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.www.statsisfun.org