2.3 Sample Surveys in the real World So far we have discussed errors in sampling due to: • choosing a sample - not being randomly selected - convenience samples - voluntary samples • bias - repeated deviation of sample statistic from the population parameter. - use random sampling to reduce sampling bias • variability - error due to how spread out the sample statistic are - increase sample size Today we will talk about non-sampling error Sep 294:38 PM Sep 243:42 PM 1 Nonsampling Errors • errors that have nothing to do with sampling • they are present even in the census • are in addition to the Margin of Error and can't be directly measured Sep 306:14 AM pg 107, 2.12 Most opinion polls can't afford to even attempt full coverage of the population of all adult residents of the United States. The interviews are done by telephone, thus missing the 6% of households without phones. Only households are contacted, so that students in dormitories, prison inmates, and most members of the armed forces are left out. So are the homeless and people staying in shelters. Because calls to Alaska and Hawaii are expensive, most polls restrict their samples to the continental states. Many polls interview only in English, which leaves some immigrant households out of their samples. Apr 1010:55 AM 2 Sampling Frame - the list from which the sample is actually chosen Sep 243:47 PM Nonsampling Errors Processing Errors - mistakes in mechanical tasks such as an arithmetic error or a data entry error Response Errors - occur when a subject gives an incorrect response such as lies about age, etc. pg 108, 2.14 In 1989, New York City elected its first black mayor and the state of Virginia elected its first black governor. In both cases, samples of voters interviewed as they left their polling places predicted larger margins of victory than the official vote counts. The polling organizations were certain that some voters lied when interviewed because they felt uncomfortable admitting that they had voted against the black candidate. Sep 294:53 PM 3 Sep 243:48 PM Nonresponse is the most serious problem facing sample surveys? Why? Sep 294:58 PM 4 Sep 243:49 PM voluntary response, convenience samples, lack of random sampling Sep 152:31 PM 5 Sep 152:39 PM Sep 152:41 PM 6 Sep 152:41 PM The financing of political campaigns is a perennial issue. Here are two opinion poll questions on this topic: Should laws be passed to eliminate all possibilities of special interests giving huge sums of money to candidates? Should laws be passed to prohibit interest groups from contributing to campaigns, or do groups have a right to contribute to the candidate they support? The first question was posed by Ross Perot, the thirdparty candidate in the 1992 presidential election. It drew a 99% "Yes" response in a mailin poll. We know that voluntary response polls are worthless, so the Yankelovich survey firm asked the same question of a nationwide random sample. The result: 800/0 "Yes;' Perot's question almost demands a "Yes" answer, so Yankelovich wrote the second question as a more neutral way of presenting the issue. Only 400/0 of a nationwide random sample wanted to prohibit contributions when asked this question. Sep 152:43 PM 7 Sep 152:44 PM Cluster Samples the researcher selects groups or clusters, and then from each cluster, the researcher selects the individual subjects by either simple random or systematic random sampling. The researcher can even opt to include the entire cluster and not just a subset from it. Mar 281:02 PM 8 Sep 152:45 PM A small village has 204 people under the age of 18, 726 adults (over 18) and 268 pensioners. Jenny wishes to carry out a survey on whether or not the village needs a new supermarket. She decides to use stratified sampling based on age group so that the sample is more representative of the whole population. Her sample size is 50 people. Work out the amount of people Jenny should select from each group. Apr 104:04 PM 9 Answer First find the amount of people in the village. 204 + 726 + 268 = 1198. Next write down the proportions of people. Fraction of children = 204/1198 Fraction of adults = 726/1198 Fraction of pensioners = 268/1198 All you need to do now is multiply these fractions by the sample size. This can easily be done using the fraction key on a scientific calculator. Amount of children = 204/1198 × 50 = 9 Amount of adults = 726/1198 × 50 = 30 Amount of pensioners = 268/1198 × 50 = 11 Just check that these numbers add up to 50 as Jenny only wants to select 50 people from her sample. 9 + 30 + 11 = 50. Apr 104:05 PM DIFFERENCE BETWEEN CLUSTER SAMPLING AND STRATIFIED SAMPLING The main difference between cluster sampling and stratified sampling lies with the inclusion of the cluster or strata. In stratified random sampling, all the strata of the population is sampled while in cluster sampling, the researcher only randomly selects a number of clusters from the collection of clusters of the entire population. Therefore, only a number of clusters are sampled, all the other clusters are left unrepresented. Mar 281:03 PM 10 Sep 152:48 PM Assignment: pg 110 # 2.57, 2.58, 2.60 pg 102 # 2.50, 2.52 2.50 Explaining confidence A student reads that we are 95% confident that the average score of young men on the quantitative part of the National } \sses~ment of Educational Progress is 267.8 to 276.2. Asked to explain the me<lning of this statement, the student says, «95% of all young men have S ﴾Qr~s between 267.8 and 276.2." Is the student right? Explain your answer. 2.52 Satisfying Congress The previous exercise describes a sample survey of 1190 adults, with margin of error ±4% for 95% confidence. (a) A member of Congress thinks that 95% confidence is not enough. He wants to be 99% confident. Hen\' would the margin of error for 99% confidence hased n the same sample compare with the margin of error for 95% confideJlce? (b) Another member of Congress is satisfied with 95% confidence, but she wants a smaller margin of error than ±4%. How can INt? get a smaller margin of error, still with 95% confidence? 2.57 Not in the margin of error A recent Gallup Poll found that 68(!!<l of adult Americans favor teaching creationism along with evolution in public schools, The Gallup press release says: For res II Its based 011 sall/ples of this size, aile can say with 95 pen'erll c0l11idwce that tfu' maximulIl error attributable to sampling and other random eHec15 is pillS or millUS 3 percentage points. I' Give one example of a source of error in the poll result that is not included in this margin of error. 2.58 What kind of error? Which of the following are sources of smllpling error and which are sources of 110l1sQmplil1g error? Explain yOll!' allswers. (a) The subject lies about pa~t drug use. (b) A typing error is made in recording the data. (c) Data are gathered b)' askjng people to maiJ in a coupon printed ina newspaper. 2.60 Polling students A high scbool chooses an SRS of 100 students from the registrar's list to interview about student life. If it sekcled two SRSs of 100 students at the same time, the two samples would give somewhat different results. Is this variation a source of sampling error or of nOl1sampling error? \Vill the survey's illlnounced margin of error lake this source of error into account? Sep 289:42 PM 11 Apr 1011:00 AM 12