7. recognizing statistical slip

8/2/2019 7. Recognizing Statistical Slip

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Critical Reading by Parlin Pardede (for FKIP use only) Page 66

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RECOGNIZING STATISTICAL SLIPS

he reading of facts presented in mathematical form seems to bother many presentday adults. Graphs, tables, and charts are just so many lines and numbers to skipover, if possible. If you dont think so, ask the next person you hear using the word

billion to tell you how much it really is. Or if he or she is talking in millions, ask what a milliondollars is, what it represents, and what you can do with it. The chances are that he or shehas little or no concept of how much a million dollars is or will do.

This ignorance of mathematical terms and concepts is quite widespread. As a result,those who present facts to the public through mathematics can easily deceive the averagereader. Statistics and charts are manipulated to prove almost anything to the naveconsumer. Unless you learn to read mathematical materials critically, you are too at themercy of the unscrupulous statistician or chart maker. The following is a brief introduction tostatistics and a discussion on the most common statistical slips you need to know in order toguard yourself against being mislead by misused statistics.

A. What is Statistics?The word statistics has two meanings. When it is used with a plural verb, it refers to

information about any phenomenon or activity expressed in numerical form, such as vitalstatistics, college enrolment figures, and opinion poll percentages. In its singular sense, itdenotes the art and science of collecting, presenting, analyzing, and interpreting numerical

data. In other words, it is, in the second sense, the tool for us to make the maximum use ofquantitative measurements and assessments.The importance of statistics in human affairs is obvious from our tendency to

associate facts closely with figures. However, raw, undigested and voluminous figures thatare carelessly accumulated are useless and even meaningless. A long list of bus-ticketnumbers amassed from tickets found in a dustbin would be of no service to anyone. Butfigures that are systematically collected and properly analyzed can be used as the basis forrational decisions and conclusions. A table that shows the quantity of bus-tickets of eachdenomination sold will, for example, help the bus proprietor to decide on whether he shouldhave more buses running short or long distances. Indeed, in an age of science when mantries to be rational, objective and systematic in as many activities as possible, the art andscience of statistics is an indispensable analytical tool.

A government in conducting the nations affairs has to make much use of statisticalanalysis. The effectiveness of a government policy or plan depends to large extent on howwell the government knows the quantitative aspects of the social, economic and physicalconditions of the country. A school building project, for example, would among other things,demand sound statistical analysis of population figures, budget and the quantitative aspectsof educational facilities.

In the business field, the total dependence of insurance companies on statisticalforecasts is well known. But other businessmen also depend on statistics in their prediction

T


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of sales and costs, their quality control, their production and marketing researches, and theirquantitative personnel records. Even a sole proprietor who makes shoes in expectation ofdemand will note the quantity of each size of shoes that is normally sold, if he does not wantto have a big stock of unsalable goods.

Research workers engaged in fields that are concerned with quantitative results alsorely heavily on statistical analysis. The methods of statistics are used to test, among otherthings, the quality of animal feeds and other farm materials, the effectiveness of new drugsand other medical developments, and the destructiveness of weapons and military tactics.Even in the literary field, statistics has been used to analyze vocabulary and to settlequestions related to disputed authorship.

But useful though statistic is, it often misused. Just as the devil can cite Scripture forhis purpose, people with vested interest may enforce figures to serve their ends.

Advertisements, for instance, abound with misleading statistical statements and reports suchas those which begin with statistics prove that and Nine out of ten university scholarsuse However, sheer ignorance and carelessness may also give rise to statistical blunders.These human weaknesses are the only explanation for some of the quantitative errors in

newspapers and magazine articles.

Of course, the way to guard oneself against being misled by misused statistics is notto shun or mistrust all figures but to become conscious of how statistical procedures may beincorrectly used. Among the most common statistical slips that might consciously orunconsciously be made are the following.

B. Common Statistical Slips1. The Deceptive Sample

Many statistics are based on a sample of the population. But no statistics is anybetter than the sample on which it is based. This sample may be too small, or biased byobvious or hidden factors, or deliberately chosen to prove the writers point. Take the

case of the Literary Digestpoll of 1936 that predicted the presidential election of AlfredLandon. The sample was composed of ten million telephone and Digestsubscribers whohad been used in a correct presidential prediction in 1932. Such a sample seemed largeenough and apparently free from bias. But the people who could afford telephones andmagazine subscriptions just werent representative of the American public in 1936. Most

Americans were still struggling with the effects of the great depression at the later date.Telephones and magazines were luxuries for many trying to make both ends meet. Thesample was economically biased; it reflected the voting preferences of a select group,


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not of the general public, and the prediction was wrong.To yield an accurate statistic, a sample must be representative of the total group. It

should be selected by pure chance under circumstances in which every person or thing inthe total group has an equal chance of being selected. This is called a random sampling.However, because it involves so great a cross section of the total population, truerandom sampling is almost prohibitive in time and cost. In its place, a stratified samplecomposed of a small group possessing those traits characteristic of the generalpopulation is commonly used. Public opinion polls, surveys of users of a certain product,sales prediction for a proposed new product, views of magazine readers, and preferencesof radio listeners and televiewers are commonly based on this stratified samplingtechnique.

