Use & Misuse of Statistics as 12.4.6 12.4.1

8/4/2019 Use & Misuse of Statistics as 12.4.6 12.4.1

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Use & MisuseUse & Misuseofof

StatisticsStatistics

A S 12.4.6; 12.4.1


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Statistics & graphs send avery powerful message topeople.

Graphs have the capability tostrengthen suggestions about

the data based on the type ofgraph, the colours used andother tools.

Just because you see a graphdoes not mean you shouldbelieve it.Examine carefully where thedata came from and what it is

telling you.


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Sources of BiasSources of BiasBias is any influence that unreasonablyaffects or sways the results of a samplesurvey or census.

This includes bad & small samples,

loaded questions, non-response bias,interviewer bias, order of questions,processing errors etc.

A survey on the effects of

passive smoking,sponsored by a majortobacco manufacturer, ishardly likely to be

impartial.

e.g

.


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Youth unemployment is over 30%;therefore 30%of S.A.s 15-19 year olds are unemployed.

Misunderstanding of definition of

unemployment as most are stillstudents.

Give possible problems with thestatistics or survey questions in thefollowing?

Too little money is being spent on welfare.

Loaded question

Would you say that traffic contributesmore orless to air pollution than industry?

Order of question putting traffic first


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Misleading GraphsMisleading GraphsGraphs can be misleading in a number ofways - scale, labels, size or missing dataetc.

There is no scale on the vertical axis. Thisperspective makes it look as though thesales for 1995 were far more than those forany other year. In fact they were identical tothose for 1997.

This 3D bar chart

looks attractive,but it is verymisleading.Why?


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What is this graphbelow trying to tell

us?

Why is the graph a poorgraph?

Puffed oats hasalmost no sugarcompared to othercereals.

No scale on axisAlthough less, it

still has a lot of

What do you now notice?


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http://mathrocks.thebernas.net/IntMath3/

Why isthis graphmisleadin

g?

It looks as if smoking is the main cause ofdeath.Also other causes are missing cancer,heart attacks, strokes, people who did not


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So to correctly interpret a graph, we

should analyze the numericalinformation given in the graphinstead of being mislead by its

general shape.

The purpose of using

graphs is usually tocompare trends or generalmagnitudes rather thanprovide precise data

points. Use a table to showprecise data points.


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Misleading numbersMisleading numbers

The proper choice of an average

statistic isnot always the mean. Medians are often

moreinformative. The problem with means is

thatthey can be easily skewed by extreme

high orlow values (outliers).

Be aware of the scale used to measurethe data.A ranking of 1 to 3 is used, where 1 =

best, to rank your drink preference.So if you prefer Coke only marginallymore than Pepsi, a ranking of 1 forCoke and 2 for Pepsi implies that you

like Coke twice as much as Pepsi.

e.g

.


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bonus for a full-time employee of theCompany

is R31,417. Use the data in the table

below todetermine if this is an accurate

statement.Annual Income (R)

25,000 18,000 32,00028,000

22,000 19,000 34,00092,00029,000 31,000 21,00026,000

The news article used the mean of thebonuses for the average annual bonus.

All but 3 of the bonuses are below thisvalue. The bonus of R92,000 has distortedthe value of the mean. A better measurefor the annual bonus would be the median,

R27,000.


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We'rewinning

cancer fightThe Weekend Australian, Saturday May 9, 1998Is there anythingmisleading aboutthe graphs?Explain.

The graphs use differentscales. It is difficult tocompare cancer

incidence rates for menand women. Also itseems as if theres agreater decrease in the

rate for the men from

Media exampleMedia example


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Source: The Mercury, 10 November, 1997

Di: 98% say it was a plotBritish Sunday newspaper The People revealedyesterday that nearly everyone who responded to

a survey organised by the paper believe Diana,Princess of Wales, was murdered. It says morethan 98 per cent of 5,600 people who rang ahotline answered "yes" to the question: "Were

Diana and Dodi killed as part of a secretoperation?" Only 93 said they believed the crashwas an accident.

It is a voluntary phone-in poll. Usuallybiased as only those with a strong viewphone in. Also the way in which thequestion was asked encouraged a "yes"response?

Why would you question the results of this

survey?


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Find three newspaper or magazine

articles that contain incorrect ormisleading analysis or presentation

of the statistics.

For each article, hand in a copy ofthe article and a short critique of theincorrect or misleading analysis or

presentation of the statistics in thearticle.

Ta

sk

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Use & Misuse of Statistics as 12.4.6 12.4.1