Chapter 5: Producing Data 5.1 – Designing Samples "An approximate answer to the right question is worth a good deal more than the exact answer to an approximate question." John Tukey

Overview If one wishes to obtain reliable statistical information from sampling, one must design the sampling process very carefully. Good sampling techniques, which involve the use of chance, can produce meaningful and useful results. Bad sampling techniques often produce worthless data. This section introduces or reinforces many important definitions.

Basic Definitions Sample: part of the population that we actually examine Census: attempts to contact every individual in entire population Design: the method used to choose the sample Sample is biased if it systematically favors certain outcomes.

Types of Sampling Methods 1.Voluntary Response –Consists of people who choose themselves. (As contrasted to being chosen by some designed process.) –Ex: Listeners calling in to respond to a question asked by a talk show host Often biased because only those with strong opinions are likely to respond

2.Convenience –Just select individuals easiest to reach –Example: Getting opinions about a political candidate by simply asking people who enter a specific store In this case, the sample may not represent the entire population Types of Sampling Methods

3.Simple Random Sample (SRS) –Sample chosen in such a way that every set of N individuals has an equal chance of being chosen. –Sample often chosen using a random digits table (Table B) Types of Sampling Methods

Steps for using Table B 1.Assign numerical labels to individuals –All labels must have the same amount of digits –Use shortest possible labels Example: If there are 10 individuals: Use 0-9. If there are 100: use Use Table B –You can start at any row, but don’t always start at the same row –Read set # of digits at a time from left to right Matches how you labeled individuals –Ignore any repeats or #’s not from individuals

Steps for using Table B 3.Indicate when to stop –If you only need 10 subjects then you must actually say that you will stop once you obtain Identify the subjects in the sample

Example: Joan’s Accounting Firm Joan’s small accounting firm serves 30 business clients. Joan wants to interview a sample of 5 clients in detail to find ways to improve client satisfaction. Apply the 4-step SRS process 1.Label 2.Table 3.Stopping Rule 4.Identify

Step 1: Assign Labels

Step 2: Use Table Enter Table B anywhere and read two digit groups. For this example lets start at line 130. Ignore numbers that are > 30 and any repeats.

Step 3: Stopping Rule Use line 130 and continue to line 131 if needed until five clients are chosen Our five clients are: 05, 16, 17, 20, 19

Step 4: Identify The five clients chosen are: 1.Bailey Trucking 2.JL Records 3.John Commodities 4.Liu’s Chinese Restaurant 5.MagicTan

4.Probability Sample –gives each member of the population a known chance of being chosen. –An SRS is one example of a probability sample which gives each member of the population an equal chance to be selected. –Other probability sampling methods may be more elaborate, but all use chance to select the sample. Types of Sampling Methods

5.Stratified Random Sample –Divides the population into strata (groups) –Do an SRS of each strata –Combine to form full sample –Ensures an equal amount from each group Example: equal amt of boys and girls Types of Sampling Methods

Ex: 2000 high school students Want a sample of 24 students With an SRS, we run the risk of getting 24 freshman We can stratify by grade –SRS of 6 students from each strata student sample

6.Cluster –Divides the pop into groups or clusters –SRS to choose desired number of clusters –All individuals in clusters chosen are used in sample Types of Sampling Methods

Ex: 2000 high school students Use homerooms as clusters Assign each homeroom a numeric label Do an SRS to pick n homerooms Sample entire homerooms that are chosen

Homework: # , , 5.10, 5.13, 5.14

7.Systematic Random Sample –Divide population by desired sample size Call this number n –Sample will be every nth person selected Ex: If population is 100 and you want 5, select every 20 th person Do not have to start at the beginning –Use an SRS to determine where to start –Gives each individual, but not each sample, and equal chance of being chosen. Types of Sampling Methods

Type of Bias 1.Undercoverage: some group was left our in the process of choosing sample –Use only home phones you will miss 7-8% 2.Nonresponse: an individual chosen for a survey cannot be reached or does not cooperate

Type of Bias 3.Response Bias: refers to a variety of things that can lead to incorrect or false repsonse –People lie –People know or think they know what you want to hear –Ex: An interviewer directly asking a person "Have you ever shoplifted?" may well get some answers that are lies. A sample design that would allow for an anonymous response would probably get more accurate results.

Types of Bias 4.Wording of the Question: can greatly influence a response. –Two people can ask the same question differently and get different results. Version 1: Do you think there should be an amendment to the Constitution prohibiting abortions? …Results (Yes = 29%, No = 62%) Version 2: Do you think there should be an amendment to the Constitution protecting the life of the unborn child?...Results: (Yes = 50%, No = 39%)

Types of Bias Wording continued… –Poorly worded questions can confuse people and often are misleading as well –Ex: Do you think it is wrong when the government doesn't interfere in potentially dangerous religious matters?YES / NO

In general… It is very hard to generalize conclusions from a sample about a population Larger samples give more accurate results Homework: # , 5.18, 5.19