Section 1.2 ~ Sampling

Introduction to Probability and StatisticsMs. Young

This section will introduce the different types of sampling methods and help you to understand the importance of choosing a representative sample

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Objective

Census – a collection of data from every member of a population Often impractical

The population might be so large that it would be too expensive or time-consuming

May interfere with the study’s overall goals Ex. ~ Testing the quality of a candy bar

Every 10 years, the U.S. Census Bureau conducts a census to obtain general information in order to make educated decisions about how federal funds should be dispersed

Census Video

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Sampling

Representative Sample Since it is typical that a census will not be obtained in a

study, it is crucial that the sample that is chosen represents the population fairly in order to conduct a study with validity With that said, you would want a representative sample – a

sample that includes characteristics that are generally the same as the characteristics of a population

Example 1: Suppose you want to determine the mean height of all students

at your school. Which is more likely to be a representative sample for this study: the men’s basketball team or the students in your statistics class?

The men’s basketball team is not a representative sample for a study of height, both because it consists only of men and because basketball players tend to be taller than average

The mean height of the students in your statistics class is much more likely to be close to the mean height of all students, so the members of your class make a more representative sample than the members of the man’s basketball team

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Bias A statistical study suffers from bias if its design or conduct

favors certain results Ex. ~ If the 5000 homes that Nielsen used as a sample

primarily consisted of people who worked night-shift, the study would show that late-night shows are unpopular

This wouldn’t be a good representation of all Americans; it would be biased

Preventing bias is a great challenge, therefore looking for

bias in a study is extremely important Here are some common ways bias occurs:

A non-representative sample If the researcher has a personal stake in a particular outcome If certain values were intentionally collected or unintentionally

collected In the reporting of the study

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Bias Cont’d… Example 2:

Nielsen Media Research earns money by charging television stations and networks for its services. For example, NBC pays Nielsen to provide ratings for its television shows. Why doesn’t NBC simply do its own ratings, instead of paying a company like Nielsen to do them?

The cost of advertising on a television show depends on the show’s ratings. The higher the ratings, the more the network can charge for advertising—which means NBC would have a clear bias if it conducted its own ratings. Advertisers therefore would not trust ratings that NBC produced on its own.

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Simple Random Samples A random sample is a sample in which every

member of the population has an equal chance of being selected to be part of the sample (not to be selected by people) Examples of ways random samples can be produced:

Having each member roll a die and then choosing everyone that rolled a 6

Assigning every member of the population to a number and then randomly picking numbers out of a hat

Assigning every member to a number and then using a random number generator on a computer or a calculator

Since a random sample gives every sample of a particular size the same chance of being chosen, it is most likely a good representation of the population as long as the sample size is large enough

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Simple Random Samples Cont’d… Example 3:

You want to conduct an opinion poll in which the population is all the residents in a town. Could you choose a simple random sample by selecting names from the local telephone book?

A sample drawn from a telephone book is not a simple random sample of the town population because phone books invariably are missing a lot of names, and therefore anyone whose name is missing has no chance of being selected

For example, the phone book will be missing names when two or more people share the same phone number but have only one listing, when people choose to have an unlisted phone number or to rely exclusively on a cell phone, or when people (such as the homeless) don’t have a telephone

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Systematic Sampling A systematic sample is created by using a system, such

as every 10th or every 50th member of the population This system should give you a representative sample as long

as there would be no reason to believe that every 10th or 50th

member would be different than the entire population Example 4:

You are conducting a survey of students in a co-ed dormitory in which males are assigned to odd-numbered rooms and females are assigned to even-numbered rooms. Can you obtain a representative sample when you choose every 10th room?

No. If you start with an odd-numbered room, every 10th room will also be odd-numbered (such as room numbers 3, 13, 23,…). Similarly, if you start with an even numbered room, every 10th room will also be even-numbered. You will therefore obtain a sample consisting of either all males or all females, neither of which is representative of the co-ed population.

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Convenience Sampling A convenience sample is a sample that

is chosen more as a convenience than as the “best” representation Ex. ~ If you were conducting a study on the

proportion of left-handed students at your school, using simple random sampling or systematic sampling would be time consuming, so you could just use the statistics class as a sample because it would be convenient

There should be no reason to believe that your statistics class would have a different proportion of left-handed students than anywhere else

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Convenience Sampling Cont’d… Example 5:

A supermarket wants to decide whether to carry a new brand of salsa, so it offers free tastes at a stand in the store and asks people what they think. What type of sampling is being used? Is the sample likely to be representative of the population of all shoppers?

A convenience sample is being used because the people happen to be in the store and are willing to participate in the taste test

It is most likely not a representative sample because different types of people shop at different times (stay-at-home Mom’s, night shift workers, etc.) and only people who like salsa will probably participate in the study

This is known as a self-selected sample – a sample in which people chose whether or not to be a part of

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Cluster Sampling

Cluster Sampling involves the selection of ALL members in randomly selected groups or clusters

Example 6: Suppose you wanted to conduct a study on the

percentage of juniors at your school that have their driver’s license. Explain how cluster sampling can be used.

The junior homeroom’s in the school would represent the population of juniors and by randomly selecting a few of the junior homerooms and surveying every student in each of those would be an example of cluster sampling

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Stratified Sampling

Strata are subgroups within the population Examples ~

If the population is all students in high school, then the strata could be the subgroups “men” and “women”

If the population is all registered voters, then the strata could be “democrats”, “republicans”, and “independents”

Stratified sampling is conducted by taking a random sample from each of the subgroups The difference between cluster sampling and

stratified sampling is that with cluster sampling every member of the randomly selected clusters are surveyed whereas in stratified sampling, a random sample of the subgroups are surveyed

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Stratified Sampling Cont’d…

Example 7: The U.S. Labor Department surveys 60,000 households

each month to compile its unemployment report. To select these households, the Department first groups cities and counties into about 2000 geographic areas. It then randomly selects households to survey within these geographic areas.

How is this an example of stratified sampling? The unemployment survey is an example of stratified sampling

because it first breaks the population (entire U.S. labor force) into subgroups (based on geographic location)

What are the strata? The strata are the 2000 geographic areas

Why is stratified sampling important in this case? Stratified sampling is important in this case because

unemployment rates may vary based on geographic location and by randomly sampling households from all the geographic locations will result in a fair representation of the entire population

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