Chapter 1: The Nature of Statistics

1.4Other Sampling Designs

Drawbacks to simple random sampling

• May fail to provide sufficient coverage when information about subpopulations is required

• May be impractical when the members of the population are widely scattered geographically

Systematic Random Sampling

• Step 1– Divide the population size by the sample size and round the

result down to the nearest whole number, m

• Step 2– Use a random-number table (or a similar device) to obtain a

number, k, between 1 and m

• Step 3– Select for the sample those members of the population that

are numbered k, k+m, k+2m, …, k+(sample size – 1)m

Systematic Random Sampling

• Easier to execute than simple random sampling

• Usually provides results comparable to simple random sampling

• Only exception…prescence of some kind of cyclical pattern in the listing of the members of the population (male, female, male, female,…)– Relatively rare

Cluster Sampling

• Step 1– Divide the population into groups (clusters)

• Step 2– Obtain a simple random sample of the clusters

• Step 3– Use all the members of the clusters obtained in

Step 2 as the sample

Disadvantage to Cluster Sampling

• Each cluster needs to mirror the entire population– Not usually the case, as members of a cluster are

frequently more homogeneous than the members of the population as a whole

Stratified Random Sampling with Proportional Allocation

• Proportional allocation– Strata are sampled in proportion to their size

• Step 1– Divide the population in subpopulations (strata)

• Step 2– From each stratum, obtain a simple random sample of size

proportional to the size of the stratum (total sample size times stratum size divided by population size)

• Step 3– Use all the members obtained in Step 2 as the sample

Multistage Sampling

• Combining of types of sampling

• Used by pollsters and government agencies

• i.e. Cut up into clusters, then do different kinds of sampling to each cluster

Practice Problems

• P. 21-22

• 1.33 – 1.37