Abuses of Statistics

Professor Kelly Jackson

Camden County College

Elements of Statistics

Beware of the term “average”

• Quantitative measure– Mean

– Mode

– Median

• Qualitative measure– Below average

• Is that bad?

– Above average• Is that good?

Think About This…

• A politician claims in a speech: “I will do whatever it takes to see that every worker in this country earns an above average wage”

• The governor states: “Our goal is to have a state where all children have above average test scores.”

Salaries for the Starting 9

• Team A50,000,00015,000,0005,000,0004,000,0003,000,0001,000,0001,000,0001,000,0001,000,000

• Team B11,000,00011,000,00010,000,00010,000,0009,000,0008,000,0008,000,0007,000,0007,000,000

Think About This…

• Consider Team A, who is telling the truth:– The owner of the team, who claims that the

average salary of a starting player is $9,000,000– The player’s union rep, who claims that the

average salary of a starting player is $3,000,000– The fan calling into “sports talk” radio, who

claims that the average salary of a starting player is $1,000,000

What is the average?

• Above average isn’t always good– A high school

principal boasts, “Our test scores are above the statewide average.”

• Statewide = 63%

• School wide = 65%

• Below average isn’t always bad– A teacher tells a

student that her test was 10 points below the class average

• Class = 90%

• Student = 80%

Percentile traps

• Percentile means what percent of the population scored below a given value– It does NOT mean the percent correct

• 70% correct could be in the 90th percentile

• 85% correct could be in the 50th percentile

– Scores are relative. We don’t know whether they are good or bad, only how they compare to one another

– The comparison “group” needs to be known to assess just what the percentile represents

The average…

• When you read or hear the word average ask yourself, “What measure is being averaged?”– Does it make sense to average this measure?

• The average woman…

• The average driver…

Which combination of scent and label color would be preferred most?

Fragrence

0 10 20 30 40

Floral

Herbal

Spice

Lemon

Numberof Teens

So what do you want for lunch?

Sandwich Type

0 10 20 30 40

Burger

Tuna

HotDog

Turkey

Numberof Teens

Condiment

0 10 20 30 40

Ketchup

Mustard

Mayo

Relish

RelishMayoMustardKetchup

Beware…

• Means are sensitive to outliers

• Medians are NOT sensitive to outliers

• Modes can not be combined

• Measures of center are not the only information about data that are important

There is more to statistics than just the average for a group

• A key concept is dispersion– What is the range of scores?– Where are the score clustered?

• Near the mean

• Near the endpoints

• Is the distribution uniform, bell shaped, skewed

Think about this…

• Look back at the two baseball teams described before.– If you are a great player, which team is the one

you would want to play for?– If you are an “OK” player, which team do you

want to play for?

• Why??

Salaries for the Starting 9

• Team A50,000,00015,000,0005,000,0004,000,0003,000,0001,000,0001,000,0001,000,0001,000,000

• Team B11,000,00011,000,00010,000,00010,000,0009,000,0008,000,0008,000,0007,000,0007,000,000

Importance of the range…

• Check for outliers• Check for low, high, and median scores

• Think about this…– You are thinking about taking one of two teachers for

chemistry. Both have a class average of 83. Ms. Smith has a range of grades from 50 – 100, Ms. Jackson has a range of grades from 75-88. Who should a good student take? Who should a poor student take?

How is the data dispersed

• Two 20 year old, college students are planning a trip for spring break. They want to meet women their own age. They call two hotels to find out the average age of the female patrons. The No-tell Motel has an average age of 21. The Sleep Inn has an average age of 30. Where do you think they will go, if they use average age as the determining factor?

Sampling Issues

• How many members are in the sample?– Too many?– Too few? (4 out of 5 dentists surveyed…)

• How representative is the sample– Who does it represent?– How can the results be generalized

• Is the sample biased?

Representative Samples

• Representative samples have the same characteristics as the population from which they are drawn

• Look at the composition of the sample to determine what population it represents

Think about this…

• 500 customers are randomly selected from the Camden County phone book. Each customer is called and asked “How many phones are in your home?” This information is used to make the claim “On average a Camden County resident has ___ phones in their home.

• Is there a problem with the sampling method used above?

Sampling issues

• Surveys– Who, what when, where, why?

• Direct vs Indirect measurement

• Definition of terms

Who, what, when, where, why

• Who did the survey? Who was surveyed?– Do they have an agenda?

• What is the question being asked?– Will people tend to answer honestly?

• When was the survey completed?– Will topic sensitivity or timing be an issue?

• Where was the survey conducted?– Will this color people’s responses?

• How was the survey conducted?– Mail, telephone, door to door, etc.

Think about this…

Source: Florida Citrus Growers Association

Any Problems With This Graph?

Direct versus Indirect

• Direct measures are always preferable to indirect measures– Determine the average weight of member of

the women’s basketball team• Indirect: ask each woman how much she weighs

• Direct: each woman steps on a scale and gets weighed

Think about this…

• When we want to weigh someone, we can put them on a scale. To take their temperature we stick a thermometer in their mouth. To measure their height, we can use a tape measure. How would you directly measure someone’s intelligence? Their self esteem?

Watch the wording

• Are the words or phrases regional?– Hoagie, sub, hero, grinder

• Do words mean the same thing to everyone?– Have you ever been the victim of sexual harassment?

• Is it absolutely clear how to distinguish between categories– Do you go to the movies frequently, sometimes,

rarely, or never?• One person’s “sometimes” is another person’s “frequently”

Think about this

• A group of Texas School teachers took a history test and failed with an average grade of 60.– Should we conclude that Texas school

teachers are deficient in history?– What questions do you have about the

statement above?

No zero starting point

• Looking at the bars, Chevy seems to outperform Toyota by about 2-1. Looking at the scale, Chevy is about 2% above Toyota.

9595.5

9696.5

9797.5

9898.5

9999.5100

Ch

evy

Ford

Toyota

Nissan

% on theroad

Think about this…

600

610

620

630

640

650

660

670

680

Male Female

Earnings

050

100150200250300350400450500550600650700

Male Female

Earnings

How does the message differ from graph to graph?

Pictographs

If you double the height and width of a picture, its area is 4 times bigger. (For 3-dimensional objects doubling all dimensions makes the object 8 times larger.)

Point of view matters

Beware of accuracy levels

• Is the information too accurate?– Look for decimal places

• Is the information too round?– Look for zeros

• Rounding is sometimes disguised– Is the following too accurate or too round?

• 760.67 million marijuana cigarettes

were smoked in the US last year

Too accurate!

• According to Mary Kay (regarding her Triple Action Eye Enhancer)– On average, after six weeks of regular use in

the crows feet area, research showed: • 23% reduction in fine lines

• 27% increase in firmness

• 23% increase in moisturization

Think about this…

• “There are 86,400 seconds in a day, fortunately Tidy Cat is at work every single one of them.”

• “A normal adult takes about 14,400 breaths each day. Fortunately, Tidy Cat is at work every single one of them.”

Compare the claims in the two ads. What is the difference between the 86400 used on the left and the 14400 used on the right?

Beware of cause and effect claims

• It is often times impossible to tell which is the cause and which is the effect.

• Just because one thing happened before the other, doesn’t mean it caused it to happen.– Often times, just before a plane experiences turbulence,

the “fasten seatbelts” sign comes on. