Chapter 12 Sample Surveys

1. Chapter 12 Sample Surveys *Sample *Bias *Randomizing *Sample Size

2. 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

3. 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

4. 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

5. 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

6. Bias • Sampling methods that, by their nature, tend to over- or under- emphasize some characteristics of the population are bias • Voluntary response samples: people choose themselves • Convenience 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

7. 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%

8. 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

9. 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

10. 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

11. 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 VS • 100 randomly selected voters in the US • Soup: cooking for a party vs your family

12. 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

13. 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)

14. Checking In • Various 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.