At the most fundamental level, we must ensure that the meaning and scope of words and terms used in an argument are consistently applied. Say, for example, we read that pollution is now ten times as bad in the suburban areas of our city as it was twenty years ago. Pollution may indeed by worse, but not by tenfold. What if the definition of pollution has changed to include air, water, noise, and garbage? This would certainly torpedo any attempt to establish a valid comparison.

Representativeness a.s.sumptions A sample is a group of people or things selected from a larger number of people or things that is presumably representative of the larger group or, as it is often said, athe population as a whole.a We have all heard such statements as: aIave never met a person from country Z whom I likeda or aI highly recommend ABC Restaurant because the three times that I have dined there the food has been delicious.a These two examples show representative sample a.s.sumptions in action. The first person obviously has not met all the people from country Z, and the second person obviously has not tried every dish in ABC Restaurant. For a sample to be representative, it must be both quant.i.tatively and qualitatively representative. For a sample to be quant.i.tatively sound, a large enough sample must be chosen. Obviously, the selection of one or two items is not enough. For a sample to be qualitatively sound, a random or diverse enough cross-sample of its members must be chosen.

What about a travel agency that claims aThree out of every four tourists recommend Morocco as a tourist destination.a For all we know, only eight tourists were surveyed, and six of these recommend Morocco as a tourist destination. In this hypothetical case, the sample of tourists chosen was too small. Now letas a.s.sume that the statistic athree out of every four tourists recommend Moroccoa was based on a sufficiently large sample of several hundred tourists. But what if all the tourists were from Africa? Or suppose all the tourists were male or owned a travel agency specializing in trips to Africa? All of a sudden, we would have doubts as to whether these several hundred tourists were representative of tourists in general, and the statement that three of four tourists recommend Morocco would be suspect.

When evaluating situations involving representativeness, the objective is to show how a particular person, place, or thing is not representative of the larger awholea and the argument is weakened or falls apart. On the other hand, show how a particular person, place, or thing is representative of the larger awholea and the argument is strengthened.

Generally, the issue will not be whether a sample is large enough but whether it is diverse enough. If the sample is not drawn from relevant representative subcla.s.ses, the sample size is of little consequence. A noteworthy real-life example is the Gallup poll, as devised by George Gallup, and used notably for predicting winning candidates in national political races. In order to generalize about the opinions of the people in an entire country with respect to a given candidate or political issue, data must be gathered from subcla.s.ses based on age, education, gender, geography, professional status, race, and perhaps even religion. Other subcla.s.ses, such as body weight and hair color, would be irrelevant. Even though there may well be millions of people in a given country, the Gallup poll requires a sample size of only about 1,800 people to be statistically accurate.

Note that a representativeness a.s.sumption is different from an a.n.a.logy a.s.sumption. An a.n.a.logy a.s.sumption might be thought of as a side-by-side comparison of two things whereas a representativeness a.s.sumption might be thought of as a vertical comparison stating that a asmaller somethinga is just like the larger whole. An a.n.a.logy a.s.sumes big aAa is equal to big aB,a but a representativeness a.s.sumption a.s.sumes little aaa is equal to big aA.a aGood Evidencea a.s.sumptions Arguments should be based on evidence which itself is valid. It is only human nature to want to choose relevant evidence that supports our stance while ignoring relevant evidence which refutes it. If we want to continue smoking, for example, we may entertain only that evidence which suits our fancy, such as asmoking helps me relax, looks cool, and keeps my weight down.a Evidence contrary to this viewpoint, such as asmoking is dangerous to my healtha or asmoking is too expensive,a is ignored. For the person who doesnat like riding motorcycles, evidence chosen might include the ideas that motorcycles are dangerous and noisy, grease and dirt may ruin your clothes, helmets are uncomfortable, only two people can ride at once, and it is hard to ride motorcycles in rainy or snowy weather. Such a list might exclude that fact that motorcycles are fun and enjoyable to ride, more maneuverable, easy to find parking s.p.a.ces for, and relatively inexpensive to purchase and maintain.

