Chapter 2 Lesson 2.2a Collecting Data Sensibly 2.2: Sampling

Census versus Sample Why might we prefer to take select a sample rather than perform a census? 1. Measurements that require destroying the item Measuring how long batteries last Safety ratings of cars 2.Difficult to find entire population Length of fish in a lake 3. Limited resources Time and money Obtaining information about the entire population is called a census. Most common reason to use a sample

Sampling: Examine a Part of the Whole Inferential Statistics: Drawing a Sample. –We’d like to know about an entire population of individuals but examining all of them is usually impractical, if not impossible. –We settle for examining a smaller group of individuals—a sample—selected from the population. –Sampling is a natural thing to do. Think about sampling something you are cooking—you taste (examine) a small part of what you’re cooking to get an idea about the dish as a whole.

Bias Samples that don’t represent every individual in the population fairly are said to be biased. –Bias is the bane of sampling—the one thing above all to avoid. –There is usually no way to fix a biased sample and no way to salvage useful information from it. The best way to avoid bias is to select individuals for the sample at random. –The value of deliberately introducing randomness is one of the great insights of Statistics. –e.g. Random Rectangles Activity

Chapter 2 Lesson 2.2a (continued) Collecting Data Sensibly 2.2: Sampling Intro Clip: Gallup Poll on the Belief in God

Sources of bias Selection bias Occurs when the way the sample is selected systematically excludes some part of the population of interest –called undercoverage 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 unlisted phone numbers – usually high-income families People without phone numbers – usually low- income families People with ONLY cell phones – usually young adults

Sources of bias Convenience sampling Using an easily available or convenient group to form a sample. – The group may not be representative of the population of interest – Results should not be generalized to the population Can also occur when samples rely entirely on volunteers or self-selected individuals to be part of the sample – called voluntary response Suppose we decide to survey only the students in our statistics class – why might that cause bias in a survey? An example would be the surveys in magazines that ask readers to mail in the survey. Other examples are call-in shows, “The Voice”, “SYTYCD”, etc. Remember, the respondent selects themselves to participate in the survey!

Sources of bias Measurement or Response bias Occurs when the method of observation tends to produce values that systematically differ from the true value in some way – Improperly calibrated scale is used to weigh items – Tendency of people not to be completely honest when asked about illegal behavior or unpopular beliefs – Appearance or behavior of the person asking the questions – Questions on a survey are worded in a way that tends to influence the response 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? People are asked if they can trust men in mustaches – the interviewer is a man with a mustache. A Gallup survey sponsored by the American Paper Institute (Wall Street Journal, May 17, 1994) included the following question: “ It is estimated that disposable diapers accounts for less than 2% of the trash in today ’ s landfills. In contrast, beverage containers, third-class mail and yard waste are estimated to account for about 21% of trash in landfills. Given this, in your opinion, would it be fair to tax or ban disposable diapers? ”

Sources of bias Nonresponse occurs when responses are not obtained from all individuals selected for inclusion in the sample To minimize nonresonse bias, it is critical that a serious effort be made to follow up with individuals who did not respond to the initial request for information People are chosen by the researchers, BUT refuse to participate. NOT NOT self-selected! This is often confused with voluntary response! The phone rings – you answer. “ Hello, ” the person says, “ do you have time for a survey about radio stations? ” You hang up! How might this follow-up be done?

Identify a potential source of bias. 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. The Digest ’ s survey of 2.3 million people came from magazine subscribers, car owners, telephone directories, etc. Selection Bias – since the Digest ’ s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! This would lead there to be an overestimate of people voting for Landon.

Identify a potential source of bias. 2) A farmer brings a juice company several crates of oranges each week. A company inspector looks at 10 oranges from the top of each crate before deciding whether to buy all the oranges. Convenience sampling – this could lead the inspector to overestimate the quality of the oranges if the farmer puts the best oranges of top.

3) The ABC program Nightline once asked whether the United Nations should continue to have its headquarters in the United States. Viewers were invited to call one telephone number to respond “Yes” and another for “No.” There was a charge for calling either number. More than 186,000 callers responded, and 67% said “No.” Voluntary response bias – In this case, those who are happy with the UN headquarters’ location already have what they want so are less likely to respond. The proportion who answered “No” is likely to be higher than the true proportion in the US who would answer “No.” Identify a potential source of bias.

HOMEWORK Pg.46: #2.23, 2.25, 2.27, 2.28, 2.32 (Finish Reading Notes 2.2)