AP STATISTICSSection 5.1 Designing Samples

Objective: To be able to identify and use different sampling techniques.

Observational Study: individuals are observed and variables of interest are measured. No influence on the responses.

Experiment: actively impose a treatment on a group in order to observe a response.

Population: the entire group of individuals that we desire information about.

Sample: a subset of the population that we actually examine in order to gather information about the population.

Census: attempts to contact every individual in the entire population.

Sampling Method: the process used to choose the sample.

Sampling frame: the actual list of individuals from which the sample is actually selected.

Types of Sampling Techniques:

1. Voluntary Response Sample: consists of individuals who choose themselves to respond to a general appeal.

2. Convenience Sample: sampling which chooses individuals that are easiest to reach.

Biased: systematically favors certain outcomes.

3. Simple Random Sample: (SRS) a sample of size n in which each individual has the same chance of being selected and each set of n individuals has the same chance of being selected.

Steps:

1. Label subjects. Using the RNT:• <10 use digits 0 – 9• 11 – 100 use digits 00 – 99• 101 – 1000 use digits 000 – 999 (and so on)

2. Select x digits at a time.

3. Skip repeats and specified digits.

4. Stopping rules

Ex. Select a sample of size 3 from students in this class using line 110 of the RNT.

4. Probability Sample: a sample chosen by chance. We must know what samples are possible and what chance each sample has.

5. Stratified Random Sample: a. Divide the population into groups of similar individuals called

strata.

b. Choose an SRS from each strata.

c. Combine all the SRSs to form the one sample

Ex. Choose a stratified random sample of size 4 from a population that has 20 individuals (15M / 5F). Use line 120 from the RNT to do so.

6. Cluster Sample:a. Divide the population into heterogeneous groups (clusters).

b. Assign each cluster a number.

c. Choose an SRS of the clusters.

d. Combine all the members of the randomly selected clusters to form the sample.

Ex of clusters:

7. Multistage Sample: restricts random selection by choosing the samples in stages. Uses multiple sampling techniques within the sampling process.

Ex.

8. Systematic Random Sample: a. Begin by finding k.

b. Think of the population in k groups.

c. Randomly select the first subject/unit by randomly selecting a number from 1 to k.

d. This subject/unit is the first member of the sample. Continue to add k to this first number to get the remaining members of the sample.

Ex. Choose a Systematic Random Sample from a class of 24 students where n = 4.

Types of Bias:

1. Undercoverage: occurs when some subgroup of the population is unintentionally left out of the sampling process.

2. Nonresponse: occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate.

3. Response bias: when the behavior of the interviewer or the respondent affects the results.

4. Wording of the Question: when the phrasing of the questions leads to biased results.

*Larger samples give more accurate and less variable results. However, if the data is poorly collected there is no way to fix biased results.