But how do the researches know that the stratified sample is really a randomsample of the total population? The truth is, they dont. Their conclusions may bedistorted by any of a dozen factors, such as the very questions asked, the emotionalreactions of those interviewed to the questions or the interviewer, or the extent to whichsocial prestige or the ego of the respondent is challenged. How accurate, for example,

can a survey of such personal matters as income, church attendance, racialdiscrimination, or wife beating really be?Considering these explanations, it is very important for everyone to look more

critically at any statistic based on sampling. Most poll results are apt to be biased, evenwhen they are not deliberately distorted. This bias is likely to be toward reflecting thethinking and actions of the person with better-than-average economic and social status.If you were the interviewer waiting outside a factory, which person would you stopthesurly-looking fellow plowing along with his head down, or the neat, smiling womanwalking leisurely homeward?

To help you read and interpret statistics based on sampling, we suggest that youask the writer such questions as: How many people are involved in these data? Whatkind of people are they? How were they selected? What are some of the factors that may

have influenced the results? What do the results prove, if anything? What kind of sensedo they make? For example, several years ago, the manufacturer of a popular brand ofcigarettes claimed that more doctors smoked his brand than any other. Are doctorsbetter judges of taste, mildness, and other cigarette qualities than any other people?

Aside from the fact that we dont know many doctors were sampled, just what does thisstatistic prove? The implication is, of course, the medical training makes one a better

judge of cigarette and more aware of their possible harmful effects. Therefore, if moredoctors smoke X brand, it must be better and less harmful than other brands. Only amoments thought will demonstrate that if X is a widely sold brand, it is likely to sell wellamong most groups,plumbers as well as doctors.

Or take the claim of the toothpaste manufacturer that six out of eight people preferthe taste of his product to that of others. Does he tell you how many people were

sampled before these results were secured? Usually not, because his researchersprobably waited until they found such a result in one small group rather than reportingon the preferences of the entire population sampled. If two toothpastes were beingcompared, we would expect five out of ten people to prefer Z paste, purely on the basisof chance. Flipping a coin several hundred times is likely to result in half heads and halftails. But in a small sample, the law of probability does not operate in the same fashion.The first ten tosses of your coin may all be heads. Thus, if the surveyors for Z toothpastetook a number of small samples, it is quite possible that they would find one in which the


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$0$25,000$50,000$75,000$100,000$125,000$150,000$175,000$200,000

$225,000$250,000

048

121620242832

3640

TotalofSalarie

s

TotalofPersonnels

Positions

Figure 1: Average Yearly

Salary--ABC Electronics

Company

results were the kind theywanted. This may be dishonestreporting of research, but itcertainly is rigged to produce thedesired results.

2. The Misleading AverageWhat is an average? It is the

most common characteristic of arelatively large number of people,or a point that divides thepopulation into two equal halvesof haves and have-nots? Or isit the total amount of certain traitdivided equally among the entirepopulation? Well, it is and it isnt.

It may be any or all of these.The term average is used loosely to describe any of three measures knowntechnically as the mode(the most frequently occurring value in a group of values), themedian(or the middle value in an array of values that range from the highest to thelowest), and the mean (or the sum of all values divided by the number of valuesincluded). When we discuss such human traits as height and weight, it doesnt mattermuch which we use, for these characteristics are distributed normally throughout thepopulation. But if we talk about incomes taxes, wattage consumption or divorce rates, itmatters a great deal which average is selected.

Lets take a case in point. The ABC electronics Company tells us that their averageemployee earned $ 10,000 last year. Sounds fairly good, doesnt it? But what does thisaverage mean? Was $10,000 the most common salary among the employees? No,

because the greatest number of employees earning any one salary, or the mode, isfound $7,000. Then what does the $10,000 mean? It must be an average of the salariespaid to the two partners who own the company ($50,000 each); the two engineers($25,000 each); a technician and a production manager ($14,500 each); two foremen($10,500 each); and the forty hourly workers who earn about $7,000 per year. All thesesalaries add up to $480,000, which divided by forty-eight employees averages $10,000.Neat, isnt it? (Would you have thought of adding in the owners shares to raise theaverage yearly salary?) But the labor union leaders arent likely to use this mean inasking for a better salary scale. They are more apt to use the mode, the point at whichmost of the employees fall on the scale of $7,000. In this case, the union could also usethe median of $7,000 because more than half of the workers earn this amount of or less.

