of the segments or strata of the population• Sometimes groups (strata) are naturally present in

the population• Between-group differences on the variable of

interest are high and within-group differences are low

• Then it makes better sense to do simple random sampling within each group and vary within-group sample size according to– Variation on variable of interest– Cost of generating the sample– Size of group in population

• Increases accuracy at a faster rate than cost

Stratified Sampling – what strata are naturally present

Consumer type Group size 10 Percent directly proportional stratified sample size

Brand-loyal 400 40

Variety-seeking

200 20

Total 600 60

Directly Proportionate Stratified Sampling

• 600 consumers in the population:

• 200 are heavy drinkers

• 400 are light drinkers.

• If heavy drinkers opinions are valued more and a sample

size of 60 is desired, a 10 percent inversely proportional

stratified sampling is employed. Selection probabilities are computed as follows:

Denominator

Heavy Drinkers proportion and sample size

Light drinkers proportion and sample size

600/200 + 600/400 = 3 + 1.5 = 4.5

3/ 4.5 = 0.667; 0.667 * 60 = 40

1.5 / 4.5 = 0.333; 0.333 * 60 = 20

Inversely Proportional Stratified Sampling

Probability Sampling Techniques

Cluster Sampling

• Involves dividing population into clusters

• Random sample of clusters is selected and all members of a cluster are interviewed

• Advantages

– Decreases cost at a faster rate than accuracy

– Effective when sub-groups representative of the population can be identified

Cluster Sampling

• Math knowledge of all middle school children in the US

• Attitudes to cell phones amongst all college students in the US

• Knowledge of credit amongst all freshman college students in the US

A Comparison of Stratified and Cluster Sampling

Stratified sampling

Homogeneity within group

Heterogeneity between groups

All groups are included

Random sampling in each group

Sampling efficiency improved by increasing accuracy at a faster rate than cost

Cluster sampling

Homogeneity between groups

Heterogeneity within groups

Random selection of groups

Census within the group

Sampling efficiency improved by decreasing cost at a faster rate than accuracy.

Probability Sampling Techniques• Systematic Sampling

– Systematically spreads the sample through the entire list of population members

– E.g. every tenth person in a phone book– Bias can be introduced when the members in the list

are ordered according to some logic. E.g. listing women members first in a list at a dance club.

– If the list is randomly ordered then systematic sampling results closely approximate simple random sampling

– If the list is cyclically ordered then systematic sampling efficiency is lower than that of simple random sampling

Non-Probability Sampling• Benefits

– Driven by convenience

– Costs may be less

• Common Uses

– Exploratory research

– Pre-testing questionnaires

– Surveying homogeneous populations

– Operational ease required

Non-Probability Sampling Techniques

• Judgmental

• Snowball

• Convenience

• Quota