Chapter 12 Sample Surveys

*Sample

*Bias

*Randomizing

*Sample Size

Sampling

We use sampling to get an idea about the whole population with out asking the entire population.

We take what we know about the sample and stretch that over everyone

To do this we have three ideas

Idea 1: Examine a Part of the Whole Draw a sample

It is impractical or sometimes impossible to survey the entire population

We examine a smaller group of the population called a sample

A small sample (if selected properly) can represent the entire population

Example: soup

Sample Surveys

Opinion polls designed to ask questions of a small group of people in hopes of learning something about the entire population

If the sample does not represent the population the information can be misleading

Bias

When selecting a sample you want to make sure that you are not over- or under- emphasizing some characteristics of the population

How will you select your sample??Phone number list??

homeless people without a land line

Internet Surveys??? people that don’t have internet

Bias

Sampling methods that, by their nature, tend to over- or under- emphasize some characteristics of the population are biasVoluntary response samples: people choose

themselvesConvenience samples: your sample is made up of

people close by

It is the most important thing to avoid when sampling the data and conclusions will be flawed

Election of 1936

Alf Landon vs Franklin Delano Roosevelt

Literary Digest mailed 10 million ballots to get a sample to predict who would be the next President

They received 2.4 million of the ballots back

They predicted that Landon would win 57% to 43%

Roosevelt won the election 62% to 37%

What Went Wrong?

Where did they get the 10 million names??The list was made up from a phone list, drivers

registration, and member lists (country clubs)

In 1986 there were enough families in the US that you could use a computer generated phone list to get a fair sample. Not from a book – missing unlisted, cell phones, and

recently moved

Idea 2:Randomize

Even though Literacy Digest polled a very large sample, their sample was flawed

Soup: add salt… taste from the top. what happens? taste from the bottom. what happens?

by stirring the soup you are randomizing the amount of salt in the whole pot making each taste more typical in terms of the amount

of salt in the whole pot

Randomizing

Randomizing protects us from the influences of all the features of our population, even ones that we may not have thought about.

It does that by making sure that on average the sample looks like the rest of the population

Idea 3: It’s the Sample Size

How big should the sample be?The number of indiviuals in the sample is al that

matters It has very little to nothing to do with the size of the

population

Example:100 randomly selected students from a college

VS100 randomly selected voters in the US

Soup: cooking for a party vs your family

The fraction of the population that you’ve sampled does not matter. It’s the sample size itself that’s important

Surprising?!?! YES!!! But very important It balances between how well the survey can measure the

population and how much the survey costs

For a survey that tries to find the proportion of the population that falls into a category you would need at least a few hundred individuals

Census

A survey to the entire population

What factors make a census difficult?difficult to complete

some people are hard to find

populations rarely stand still people die, move, babies are born, opinions change

more complicated that sampling team effort, population needs to cooperate

US Census records too many college students because they are being counted twice (home and school)

Checking InVarious claims are often made for surveys. Why is each of

the following claims not correct? It is always better to take a census than to draw a sample.

Stopping student on their way out the cafeteria is a good way to sample if we want to know about the quality of the food there.

We drew a sample of 100 from the 3,000 students in a school. To get the same lever of precision for a town of 30,000 residents, we’ll need a sample of 1,000.

A poll taken at our favorite website (www.statsisfun.org) received 12,357 responses. The majority said they enjoy doing doing statistics homework. With a sample size that large, we can be pretty sure that most Statistics students feel this way, too.