Data Collection and Interpretation
Data Collection and Interpretation
Data interpretation is part of daily life for most people. Interpretation is the process of making sense of numerical data that has been collected, analyzed, and presented. People interpret data when they turn on the television and hear the news anchor reporting on a poll, when they read advertisements claiming that one product is better than another, or when they choose grocery store items that claim they are more effective than other leading brands.
A common method of assessing numerical data is known as statistical analysis , and the activity of analyzing and interpreting data in order to make predictions is known as inferential statistics . Informed consumers recognize the importance of judging the reasonableness of data interpretations and predictions by considering sources of bias such as sampling procedures or misleading questions, margins of error , confidence intervals , and incomplete interpretations.
Why Is Accurate Data Collection Important?
The repercussions of inaccurate or improperly interpreted data are wide-ranging. For example, every 10 years a major census is done in the United States. The results are used to help determine the number of congressional seats that are assigned to each district; where new roads will be built; where new schools and libraries are needed; where new nursing homes, hospitals, and day care centers will be located; where new parks and recreational centers will be built; and the sizes of police and fire departments.
In the past 30 years there has been a major shift in the U.S. population. People have migrated from the northern states toward the southern states, and the result has been a major shift in congressional representation. With a net change of nearly 30 percent (a 17 percent drop in the Northeast and Midwest coupled with a 12 percent gain in the South), the South has gone from a position of less influence to one of greater influence in Congress as a result of population-based reapportionment . This is just one of many possible examples that reveal how data gathering and interpretation related to population can have a marked affect on the whole country.
Gathering Reliable Data
The process of data interpretation begins by gathering data. Because it is often difficult, or even impossible, to look at all the data (for example, to
poll every high school student in the United States), data are generally obtained from a smaller unit, a subset of the population known as a sample . Then data from the sample are used to predict (or infer) what the characteristics of the population as a whole may be. For example, a telephone survey of one thousand car owners in the United States might be conducted to predict the popularity of various cars among all U.S. car owners. The one thousand U.S. car owners who are surveyed are the sample and all car owners in the United States are the population.
But there both an art and science to collecting high-quality data. Several key elements must be considered: bias, sample size, question design, margin of error, and interpretation.
Avoiding Bias. In order for data interpretation to be reliable, a number of factors must be in place. First and perhaps foremost, an unbiased sample must be used. In other words, every person (or item) in the population should have an equal chance of being in the sample.
For example, what if only Ford owners were surveyed in the telephone survey? The survey would be quite likely to show that Fords were more popular. A biased sample is likely to skew the data, thus making data interpretation unreliable. If we want to know what sorts of cars are preferred by U.S. car owners, we need to be sure that our sample of car owners is representative of the entire car owner population.
One way of ensuring an unbiased sample is to choose randomly from the population. However, it is often difficult to design a study that will produce a truly unbiased sample. For example, suppose a surveyor decides to choose car owners at random to participate in a phone interview about car preferences. This may sound like a good plan, but car owners who do not have telephones or whose telephone numbers are unavailable will not have a chance to participate in the survey. Maybe car owners with unlisted telephone numbers have very different car preferences than the broader population, but we will never know if they are not included in the sample.
Biased sampling continues to challenge census takers. In 1990, nearly 35 percent of the households that were mailed census forms did not mail them back. If a form is not returned, the Census Bureau must send someone to the person's house. Even with census takers visiting homes door to door, the Census Bureau was still unable to contact one out of every five of the families who did not return their census form.
Although this may not sound like a lot, consider that in 1990 there were approximately 250 million people in the United States. If a household contains an average of four people, that means that there were 62.5 million forms mailed out. Multiplying that figure by 35 percent (the number of households that did not return the forms) gives the staggering figure of 21.875 million forms that were not returned. Of the 21.875 million households that did not return forms, census takers were unable to track down 20 percent, or 4.375 million households.
Why is this biased sampling? It is believed that of the more than 4 million households not counted, the overwhelming majority was from poorer sections of large cities. This implies that certain parts of the country may be over-represented in Congress and are the recipients of more federal funds than may be deserved.
Achieving a Large Enough Sample. A second important factor in data collection is whether the chosen sample is large enough. Are one thousand car owners a sufficient number of car owners from which to infer the opinion of all car owners? In order to answer this question, the margin of error needs to be calculated.
The margin of error is a statistic that represents a range in which the surveyor feels confident that the population as a whole will fall. A sufficient sample size needs to have a small margin of error, usually around 5 percent. To determine the margin of error (m ), divide one by the square root of the sample size (s ): . Therefore, the sample of one thousand car owners gives us a margin of error of about 3 percent, an allowable margin of error.
Asking the Proper Questions. Informed citizens who are assessing survey results must consider the type of questions that are asked when a survey is conducted. Were the questions leading? Were they easy or difficult to understand? For example, suppose a study carried out by a local ice cream manufacturer states that 75 percent of Americans prefer ice cream. It seems self-evident that an ice cream company would not report a study that showed Americans do not like ice cream. So perhaps the question in the study was leading: for example, "Do you prefer ice cream or spinach?" It is therefore important to find out exactly what questions were asked and of whom.
Giving a Proper Interpretation. Data are often interpreted with a bias, and the results can therefore be misleading or incomplete. For example, a bath soap company claims that its soap is 99 percent pure. This statement is misleading because the soap manufacturer does not explain what "pure" is. When reading an unclarified percentage such as in the previous example, one needs to ask such questions. An example of another incomplete or misleading interpretation is that the average child watches approximately 5 hours of television a day. The reader should question what an "average child" is.