One of the hallmarks of objective thinking is that we should invite all relevant evidence to bear on an issue or decision at hand. We should not ignore or slant evidence if what we seek is the atruth.a The legal system followed by most countries throughout the world is modeled on the adversarial justice system. These systems of justice lend themselves to the slanting of information and evidence. Trial lawyers for the defense and prosecution present evidence in a way which maximizes the chances of their winning cases. It is important to note, however, that judges and juries must remain impartial if fairness is to be achieved.

Cause-and-Effect a.s.sumptions Does one event really cause another? Cause and effect is concerned with the relationship (or non-relationship) between two events. We call the first event the cause and the second event the effect. When we write this as a formula, we use A for the cause and B for the effect: A a' B.

As depicted in Exhibit 4.1, cause-and-effect relationships arise under six potential categories. These include the following: Exhibit 4.1 a" Coincidence, Correlation, and Causation The first question we ask when a cause-and-effect a.s.sumption is on the horizon is whether any relationship exists between two items. There may not be any plausible relationship. For example, aThe street light turned red just before the cat fell out of the tree; therefore, the red light caused the cat to fall out of the treea has no plausible causal relationship (mere coincidence). Next, a.s.suming a relationship exists, we ask whether the two events are causally related or merely correlated. If a correlation exists, we seek to determine whether that correlation is low or high. If causally related, we seek to determine whether the two events are legitimately correlated or whether alternative or reverse causation is at work.

Here are further explanations of the categories highlighted in the previous chart.

I. Mere Coincidence aEvery time I sit in my favorite seat during a playoff game, our team wins.a It is unlikely that your aluckya seat is causing your sports team to win. And it is equally unlikely that a regular or abada seat will cause your team to lose.

II. Low Correlation An example of low correlation might be the opening of new health clubs in your city and the general level of fitness among citizens in your city. Obviously, the opening of health clubs with facilities that include weight-lifting cla.s.ses, aerobic cla.s.ses, and exercise machines will have some effect on the fitness level of people in general. But, practically, it will not have a great deal of impact. The direct impact of a small number of health club members on a cityas larger population is limited. Even if there is a general trend toward more fitness in your city, it may be because people walk, ride bikes, and take hikes more often. Individuals may partic.i.p.ate in these activities and not be a.s.sociated with health clubs.

III. High Correlation (but not causation) Certain factors or characteristics are strongly correlatedaa"afor example, being tall and being a National Basketball a.s.sociation player. Not every player in the NBA is tall, but the vast majority of players are. We can safely say that there is a strong correlation between being tall and being an NBA player. A cla.s.sic example in business is a companyas sales and advertising costs. The more a company spends on advertising, the greater its sales. (The correlation between advertising and sales is approximately +0.8.) Other examples might include hot weather and ice cream sales, or rainy weather and umbrella sales. Strongly correlated events may be talked about as if they are causally related. It is important to be able to draw the line between high correlation and actual causation.

IV. Legitimate Causation The law of gravity indicates a causal relationship. I throw an apple up into the air and it comes back down. Other events are so highly correlated that for all practical purposes they are a.s.sumed to be causally related a" for example, the amount of coffee consumed and the amount of coffee beans consumed or the number of babies born and the number of baby diapers used. However, it would not be accurate to say the number of coffee beans grown or the number of baby diapers manufactured.

V. Alternative Explanation Alternative explanation technically can be called alternative causal explanation. Here we agree on a single conclusion (the effect) but differ as to which is the correct cause. We must always be on guard for the existence of another cause whenever it looks as though two events are otherwise causally related. A business may have increased its advertising budget and seen an increase in sales. It is easy to view these two events as causally connected. But advertising may be having little or no effect on sales. The reason that sales have increased may be that a major compet.i.tor of the company went out of business. Another example occurs when John is speaking to Alice: aItas plain to see that the recent spate of high school shootings is the result of viewing violent TV programming.a Whoas to say that the high school shootings are not instead the result of more lax gun laws, dwindling educational standards, or weakened religious following? (In this case, it is not A that is causing B but rather C that is causing B.) Or maybe a third factor is causing both A and B. For example, perhaps both the increase in high school shootings and the increase in violent TV programming are the result of a third factor, e.g., breakdown of the family unit. (In this latter case, it is not A that is causing B but rather C that is causing both A and B.) VI. Reverse Causation Does your favorite commercial author sell a lot of books because he or she is famous, or is he or she famous as a result of selling lots of books? Reverse causation is tricky. You think X is causing Y, but in reality it is Y that is causing X. The following example helps ill.u.s.trate this point. Say you notice that a young woman at work named Sally is always working hard. And you say to yourself one day: aSally is a hard worker. No wonder our boss gives her the toughest a.s.signments.a The argument becomes, aBecause Sally is such a hard worker, our boss gives her the toughest a.s.signments.a But could the reverse be true? What if Sally is lazy and not naturally such a hard worker, but rather works hard only because she happens to be given the toughest projects? Now the argument becomes: aBecause Sally is given such tough work projects, she is therefore forced to work hard!a Children may reveal funny examples to illuminate the concept of reverse causation. Young children may believe that firemen cause fires, for every time they see a picture or a video of a fire there are firemen at the scene. Eventually, the reverse is confirmed to be true: aFires cause firemen.a As an historical example, when researchers first started testing the hypothesis that asmoking causes cancer,a one of the first things they considered was the reverse hypothesis a" the idea that people who have cancer might try smoking (i.e., cancer causes smoking). Not surprisingly, this hypothesis proved groundless. However, in many other situations it is difficult to distinguish between the cause and the effect. Consider the statement: aYouare good at the things you like.a The cause-and-effect argument becomes, aYou like things [cause], and therefore you become good at them [effect].a But could it be that you find yourself good at some things and then learn to like them?

Implementation a.s.sumptions Some years ago, an article in a Western travel magazine stated: aBecause air travel is becoming so convenient and because people have greater disposable incomes, soon everyone will have been to Africa to see the lions.a Yet today, few people outside of Africa can claim to have been to Africa to see the lions. What accounts for the discrepancy between the travel magazine article and people actually going to visit Africa and the lions? Was the article wrong about plane travel becoming more convenient or people having higher levels of disposable income? The magazine was not likely wrong in these respects. However, the article was incorrect in its prediction that aeveryonea (or, less literally, amany peoplea) would go to Africa to see the lions. The discrepancy between an otherwise sound plan and action is based on the a.s.sumption that a sound plan must necessarily achieve its desired result. This is not necessarily so.

Why do plans not always work? There are essentially four major reasons that plans do not work: (1) an individual or organizationas lack of desire, motivation, or perseverance; (2) an individual or organizationas lack of prerequisite skill or technological capability to carry out the plan; (3) lack of required opportunity or wherewithal a" e.g., economic resources a" to commence or complete a given task; and (4) unantic.i.p.ated bottlenecks or consequences (physical, financial, technological, or logistical) arising from the planas implementation. aImplementation a.s.sumptionsa are grounded on the idea that a plan will work because of an absence of the kinds of deficiencies previously cited.

First, an individual or organization may lack desire, motivation, or perseverance to carry out a plan. There is a saying that aone who can read but doesnat is no better than one who cannot read.a The ability to do something is not the same thing as actually using that skill. We all know of examples of extremely talented individuals who lack the focus or perseverance to achieve their true potential.

