■ Does having a high IQ indicate that you will have a high income level? If research at five area hospitals shows that dur- ing a full moon, 4% more babies are born on average than on nights in which there is no full moon, you could say there is a small but positive correlation between the two sets of data. In other words, there appears to be a connection between full moons and birth rates. However,many studies have shown that any per- ceived correlation is due in fact to chance. There is no evidence to support the theory that the phases of the moon affect human behavior in any way.So, even when there is a positive correlation, it does not necessarily mean there is a cause and effect relationship between the two elements in the correlation study. For the second question, if a study showed that Americans with the top 5% of IQ scores made an aver- age of $22,000 a year, while those in the middle 5% made an average of $40,000, you would say there is a negative correlation between IQ and income levels. To describe the results of the study,you could say that there is no evidence that IQ determines income level. In other words, you do not need to have a high IQ to make a lot of money. This conclusion is obvious. But let’s look at how these same correlation study results can be used to come up with a ridiculous conclusion. The second example shows that there is no connection between a high IQ and a high income level. Is that the same as say- ing that “the dumber you are, the more money you will make?”Of course it isn’t. This type of conclusion shows one of the dangers of correlation studies. Even if the study uses accurate data, the way in which it is inter- preted can be wrong, and even foolish. When you encounter a correlation study, as with survey and poll results, do not assume the numbers and conclusion are correct. Ask questions, and look at supporting data. Does the study make sense? Or does it seem too convenient for the advertiser/politician/new reporter/ author who is using it? Think critically, and do not rely on anyone’s numbers until you determine they are true and valid. Practice Which answer(s) could be appropriate conclusions for the following correlation study? Researchers wanted to know if the use of night- lights or room lights in children’s bedrooms leads to nearsightedness. They conducted a study which showed that while only 10% of children who didn’t use nightlights developed nearsightedness, 34% of children who used a nightlight and 55% of those who slept with an overhead light on developed near- sightedness. a. Nightlights and room lights cause nearsightedness. b. Children with nearsightedness use nightlights more than children with 20/20 vision. c. Nightlights help you see better in the dark. d. Children with one or both parents having near- sightedness use nightlights more that children whose parents have 20/20 vision. Answer There are two possible answers to this question. Choice b is the best explanation for the study. However, there are studies that indicate that nearsightedness is inher- ited, rather than gotten from use of a nightlight or any other outside factor. Therefore, choice d is also correct. – MISUSING INFORMATION—THE NUMBERS GAME– 82  Statistics Statistics is simply a mathematical science that gathers information about a population so that population may be described usefully. Statistics are often used to draw conclusions and make decisions based on that infor- mation. So, what’s the problem? Statistics are complicated and their problems can be numerous. In general, though, problems with sta- tistics are similar to those of other types of numerical data; namely, they can be gathered, analyzed, and/or interpreted incorrectly, or mishandled by someone with a bias. Let’s look at two common problems with sta- tistics. The first question to ask is, is the statistic mean- ingful? Many parents worry, for instance, when they hear that the average baby walks at 13 months. They conclude that there must be something wrong with their 18-month-old who is still crawling. But, it has been proven that babies who walk later have no devel- opmental differences at age two from their early-walk- ing peers. In other words, the statistic is not meaningful; there is nothing wrong with an 18-month-old who is still crawling. Another example: when standardized test scores were analyzed across the country, it was concluded that students from wealthy communities were smarter than students in poorer communities because their scores were higher. Is this a meaningful, accurate conclusion? Probably not. It does not take into account the many other variables that can account for lower test scores, such as inferior preparation, fatigue, and even break- fast on the day of testing. Practice Evidence shows that most car accidents occur on days with clear weather than on days when it is snowing. Can you conclude that it is safer to drive when it is snow- ing? Why, or why not? __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ Answer No, the conclusion that it is safer to drive in the snow is wrong. There are other factors influencing this sta- tistic, such as there are more clear days than snowy days, and more people are probably on the road in clear weather than snowy weather. A second question to ask: is the statistic given in such a way that it misrepresents the data collected? Does it make the data sound better or worse than it is? Suppose a survey was done to see how many children live below the poverty line. We hear it reported on the news: “80% of all children live above the poverty line.” What about the 20% who live below it? The declaration of the 80% sounds good, while shifting the focus away from the millions of children who are poor. What about: “Women earn an average of 70 cents for every dollar earned by a man.”This sounds unfair, but