Section 4.1 Why Take Samples and

Why Take Samples and How Not To Section 4.1 Why Take Samples and How Not To

Read Activity 4.1a on pages 220 – 222 before class tomorrow Time in the Hospital Read Activity 4.1a on pages 220 – 222 before class tomorrow

Population: set of people or things that you want to know something about. Population changes depending on your particular interest

Population Changes Issue Population Presidential election ??

Population Changes Issue Population Presidential election US citizens 18 & ↑

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election ??

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election state citizens 18 & ↑

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election state citizens 18 & ↑ Senior class election ??

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election state citizens 18 & ↑ Senior class election all seniors

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election state citizens 18 & ↑ Senior class election all seniors Food for our class party ??

Population Changes Issue Population Presidential election US citizens 18 & ↑ Gubernatorial election state citizens 18 & ↑ Senior class election all seniors Food for our class party members of this class

Units are the individual elements of the population

Units are the individual elements of the population Population size is the number of units

Census What is a census?

Census Census: when we collect data on the entire population

Census Census: when we collect data on the entire population Often times, we can’t get data from whole population so we use a subset called a sample. Sample is set of units you study

Parameter is the characteristic of the population in which we are interested Examples: population mean, population standard deviation

Statistic is a numerical summary of the sample Parameter is the characteristic of the population we are interested in Examples: population mean, population standard deviation Statistic is a numerical summary of the sample Examples: sample mean, sample standard deviation

Why take a sample? Taking a census would give us an accurate representation of the population’s characteristic in which we are interested Why would we ever take a sample of the population rather than always using a census?

Why take a sample? Consider the following situations: 1) determining ratings for TV shows 2) who is favored to win an election 3) tensile strength of steel bars 4) quality control of chocolate chip cookies

Why take a sample? 1) 2) 3) 4)

Why take a sample? 1) sampling can save time 2) 3) 4)

Why take a sample? 1) sampling can save time 2) sampling can save money 3) 4)

Why take a sample? 1) sampling can save time 2) sampling can save money 3) testing sometimes destroys items 4)

Why take a sample? 1) sampling can save time 2) sampling can save money 3) testing sometimes destroys items 4) sampling can make it possible to collect more or better information on each unit

Page 220, D1

Page 220, D1 a. Census. Each new car is inspected. This procedure is used because every customer expects his or her new car to be perfect. Also, if a safety-related problem gets by in even one car, the cost is high.

Page 220, D1 b. Sampling. Counting the chocolate chips in a cookie is destructive, and counting all the chips in every cookie is time-consuming.

Page 220, D1 c. Sampling. Theoretically, elections in the United States are a census of eligible voters, but because not everyone who is eligible actually votes, elections are in practice a nonrandom sample.

Page 220, D1 d. Sampling. Not every movie theater owner reports ticket sales every weekend.

Page 220, D1 e. Sampling. With thousands of teachers in the Los Angeles area, it would be too time-consuming and expensive to do in-depth interviews with all of them. Sampling also makes it possible to collect more or better information from teachers interviewed.

Samples Trustworthy? Recall, we use samples to learn something about a population

Samples Trustworthy? Recall, we use samples to learn something about a population Good sample is representative, that is, it looks like a small version of the population

Samples Trustworthy? Recall, we use samples to learn something about a population Good sample is representative, that is, it looks like a small version of the population Some samples are more trustworthy (representative of the population) than others.

2 ways to get untrustworthy sample (1) bias in way sample is selected

2 ways to get untrustworthy sample (1) bias in way sample is selected (2) bias in way you get a response from units in your sample

Bias A biased person unreasonably favors one point of view over another Biased opinion is not objective, or not balanced In statistics, a biased sampling method is unbalanced

Danger of Biased Sampling Biased sampling method produces samples such that the estimate from the sample, or statistic, is larger or smaller on average than the population parameter being estimated

Biased vs Nonrepresentative Bias is a property of sampling method Nonrepresentative is a property of a specific sample

Biased vs Nonrepresentative Bias is a property of sampling method Nonrepresentative is a property of a specific sample You can not tell if a sample is nonrepresentative, but you can tell if a sampling method is biased

Page 223, D3

Page 223, D3 All are possible. An unbiased sample-selection method will result in some samples that are representative and some that are not. A biased selection method produces samples where the estimate from the sample is too large or too small on average. But some samples are likely to have estimates that are about right.

Sample selection bias is present in a sampling method if samples tend to result in estimates of population parameters that systematically are too high or too low

Types of Bias Size bias: method that gives larger units a greater chance of being in the sample Using map to select farms to sample Different sizes of slips of paper

Types of Bias Volunteer sample: those who care about the issue will be overrepresented, those who don’t care as much may not be represented at all Polling radio station listeners Town Hall meeting on recycling

Types of Bias Convenience sample: units chosen are those that are easy to include “ask your friends” Your 1st quarter project

Types of Bias Judgment sample: rely on judgment of an expert to choose a sample that he or she considers representative Experts may overlook important feature of a population Example: 1948 presidential election: Truman vs Dewey

Unbiased Sampling Method Requires all units in population have a known chance of being selected

Unbiased Sampling Method Requires all units in population have a known chance of being selected Notice this says a known chance of being selected, not necessarily an equal chance of being selected

Unbiased Sampling Method Requires all units in population have a known chance of being selected You must prepare a “list” of population units called a sampling frame or frame, from which you select the sample

More Bias - - Not just from Method Bias can also occur in the responses from the sample

Nonresponse bias: not uncommon for 40% of the people contacted to refuse to answer a survey

Questionnaire bias: arises from how the question is asked Bias can result from tone of voice of interviewer, appearance of interviewer, the order in which questions are asked, and other factors Most important source of questionnaire bias is _______?

Most important source of questionnaire bias is the wording of the question. Those who report the results of a survey should always include the exact wording of the question.

Incorrect responses: (a) people lying or responding in a way they think the interviewer wants them to respond

Incorrect responses: (a) people lying or responding in a way they think the interviewer wants them to respond (b) more likely to come from inaccurate measuring devices including inaccurate memories of people interviewed in self- reported data

Questions?