Graphically, these data could have been presented somewhat as in Figure 1 (but, of

course, no statistician attempting to please the owners of The ABC electronics Companywould have used such a method of presenting the facts.)

The next time you read something about an average, ask yourself, Whataveragemean, mode, or median? Or Average of what? Who and what are includedhere? Here are typical average figures found in a recent publication. Just what do theymean?

A leading magazine reports an average of 6.02 hours of televiewing per day inAmerican home. Last years figure is given as 5.81 hours per day. It concludes, The


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0123456789

10

7576777879808182838485

Percentage

Year

Figure 3: Increase

in Unit Cost (in %)

0

2.5

5

7.5

10

75 76 77 78 79 80 81 82 83 84 85

Percentage

Year

Figure 4: Increase in Unit Cost (in %)

glass screen is really taking over.These figures have an artificial

note on authenticity because of the useof the decimal figures. It sounds moreaccurate to say 6.02 hours rather thansimply 6 hours. But how many homeswere involved in this survey? The finedistinctions implied in the decimals areabsurd unless the sample was quitelarge.

How was the survey done? Bywhom? By calling on the phone and

asking how many hours a day the TV set was used? Werereliable time-sampling measures used to determine theactual amount of televiewing? Are these figures offered

by TV manufacturers or broadcasting chains who,perhaps, have an ulterior movie? As for monopolizingthe televiewers day, how much of a real difference isthe .21 or an hour (thirteen minutes)? Is theconclusion based on a significant difference? Do thesefacts add up to anything at all? Do they even indicate areliable trend?

3. Plausible Charts and GraphsIn the effort to make mathematical concepts

more palatable, or more shocking,writers often employ a pictorial or

graphic presentation. Like moststatistical data, this method can bemanipulated to convey almost anydesired impression. For example,suppose you were a productionmanager trying to show topmanagement why the unit cost of yourproduct had risen in the past decade.

You are trying to convince topmanagement that the sales manager ismistaken in opposing a repricing of theproduct. Which of the following chartswould you present? Figure 2, 3, or 4?

These graphs are all accurate and honest, but there is a great deal of difference inthe impression they create. Figures 2 and 4 imply a fairly constant but gradual increasein the unit cost. In Figure 3, the rate of increase seems terrific. The trick, of course, ismerely to narrow the horizontal interval in the graph and expand the vertical interval. Ifyou do this, you automatically come up with a startling picture. Push the base line closertogether, and your line shoots up. Or to produce the opposite effect, merely lengthen thebase line as in Figure 4. What do you want to prove? Pick your own chart.

0

5

10

15

75 76 77 78 79 80 81 82 83 84 85

Percent

age

Years

Figure 2: Increase in Unit

Costs (in %)


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4. Presenting the Facts without a Reference Point.There is another technique of manipulating graph

that isnt quite as obvious but helps to strengthen yourdata. This is presenting the facts without a referencepoint. If the possible range of data and the zeroreference point are omitted, it becomes much easierto prove your point, whatever it may be. Figure 5 is anexample of this type of graph. Visually, you are led tobelieve that frozen food consumption has growntremendously in the period from 1967 to 1975. Buthow much actual increase does this represent? Onepercent? Ten percent? One hundred percent? There isno way of knowing from the graph.

In addition to that, percentages un-accompanied by actual-al numbers may also givemiss-leading impressions. To say that 75% of an experimental group found X brand tobe better than all other brands, sound very impressive. Nevertheless, the person who

asserts this may deliberately leave out the fact that only four people formed theexperimental group. Indeed if small groups ofpeople are tested, an experimenter will by sheerchance, certainly get a group that yields apercentage suitable for his purpose. Figure 6 isan example of such vague graphs that was usedby a major automobile manufacturer to boostthe sales of the latest models. Because nospecific models are mentioned, this graph tellsthe prospective purchaser nothing about anyparticular type of automobile.

The same auto manufacturers are currently claiming that their cars have improved

48 percent in quality in recent productions. Improved how48 percent better than what?To a cynical listener, this claim might mean that the car quality must have been prettybad, if this much improvement was possible. But, of course, you are not supposed tointerpret this advertising nonsense in this fashion.