Considering Margin of Error. Margin of error is important to consider when statistics are reported. For example, we might read that the high school dropout rate declined from 18 percent to 16 percent with a margin of error of 3 percent. Because the 2-percentage point decline is smaller than the margin of error (3 percent), the new dropout rate may fall between 13 percent to 19 percent. We cannot be entirely sure that the high school dropout rate actually declined at all.
Confidence intervals, a term usually employed by statisticians, and related to margins of error, is reported by a percentage and is constructed to relay how confident one can be that the sample is representative of the population. The producers of this survey may only be 95 percent confident that their sample is representative of the population. If this is the case then there is a 5 percent chance that this sample data does not typify or carry over to the population of the United States. The margin of error represents the range of this 95-percent confidence interval (the range that represents plus or minus two standard deviations from the mean ).
Understanding and Interpreting Data
Figuring out what data means is just as important as collecting it. Even if the data collection process is sound, data can be misinterpreted. When interpreting data, the data user must not only attempt to discern the differences between causality and coincidence, but also must consider all possible factors that may have led to a result.
After considering the design of a survey, consumers should look at the reported data interpretation. Suppose a report states that 52 percent of all Americans prefer Chevrolet to other car manufacturers. The surveyors want you to think that more than half of all Americans prefer Chevrolet, but is this really the case? Perhaps not all those surveyed were Americans. Also, the 52 percent comes from the sample, so it is important to ask if the sample was large enough, unbiased, and randomly chosen. One also needs to be aware of margins of error and confidence intervals. If the margin of error for this survey is 5 percent than this means that the percentage of car owners in the United States who prefer Chevrolet could actually be between 47 and 57 percent (5 percent higher or lower than the 52 percent).
Similar questions are important to consider when we try to understand polls . During the 2000 presidential race, the evening news and newspapers were often filled with poll reports. For example, one poll stated 51 percent of Americans preferred George W. Bush, 46 percent preferred Al Gore, and 3 percent were undecided, with a margin of error of plus or minus 5 percent.
The news anchor then went on to report that most Americans prefer George W. Bush. However, given the data outlined above, this conclusion is questionable. Because the difference between George W. Bush and Al Gore is the same as the margin of error, it is impossible to know which candidate was actually preferred. In addition, if we do not know any of the circumstances behind the poll, we should be skeptical about its findings.
As another example, consider census data that shows a radical increase in the number of people living in Florida and Arizona along with a decrease in the number of people living in New York. One could easily (and falsely) conclude that the data "proves" that people are finding New York to be a less desirable place to live and therefore are moving away.
But this hasty conclusion could be missing the big picture. What if the data also reveals that the average age of New Yorkers has dropped since 1990? Further interpretation of the data may reveal that when New Yorkers grow older, they move to warmer climates to retire. This illustrates why data must be thoroughly interpreted before any conclusions can be drawn.
A Data Checklist. When reading any survey, listening to an advertisement, or hearing about poll results, informed consumers should ask questions about the soundness of the data interpretation. A recap of key points follows.
- Was the sample unbiased (representative of the whole population)?
- Was the sample large enough for the purpose of the survey (margin of error of the sample)?
- What type of questions did the surveyor ask? Were they simple and unambiguous? Were they leading (constructed in such a way to get the desired response)?
- Can the conclusions drawn be justified based on the information gathered?
- How was the survey done (mail, phone, interview)? Does the survey report mention margins of error or confidence intervals, and, if so, are these such that the conclusions drawn are warranted?
By using these checkpoints and learning to think critically about data collection and interpretation, individuals can become more savvy consumers of information.
see also Census; Central Tendency, Measures of; Graphs; Mass Media, Mathematics and the; Predictions; Randomness; Statistical Analysis.
Rose Kathleen Lynch and
Philip M. Goldfeder
Campbell, Stephen K. Statistics You Can't Trust: A Friendly Guide to Clear Thinking about Statistics in Everyday Life. Parker, CO: Think Twice, 1999.
Dewdney, A. K. 200% of Nothing. New York: John Wiley & Sons, Inc., 1993.
Dorling, Daniel, and Stephen Simpson, eds. Statistics in Society: The Arithmetic of Politics. London U.K.: Oxford University Press, 1999.
Moore, David S. The Basic Practice of Statistics. New York: Freeman, 2000.
Paulos, John A. Innumeracy: Mathematical Illiteracy and Its Consequences. New York: Hill and Wang, 1988.
———. A Mathematician Reads the Newspaper. New York: Basic Books, 1995.
Triola, Mario. Elementary Statistics, 6th ed. New York: Addison-Wesley, 1995.
U.S. Census Bureau. <http://www.census.gov>.
BIAS IN NEWS CALL-IN POLLS
Many news programs have call-in polls. The results of the poll are usually shown later in the program. This type of data collection is very unreliable because the information is coming from a biased sample.
People who watch or listen to the news make up only a small percentage of the population. Of that group, only an even smaller percentage will call to offer their opinion. And of those who call, more are likely to disagree with the question because people with strong feelings against an issue are more likely to respond.
AN UNNECESSARY SCARE
A January 1991 report by the American Cancer Society proclaimed the odds of a woman getting breast cancer had risen to one in nine. For obvious reasons, this scared women all over the country. The research was sound but was based on a lifetime of over 110 years. In other words, if a woman lives to be 110 years old, there is an 11 percent chance she will get breast cancer. The odds for a woman under 50 are closer to one in a thousand, or 0.1 percent. There was nothing wrong with the sampling—but the interpretation and presentation of the data were incomplete.
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