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CHAPTER 11: Data Analysis and Interpretation: Part I. Describing Data, Confidence Intervals, Correlation 361BOX 11.2THE MARGIN OF ERROR IN SURVEY RESULTSAs you learned in Chapter 5, survey researchrelies heavily on sampling. Survey research isconducted when we would like to know the characteristicsof a population (e.g., preferences, attitudes,demographics), but often it is impracticalto survey the entire population. Responses froma sample are used to describe the larger population.Well- selected samples will provide good descriptionsof the population, but it is unlikely thatthe results for a sample will describe the populationexactly. For example, if the average age ina class room of 33 college students is 26.4, it isunlikely that the mean age for a sample of 10 studentsfrom the class will be exactly 26.4. Similarly,if it were true that 65% of a city’s population favorthe present mayor and 35% favor a new mayor,we wouldn’t necessarily expect an exact 65:35split in a sample of 100 voters randomly selectedfrom the city population. We expect some “slippage”due to sampling, some “error” between theactual population values and the estimates fromour sample. At issue, then, is how accurately theresponses from the sample represent the largerpopulation.It is possible to estimate the margin of errorbetween the sample results and the true populationvalues. Rather than providing a precise estimateof a population value (e.g., “65% of thepopulation prefer the present mayor”), the marginof error presents a range of values that arelikely to contain the true population value (e.g.,“between 60% and 70% of the population preferthe present mayor”). What specifically is thisrange?The margin of error provides an estimate ofthe difference between the sample results andthe population values due simply to chance orrandom factors. The margin of error gives us therange of values we can expect due to samplingerror— remember that we expect some error;we don’t expect to describe the population exactly.Let us assume that a poll of many voters istaken and a media spokesperson gives the followingreport: “Results indicate that 63% of thosesampled favor the incumbent, and we can saywith 95% confidence that the poll has a marginof error of 5%.” The reported margin of error withthe specified level of confidence (usually 95%)indicates that the percentage of the actual populationwho favor the incumbent is estimated to befound in the interval between 58% and 68% (5%is subtracted from and added to the sample valueof 63%). It’s important to remember, however,that we usually don’t know the true populationvalue. The information we get from the sampleand the margin of error is the following: 63% ofthe sample favor the incumbent, and we are 95%confident that if the entire population were sampled,between 58% and 68% of the populationwould favor the incumbent. This can be representedon a graph by plotting the value obtainedfor the sample (63%), with error bars representingthe margin of error. Figure 11.1 displays errorbars around the sample estimate.Margins of error are routinely included in mediareports of national surveys. The goal of thesesurveys is to tell you with a “margin of error” whatthe true population value is. Similarly, the goalof many scientific studies is to tell you the marginof error, now usually called a confidence interval,for an estimate of a population value.FIGURE 11.1 Error bars are used to represent themargin of error for the estimate of thepopulation value.Percentage75706560550We can be 95%confident that theinterval contains thetrue population value.