There is nothing wrong with this chart from the advertisers viewpoint, or from thenave readers interpretation. He or she gets the point. But from the standpoint ofaccuracy and sincerity, there is much to be desired. But no one would stoop so low, yousay. Darrel Huff gives numerous samples drawn from reputable newspapers andmagazines in his interesting bookHow To Lie with Statistics (New York: Norton 1954).The author gives common methods of producing striking statistics with weak data. *****

EXERCISE 71

Read the following passages and choose the appropriate letters to show any statistical slipsyou discover in each passage.

1. The causes of the American Civil War are numerous, but very few historians agree aboutthe most significant causes. Some of them cite economic differences between the Northand the South. Others say that the North and the South really were different cultureswith different histories. Some others emphasize the issue of slavery as the major causeof the Civil War.

Figure 6: Increase in gasoline mile-age

in the latest Ford Models.

48%

1967

1970

1975

Figure 5: Frozen Food

Consumption


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A.Presentation of Facts Without a Reference Point C. Misleading AverageB. Manipulated Charts And Graphs D. Deceptive Sample

2. An educational report recently revealed an increase in Malaysian senior high schoolstudents mastery of English in the last three years. The English average score achievedby the students in the National Final Test in Kuala Lumpur was 76 (2001), 82 (2002) and90 (2003). In Selangor the average score was 74 (2001), 84 (2002) and 88 (2003); andin Serawak 72 (2001), 80 (2002) and 84 (2003). Hearing this, Malaysian Minister ofEducation and Science congratulated all English teachers and asked them to do better.

A.Presentation of Facts Without a Reference Point C. Misleading AverageB.Manipulated Charts And Graphs D. Deceptive Sample

3. A sociological study on single people conducted in Jakarta was completed recently. 35adult males and 35 adult females were asked to fill in a questionnaire in order to see

whether they tended to get married or to stay single. The results showed that poor adultmales were more likely to be single than wealthy adult males. The results for femaleswere the opposite. Wealthy women were much more likely to be single than poorwomen. Another interesting finding in the study was that women would like to getmarried when they were between 24 to 35 years old, whereas men thought its quite OKif they got married when they were between 30 to 50 years old.


4. (Letter of Recommendation from an auto-manufacturer to a major) First of allcongratulation for your inauguration as the major of one of the busiest industrial city in

our country. I support your plan to change the old city-buses in order to provide bettertransportation to the whole people in your city. In relation to that, let me inform you thatmy factory has just designed and begun to produce the most economical bus in theworld. With 35 seats and fully air-conditioned, the bus needs only 12.5 liters of gasolineto reach 50 kilometers. You can buy our product as many units as possible with the mostreasonable price.


5. In a recent publication it was reported that most Indonesians have increased their

incomes over the past years. Seventy-nine per cent of sixty farmers interviewed said thattheir harvest increased between fifteen to twenty percent in the last two years. Ninetypercent of 100 persons working in professional and technical occupations interviewed inJakarta, Medan, Surabaya and Bandung admitted that their monthly salary increasedaround fife to ten per cent. Eighteen out of twenty sales workers in Jakarta and Surabayaresponded that their sales increased about six percent every month. Ninety per cent oftwelve managers and administrators working in Jakarta and Tangerang said theirincomes increased around four per cent. Finally, almost 99% of 28 persons working as


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transportation operators admitted to get about seven percent increase in their monthlyincomes.

A.Presentation of Facts Without a Reference Point C. Misleading AverageB.

Manipulated Charts And Graphs D. Deceptive Sample

6. Afghanistan was a frustrating and senseless struggle. Three out of four experts on FarEast in The Washington University commented that fighting the Mujahiddin guerillaswould give more loss than benefits. Ninety percent of political leaders interviewed by theWashington Post warned the President of the United States that this war could never bewon. Nine out of ten American soldiers who returned from Afghanistan last month saidthat Mujahiddin fighters couldnt be subdued by sophisticated military weapons. It wasalso reported that more than a half of American soldiers posted in village 150 kilometersto the south of Kabul died senselessly at the hand of Mujahiddin guerillas hiding in thedeserts of the country.

A. Presentation of Facts Without a Reference Point C. Misleading AverageB. Manipulated Charts And Graphs D. Deceptive Sample

7. According to some proponents of feminist movement, American society still commits sexdiscrimination in the area of pay. To support this opinion, they claim that the averageweekly income for a woman in 1993 was $320, and for a man was $ 443. In my opinion,however, the reason for this difference is not sex discrimination, but the fact that womentend to enter low-paying jobs. In the legal and medical professions, for example, 85% oflawyers and doctors are men (although this situation is changing). In technicalprofessions, more than 90% of all engineers are men. Women, on the other hand, havebeen the majority in jobs that are not well paid. Statistics show that 99 out of 100secretaries are women, and 90% of all nurses and primary school teachers are female.