Second, the required skill or technological capability to carry out the plan may be lacking. Consider the statement a high school graduate made: aEither Iam going to medical school or I am going to join the military and become a member of the Special Forces.a This a.s.sumes that the person has the talent and perseverance to get accepted to medical school en route to becoming a doctor. It equally a.s.sumes the physical and technical skill, mental toughness, and temperament to make it through training en route to being selected as a member of the Special Forces.

Third, we cannot a.s.sume that an individual or organization has the required opportunity or financial wherewithal, that is, economic resources, to complete a given task. In the example above, the high school graduate a.s.sumes that in the case of medical school, he or she has the ability to also obtain loans and other forms of financial aid required to complete medical studies.

Fourth, in terms of unantic.i.p.ated bottlenecks or consequences, think what would happen if everyone pursued the proposed plan. For example, your office may be considering the installation of a new computer e-mail system, which many believe will resolve your companyas communication problems. But what if everyone uses the computer system at the same time? The system might just crash because it is unable to accommodate all users (technological limitations).

Be suspicious of any claim that suggests that legislation can solve a problem. Legislation can certainly be used to discourage or limit undesirable actions, but it does not prevent them per se. Legislation to prevent discrimination, for instance, may not work if people themselves are unwilling to stop discrimination. Likewise, pa.s.sing a law to increase fines for people parking their cars illegally in front of prestigious shopping venues will not necessarily stop shoppers from parking their cars, particularly wealthy consumers who may nonetheless decide to park illegally and accept higher fines.

The following section provides an opportunity to solve critical reasoning problems. These multiple-choice problems are grouped according the five categories introduced here: comparison and a.n.a.logy a.s.sumptions, representativeness a.s.sumptions, agood evidencea a.s.sumptions, cause-and-effect a.s.sumptions, and implementation a.s.sumptions.

TESTING CRITICAL REASONING.

Tip #23: Watch for ascope shifts,a which occur when one term is subst.i.tuted for another as an argument unfolds.

Problem 12: Crime According to an article in the Life and Times section of the Sunday newspaper, crime is on the downturn in our city. Police initiatives, neighborhood watches, stiff fines, and lengthened prison terms have all played a significant role in reducing the number of reported crimes by 20 percent.

Which of the following would most weaken the belief that crime has decreased in our city?

A)*In its Sunday newspaper, a neighboring city has also reported a decrease in crime.

B)*Police officers were among those citizens who voted for a bill to support police initiatives to reduce crime in our city.

C)*Most of the recent police arrests were repeat offenders.

D)*The author of the article includes white-collar crime in his definition of crime, thus increasing the number of reported crimes.

E)*It is possible for reported crime to have gone down while actual crime has remained the same or actually gone up.

See solution Tip #24: Changes in definition destroy the ability to make valid comparisons.

Problem 13: Hyperactivity Viewing children as more hyperactive today than they were ten years ago, many adults place the blame squarely on the popularity of video games and multimedia entertainment.

Which of the following revelations would most undermine the argument above?

A)*Even if children today are more hyperactive than they were ten years ago, they are widely viewed as more spontaneous and creative.

B)*The claim that children are more aggressive today is a more serious charge than their being considered more hyperactive.

C)*Childrenas books published in recent years contain on average more pictures than do childrenas books published in the past.

D)*More types of behavior are deemed hyperactive today than were ten years ago.

E)*Incidences of ailments such as Attention Deficit Hyperactivity Disorder (ADHD) are reported to be on the increase in recent years.

See solution Tip #25: If a situation involves a asurvey,a check to see if the survey is based on a sample which is both quant.i.tatively and qualitatively representative.

Problem 14: Movie Buffs According to a recent survey, any sequel to the movie Victimas Revenge will not fare well. Respondents to a recent survey of moviegoers leaving Sunday matinees around the country indicated that movies based on serial killers with psychopathic tendencies have fallen out of vogue with current movie buffs. Therefore, if movie studios want to produce films that are financially successful, they should avoid producing such films.

Which of the following would most weaken the idea that film studios should stop production of stories and dramas based on serial killers with psychopathic tendencies?