it does not tell you which jobs are being compared, how long men and women have worked at those jobs, and whether men work longer hours because they do not take as much responsibility for child care. – MISUSING INFORMATION—THE NUMBERS GAME– 83 Practice Researchers found that 98% of juvenile offenders com- mitting serious crimes watch violent TV shows on a regular basis. If you are an advocate for a reduction in TV violence, how would you use this statistic? What if you were an advocate for freedom of expression on tel- evision? __________________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ Answer As an advocate for a reduction in TV violence, you would probably say, “watching violence on TV turns our young people into criminals.” If you were an advo- cate for freedom of expression on television, you might find out the real number of young people in the 2%. Let’s say it is 3 million. You might conclude that “mil- lions of children watch violent programs regularly, and they don’t end up as criminals.” Another common way in which statistics are manipulated is by leaving out key information. For instance, a company claims it is edging out its com- petitor with higher sales. They are correct in stating that they have had a 50% increase in sales, compared with only a 25% increase for their competitors. Is their claim valid? You can’t know unless you have more informa- tion. What if the competitor sold two thousand bicy- cles last year, and 2,400 this year; the other company sold 40 bicycles last year, and 60 this year. Edging out the competition? Hardly. When you hear a statistic, either in an advertise- ment, a political speech, a newspaper article, or other source, remember that it is not necessarily true. Then, ask yourself three questions: Is the statistic meaning- ful? Does it deliberately misrepresent the data collected? Does it give you all the information you need to eval- uate it? Thinking critically about statistics will help you to avoid making the wrong conclusions, or relying on information that is faulty or simply untrue. Practice What is wrong with the following statement? Russians are better off than ever; their average worker’s annual salary is now $20,000. Answer Compared with what? This statistic is meaningless as it is stated because it leaves out too much information. There is a big difference between the salaries of the wealthy business class and the workers. Inflation is also a factor. If $20,000 is worth less now than it was five years ago, the average worker could be doing worse than ever.  In Short It is just as easy to deceive with numbers as it is with words. Surveys, studies, and statistics are conducted and interpreted by researchers who might have a bias, or simply lack the skills necessary to do their jobs prop- erly. Therefore, it is important to evaluate numbers before accepting them as truth. Ask questions about how the information was gathered, what its margin of error is, and how meaningful it is. Does the conclusion make sense, or does it seem to distort the findings? Thinking critically about the many numbers you encounter will help you to rely only on information that is objective and accurate. – MISUSING INFORMATION—THE NUMBERS GAME– 84 – MISUSING INFORMATION—THE NUMBERS GAME– 85 Skill Building Until Next Time ■ Watch a news broadcast and listen for the results of a survey or poll. Does the newscaster tell the margin of error? Why is it important to know this number? ■ Look for a print advertisement that includes a statistic. Why was it included? Does it seem accu- rate and objective? How else could the advertiser have made the point without using numbers? [...]... bias and stereotyping, need to be recognized so you can consciously exclude them Acknowledging emotions, rather than letting them take over, or trying to ignore them, will help you improve your critical thinking skills Skill Building Until Next Time ■ ■ The next time you attend a sporting event, or watch one on television, pay attention to the fans when the... premises, which you can agree with Then, the meaning of a critical word is changed and an illogical or faulty conclusion is drawn If you follow the argument, you could fall into the trap of agreeing with something you would never have otherwise accepted The best way to handle this fallacy is to get information Ask for clear definitions of any critical terms that could be used in different ways When you... premises are both true There is an equivocation in the meaning of the word “nothing;” in the first premise, it means “not a thing,” and in the second premise, it means “no other possible thing.” Using a critical word with two different meanings makes the argument invalid Now you see how one word with two different meanings can be an equivocation The other way in which reasoning may be deemed invalid due... specific ways in which inductive reasoning goes wrong Skill Building Until Next Time You are always drawing conclusions from your observations Pay attention to this inductive reasoning and evaluate your skills Are you using common sense and/or past experience? Have you noticed a key difference, or compared two similar events? Become a better user of inductive reasoning by being aware of when and how you . completely ignore your feelings when engaged in critical thinking? Surprisingly, the answer is no. Emotions or feelings have a place in critical thinking, just as logic and reason do. But they. held belief that emotions are an enemy of critical thinking. The theory goes that the head is rational, while the heart is emotional, and any objective thinking or decision making should be done. findings? Thinking critically about the many numbers you encounter will help you to rely only on information that is objective and accurate. – MISUSING INFORMATION—THE NUMBERS GAME– 84 – MISUSING