To conclude, their tendency to work in low-paying jobs is the reason why the averageincome obtained by women is lower than those of men.

A. Presentation of Facts Without a Reference Point C. Misleading AverageB. Manipulated Charts And Graphs D. Deceptive Sample

EXERCISE 72Read the following Report which appeared in The Straits Times, Singapore, on 6th August1973. Criticize the deductions made from the statistics of Singapores traffic.

Its Safer to cycle

than to drive or walk

ROAD casualty figures show that it is safer to ride a bicycle than drive a car or walk.The chances of survival under the hectic conditions of Singapores traffic congested

roads would seem to favor the cyclist consistently over the last ten years.


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EXERCISE 73The following graphs show increase in average income of workers. On what occasionsshould they be used?

EXERCISE 74These statistics refer to the average monthly expenditure of the families of 3 different

income groups in a recent year. Study them carefully and answer the questions that follow.

1. Look at the food expenditure figures of the first two income groups. How can the twopercent-ages in each income group be the same when the actual amount in dollars spent onfood for rural and urban families are different?

020406080

100120

Dec Aprl Aug Dec

( $ )

Graph 1

70

80

90

100

110

120

Dec Aprl Aug Dec

( $ )

Graph 2

10

100

1000

Graph 3

70

80

90

100

110

120

$

Graph 4


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Expenditure Patterns of Different Income Groups

Income Group$300-$400 monthly



URBAN RURAL URBAN RURAL URBAN RURAL

Value in$ ( %)

Value in$ (%)

Value in$ ( %)

Value in$ (%)

Value in$ ( %)

Value in$ (%)

FoodDrinks & tobaccoClothingHousehold goodsFuel & powerTransportServicesSundry itemsRent, etc

185 (52)18 (5)11 (3)

5 (2)14 (4)11 (3)

40 (11)39 11)34 (9)

178 (52)25 (8)23 (7)

8 (2)10 (3)18 (5)25 (7)46 (13)48 (6)

279 (40)24 (4)27 (5)

8 (1)24 (4)36 (6)74 (12)78 (13)10 (3)

229 (47)33 (7)29 (6)10 (2)13 (3)41 (8)45 (9)70 (14)20 (4)

350 (35)100 (10)

50 (5)20 (2)40 (4)60 (6)

150(15)130 (13)100 (10)

272 (34)112 (14)

48 (6)16 (2)24 (3)56 (7)96 (12)

128 (16)48 (6)

Total 357 343 595 490 1000 700

2. Which of the following statements are false? How do you know that they are false?

a. People in urban areas spend proportionally more of their income foods than do people inrural areas. This is proved by a comparison between the figures $185 and $178, $279 and$229, and $350 and $272.

b. People in rural areas evidently do not get as hungry as the people in rural areas. This isproved by the fact that they spend less on food.

c. People in urban and rural areas spend about the same proportion of their income on food.d. Since people in the $401-$600 income group spend only 47% of their income on food,

they obviously eat less than people in the $300-$400 income group who spend 52% oftheir income on food.

3. Which of the following statements are false? How do you know that they are false?

a. People in urban areas spend proportionally more of their income foods than do people inrural areas. This is proved by a comparison between the figures $185 and $178, $279and $229, and $350 and $272.

b. People in rural areas evidently do not get as hungry as the people in rural areas. This isproved by the fact that they spend less on food.

c. People in urban and rural areas spend about the same proportion of their income onfood.

d. Since people in the $401-$600 income group spend only 47% of their income on food,they obviously eat less than people in the $300-$400 income group who spend 52% oftheir income on food.

4. Using the statistics as your evidence, write accurate statements concerning the amountspent in urban and rural areas on each of these: clothing, transport, services and rent. Makeup four separate statements which compare the amount spent on each item. Then try toexplain the difference between the amounts.


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______________________________________________________________________________________________________

______________________________________________________________________________________________________

______________________________________________________________________________________________________

5. Which of these statements are correct? Give reasons for your answer.

a. It is clear that people in rural areas must be drunkards.

b. The lack of entertainment facilities in the rural areas may partly account for the loweramount spent on services.

c. The wealthier you become in an urban area, the less you spent on rent.

d. The average monthly income is higher in urban areas than in rural areas.

e. The more wealthy a family is, the smaller will be the proportion of its income spent onfood and other necessities of life.

f. Expenditures on luxuries and recreation vary directly with the average monthly income.

7. recognizing statistical slip

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