A)*Movie stars have a significant following of people who see their every film.

B)*People who attend Sunday matinees are not representative of the views of the moviegoing population as a whole.

C)*The film Psycho, originally directed by Alfred Hitchc.o.c.k, was a big hit in 1960 and was remade in 1998.

D)*Both student enrollment in college criminology courses and book sales based on the lives of real-life serial killers are up.

E)*The cost of making such movies requires skillful actors who can portray emotional conflict and intellectualism, and these actors demand high salaries.

See solution Tip #26: Representativeness a.s.sumptions are based on the idea that some smaller factor is representative of the larger whole.

Problem 15: Bull Market aWow, the economy of India sure is strong. The National Stock Exchange (NSE) has gone up by more than 1,000 points since the beginning of the year.a Which of the following would lend the strongest support for the speakeras comments above?

A)*The National Stock Exchange (NSE) is a fair indicator by which to judge the strength of the overall Indian economy.

B)*The Bombay Stock Exchange (BSE) index has also gone up nearly 500 points since the beginning of the year.

C)*The National Stock Exchange (NSE) index was actually down during this exact time last year.

D)*During the same time period in which the Indian economy was considered strong, the economies of Asia and Europe were also considered strong.

E)*The National Stock Exchange (NSE) Index, historically, is subject to great fluctuations.

See solution Tip #27: Broadly speaking, representativeness a.s.sumptions occur anytime that we argue from the particular to the general.

Problem 16: Putting Are you having trouble getting the golf score you deserve? Is putting your pariah? The new Sweet Spot Putter is designed to improve your golf game overnight without intensive lessons. Even rank amateurs can dramatically increase their putting accuracy by 25 percent. You too can achieve a low golf score with the new Sweet Spot Putter.

Someone who accepted the reasoning in the advertis.e.m.e.nt above would be making which one of the following a.s.sumptions?

A)*Without quality equipment, a golf player cannot improve his or her game.

B)*The new Sweet Spot Putter will improve an amateuras game more than it will improve a professionalas game.

C)*The quality of a personas golf game is largely determined by the accuracy of his or her putting.

D)*The new Sweet Spot Putter is superior to any other putter currently on the market.

E)*Lessons are not as effective at improving the accuracy of a playeras putting as is the use of quality equipment.

See solution Tip #28: Check to see whether evidence has been handpicked to support a claim being made. Otherwise we may fall victim to aproof by selected instances.a Problem 17: Criticas Choice In a newly released book, Decline of the Novelist, the author argues that novelists today lack technical skills that were common among novelists during the past century. In this regard, the book might be right, since its a.n.a.lysis of 200 novels a" 100 contemporary and 100 non-contemporary a" demonstrates convincingly that few contemporary novelists exhibit the same skill level as that of non-contemporary novelists.

Which of the following points to the most serious logical flaw in the criticas argument?

A)*The t.i.tle of the authoras book could cause readers to accept the bookas thesis even before they read the literary a.n.a.lysis of those novels that supports it.

B)*There could be criteria other than the novelistas technical skills by which to evaluate a novel.

C)*The novels the critic chose to a.n.a.lyze could be those that most support the bookas thesis.

D)*The particular methods novelists currently use may require even more literary skill than do methods used by writers of screenplays.

E)*A reader who was not familiar with the language of literary criticism might not be convinced by the bookas a.n.a.lysis of its 200 novels.

See solution Tip #29: aEvidence omitteda may hold the key to determining an argumentas validity.

Problem 18: Temperament Steve: aRick and Harriet, two of my red-haired friends, are irritable. It seems true that red-haired people have bad tempers.a John: aThatas ridiculous. Red-haired people are actually quite docile. Jeff, Muriel, and Betsy a" three of my red-haired friends a" all have placid demeanors.a Which of the statements below provides the most likely explanation for the two seemingly contradictory statements above?

