An observational study observes individuals and measures variable of interest but does not attempt to influence the responses. Often fails due to lurking variables.

An experiment, on the other hand, deliberately imposes some treatment on individuals in order to observe their responses. Is the preferred method of gaining knowledge

since it allows us to control lurking variables.AP Statistics, Section 5.1, Part 1 2

The entire group of individuals that we want information about is called the population.

A sample is a part of the population that we actually examine in order to gather information.

The units are the individuals on which the experiment is performed.

AP Statistics, Section 5.1, Part 1 3

Sampling involves studying a part in order to gain information about the whole.

Sample Frame is the actual set of units from which a sample has been drawn.

A census attempts to contact every individual in the entire population.

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Getting a portion of the population is not difficult.

Getting a good unbiased sample is difficult.

Creating a plan to do this is called “sample design”.

AP Statistics, Section 5.1, Part 1 5

Voluntary response sample (example: Call in opinion polls).

The problem with call in opinion polls is that the people who answer the polls tend to have strong opinions, especially strong negative opinions.

This sample is biased; this sample is not representative of the population.

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Convenience sample (example: Mall intercept interviews)

Convenience sampling may not get you access to all the people in the population.

Interviewers often avoid people who may make them feel uncomfortable.

This sample is biased; this sample is not representative of the population.

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The design of a study is biased if it systematically favors certain outcomes.

You are conducting an observational study on how many students in you class like your math teacher. State if the following is an example of:

Convenience sampling Voluntary Response sampling A good sampling design Not even sampling

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The easiest way to sample is to use a “simple random sample”

A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Avoids favoritism by the selectors and self-

selection by the respondents. AP Statistics, Section 5.1, Part 1 10

Choose an SRS in two steps: Step 1: Label. Assign a numerical label

to every individual in the population.▪ Use the smallest amount of digits possible. ▪ Each label must contain the same amount of

digits. Step 2: Random Assignment.

▪ Random number table (Table B)▪ Random number generator (RandInt in the TI-

83)AP Statistics, Section 5.1, Part 1 11

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A method of selecting members from a larger population according to a random starting point and a fixed, periodic interval. Typically, every “nth” member is selected from the total population.

Ex: A cop at a checkpoint decides to speed check every 10th car that passes him.

To select a stratified random sample, first divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample.

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Convenience – it is easier to sample smaller groups.

Coverage – representation from each group is assured.

Precision – gives estimates closer to the true value of the population than an SRS.

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Good sampling technique uses random selection to reduce the possibility of bias.

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Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Surveys of households leave out homeless

people, prison inmates and college dorms… Opinion polls by telephone leaves out people

with out phones, or are not listed…Nonresponse occurs when an

individual chosen for the sample can’t be contacted or does not cooperate.

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Response bias. Respondents may lie if they feel uncomfortable telling the truth. The interviewer’s attitude towards some

answers may influence how the respondents answer.

Ex. The interviewer wears an anti-abortion shirt while asking people about their views on abortion.

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Wording of questions. “It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail and yard wastes are estimated to account for about 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?”

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“Do you own or have you ever own a fur coat?”

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We want to make inferences about the population as a whole.

We can’t afford to talk to everyone.Even though two samples, following

the same design most probably will give us different results, those results are reasonable estimates of the population as a whole

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Properly designed samples avoid systematic bias, but their results are rarely accurate and vary from sample to sample. (Sampling Error)

Large random sample give more precise results than smaller sample.

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