Inference for Sampling The purpose of a sample is to give us information about a larger population. The process of drawing conclusions about a population on the basis of sample data is called inference. Why should we rely on random sampling? To eliminate bias in selecting samples from the list of available individuals. The laws of probability allow trustworthy inference about the population Results from random samples come with a margin of error that sets bounds on the size of the likely error. Larger random samples give better information about the population than smaller samples.

Sample Surveys: What Can Go Wrong? Most sample surveys are affected by errors in addition to sampling variability. Good sampling technique includes the art of reducing all sources of error. Definition Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. A systematic pattern of incorrect responses in a sample survey leads to response bias. The wording of questions is the most important influence on the answers given to a sample survey.

Sampling errors: Nonsampling errors: Undercoverage Voluntary response Convenience sample Nonsampling errors: Nonresponse Response bias Wording of the question

Bias A systematic error in measuring the estimate favors certain outcomes Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method!

Sources of Bias things that can cause bias in your sample cannot do anything with bad data

Remember – the way to determine voluntary response is: An example would be the surveys in magazines that ask readers to mail in the survey. Other examples are call-in shows, American Idol, etc. Remember, the respondent selects themselves to participate in the survey! People chose to respond Usually only people with very strong opinions respond Remember – the way to determine voluntary response is: Self-selection!!

Convenience sampling Ask people who are easy to ask An example would be stopping friendly-looking people in the mall to survey. Another example is the surveys left on tables at restaurants - a convenient method! Ask people who are easy to ask Produces bias results The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines!

Undercoverage some groups of population are left out of the selection process People with unlisted phone numbers – usually high-income families People without phone numbers –usually low-income families Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected! People with ONLY cell phones – usually young adults

Nonresponse One way to help with the problem of nonresponse is to make follow contact with the people who are not home when you first contact them. occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponse People are chosen by the researchers, BUT refuse to participate. NOT self-selected! This is often confused with voluntary response! Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse!

Response bias occurs when the behavior of respondent or interviewer causes bias in the sample wrong answers Suppose we wanted to survey high school students on drug abuse and we used a uniformed police officer to interview each student in our sample – would we get honest answers? Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.

Wording of the Questions Questions must be worded as neutral as possible to avoid influencing the response wording can influence the answers that are given connotation of words use of “big” words or technical words – if surveying Podunk, AR, then you should avoid complex vocabulary. The level of vocabulary should be appropriate for the population you are surveying – if surveying doctors, then use more complex, technical wording.

Source of Bias? Undercoverage – since the Digest’s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible) 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 2.8 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc.

Convenience sampling – easy way to collect data 2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at UAFS. You collect register receipts for students as they leave the bookstore during lunch one day. Convenience sampling – easy way to collect data or Undercoverage – students who buy books from on-line bookstores are included.

(other answers are possible) 3) To find the average value of a home in Fort Smith, one averages the price of homes that are listed for sale with a realtor. Undercoverage – leaves out homes that are not for sale or homes that are listed with different realtors. (other answers are possible)

Undercoverage - only people with internet access could respond 4) A new and somewhat controversial polling procedure that replaces the phone with the Internet is being used to conduct surveys. One criticism is that Internet users as a whole are still too highly educated and urban to produce results that accurately reflect all Americans. Undercoverage - only people with internet access could respond

Non-Response Bias…only 2000/19,000 replied 5) “More than half of California’s doctors say they are so frustrated with managed care they will quit, retire early, or leave the state.” This statement comes from a survey conducted by the California Medical Association in which surveys were sent to 19,000 doctors and 2000 completed surveys were returned. Non-Response Bias…only 2000/19,000 replied