Chapter 10 Samples

Recap The population of interest is the big group we wish to learn about. It is often impossible or impractical to study the whole population of interest. A sample is a smaller group of the population that we study to try to learn about the whole population.

3 Main Ideas of Sampling Idea 1: Examine Part of the Whole Study a sample to learn about the population. To work, a sample must be representative of the population. Samples that do not reflect the population well are biased. Avoiding bias is the biggest challenge of sampling. Example: Tasting a soup while you are cooking to see if it tastes good.

3 Main Ideas of Sampling Idea 2: Randomize Randomization helps ensure that the sample represents (or looks like) the population. Randomization protects against bias from variables we may not realize are important. Example: After you add salt to the soup, you stir it before you taste it again. Stirring randomizes (mixes in) the salt so that the next sample taste has the “same” amount of salt as the rest of the soup.

3 Main Ideas of Sampling Idea 3: It’s the Sample Size that Matters The size of the population doesn’t matter, only the size of the sample is important. Example: If you make a bigger pot of soup, you still take the same size taste to test it. The sample just needs to be big enough to represent the population. Example: A sample of broth needs just a few drops. If there are peas, carrots and celery in the soup, you need a big enough spoon to make sure you get some of each.

Why Not Use a Census? A census is a sample that includes the whole population. It is difficult to get everyone. It takes too long. It is very expensive. You may not want to use up the whole population. Example: If you sampled all of the Twinkies to make sure they were OK, you wouldn’t have any left to sell!

Are Samples Representative? Example: Here are summary statistics of some variables for two samples. Age (years) # Children Income ($) 61.4 1.54 39,100 61.2 1.51 38,800 Since the data are similar for all of the variables, we can conclude that the two samples are probably representative of the population.

Statistics vs. Parameters Statistics are calculations from the sample data that help summarize the data. They are exact for that sample. Example: The average weight of 2 year olds. Parameters are similar summaries of the entire population. They are never known exactly, they are estimated from the sample statistic.

Sample Designs Simple Random Sample (SRS) Make sure that each person, and each combination of people have an equal chance of being included in the sample. Choose a sample frame (list of people from which to draw the sample). Assign a number to each person. Pick the sample from a random number list or random number generator.

Sample Designs Example: There are 80 students in a class. Select a sample of 5 from the following random number list: 05166 29305 77482. First number the students from 1-80. Since we have 80 students, we need two digits numbers to ensure we can select anyone. Read the random number list two digits at a time to select students until you have 5. Ignore duplicate numbers or numbers bigger than 80. The numbers chosen are 5, 16, 62, 77 and 48.

Sample Designs Stratified Sampling Divides the population into strata (groups of similar individuals). Take a random sample from each group in proportion to its size. Reduces sample variation for that variable. Example: If a college is 60% male and 40% female, group the students by gender and take a random sample of 60 males and 40 females.

Sample Designs Cluster Sampling Divide the population into clusters (groups that are located near each other). Choose one or more clusters, then take a census of the chosen clusters (sample the whole cluster). Can be much more convenient and cheaper. Not accurate if clusters are not representative. Example: Choose a few random pages of a book and count the sentence lengths on those pages.

Sample Designs Systematic Samples Use a system or set of rules to select the sample. Example: Number the people in the sample frame. Randomly choose a number between 1 and 10. Start with that number, and choose every 10th person to be in the sample. Each person still has an equal chance of being in the sample, but not each group of people. Can be much cheaper than a SRS.

Sample Designs Multistage Samples Combine two or more sampling methods. Example: Pick a city (cluster), then group by gender (strata), then pick a random sample from each gender.

Bad Sampling Techniques Voluntary Response Sampling - A large group is invited to respond; those who do become the sample. Almost always biased (Voluntary Response Bias) Results are almost always wrong Examples: Call in shows, internet polls, letters to congressmen.

Bad Sampling Techniques Convenience Sampling – Choosing people who are easy to sample. Not representative, so results are often wrong. Example: Shopping mall polls.

What Can Go Wrong? It can be hard to find a good sample frame. Example: We want to take a survey to see who will win the election. We use a voter registration list as the sample frame. Many registered voters will not actually vote. Non-voters may have a different response than voters, introducing bias into the results.

What Can Go Wrong? Undercoverage – some portion of the population is under-represented or missed entirely. Non-response Bias – People from whom we get no response may have different opinions from those who do. Can cause voluntary response bias. Can cause undercoverage.

What Can Go Wrong? Response Bias – Things that influence the response. Wording of the question. Example: 53% approved this question After 9/11, President Bush authorized government wiretaps on some phone calls in the US without getting court warrants, saying this was necessary to reduce the threat of terrorism. Do you approve or disapprove of this? But only 46% approved this question After 9/11, President Bush authorized government wiretaps on some phone calls in the US without getting court warrants. Do you approve or disapprove of this?

What Can Go Wrong? Response Bias – Things that influence the response. People trying not to offend the interviewer. Example – Having a man with tattoos ask “Would you hire a man with a tattoo?” People not wanting to reveal private information or admit to illegal activity. Insulting question. Example: Did you understand our “Instructions for Dummies”?

What Can Go Wrong? Response Bias – Things that influence the response. People not understanding the question. Example – “Are any members of your family union members?” Is my family just my wife and kids, or does it include parents, grandparents, etc. People not knowing the subject. Example: “Do you approve of the recent action by the Secretary of Labor?” Most people won’t know who that is; even fewer will know what he or she just did.