A)*The number of red-haired people whom Steve knows may be different from the number of red-haired people whom John knows.

B)*The number of red-haired people whom both Steve and John know may not be greater in total than the number of non-red-haired people whom both Steve and John know.

C)*It is likely that Steve or John has incorrectly a.s.sessed the temperament of one or more of his red-haired friends.

D)*It is likely that both Steve and John have friends who are not red-haired and yet also have bad tempers.

E)*The examples that Steve uses and the examples that John uses to support their conclusions are likely both valid.

See solution Tip #30: Correlation does not equal causation.

Problem 19: Cyclist Touring professional cyclists have been shown to have between 4% and 11% body fat. If we could all decrease our body fat to that level, we could all cycle at a world-cla.s.s level.

Which one of the following most accurately characterizes the method of reasoning used in the above statements?

A)*Its conclusion is based on evidence, which in turn, is based on its conclusion.

B)*It ill.u.s.trates the absurdity of the argument by reaching an illogical conclusion.

C)*It a.s.sumes a causal relationship between two highly correlated events.

D)*It uses flawed evidence to support its conclusion.

E)*It a.s.sumes what it seeks to establish.

See solution Tip #31: Cause-and-effect a.s.sumptions are grounded in the idea that because one event follows another in time, the first of the two events is the cause and the second is the effect.

Problem 20: SAT Scores Parents are too easily impressed with the recent rise in average SAT scores at the top American undergraduate universities and colleges. Unfortunately, this encouraging statistic is misleading. Scores have risen not because students possess better math, English, and writing skills but because students are better at taking tests. For those students accepted as undergraduates at the top universities and colleges, studies confirm that skills in the basics of reading, writing, and mathematics have been on the gradual decline over the past twenty years.

The author argues primarily by A)*Denying the accuracy of his opponentsa figures B)*Finding an alternative explanation for his opponentas evidence C)*Introducing irrelevant information to draw attention away from the main issue D)*Employing circular reasoning E)*Suggesting that his opponentas evidence may be flawed See solution Tip #32: When tackling cause-and-effect scenarios, think first in terms of alternative causal explanations. If an argument suggests that A is causing B, then check to see that another cause, namely C, is not instead causing B.

Problem 21: Valdez Since Ana Valdez was installed as president of the Zipco Corporation, profits have averaged 15 percent each year. During her predecessoras tenure, the corporationas profits averaged only 8 percent per year. Obviously Ms. Valdezas aggressive international marketing efforts have caused the acceleration in the growth of Zipcoas profits.

Which of the following, if true, would most weaken the conclusion drawn above?

A)*During the tenure of Ms. Valdezas predecessor, the corporation began an advertising campaign aimed at capturing consumers in developing countries between the ages of nineteen and twenty-five.

B)*The corporationas new manufacturing plant, constructed in the past year, has a 35 percent greater production capacity.

C)*Since Ms. Valdez became president, the corporation has switched the primary focus of its advertising from print ads to radio and television commercials.

D)*Ms. Valdez hired a well-known headhunting firm which found talented vice-presidents for two of the corporationas five divisions.

E)*Just before Ms. Valdez took over as president, her predecessor, Mr. Jones, directed the acquisition of a rival corporation, which has nearly doubled the corporationas yearly revenues.

See solution Tip #33: A more complex form of alternative explanation occurs when two effects result from a single cause. Thus, if an argument suggests that A is causing B, consider the possibility that another cause, namely C, could be causing both A and B.a Problem 22: Headline The headline of the College Tribune reads: aObesity Linked to Depression.a Which of the following, if true, would most weaken the implied conclusion drawn between becoming overweight and falling into depression?

A)*An obese person may not understand why he or she is depressed or how to escape from the throes of depression.

B)*Depression can also result from things other than obesity.

C)*Low self-esteem is frequently cited as the cause of both obesity and depression.

D)*A person twice as overweight as another person is not likely to be twice as depressed.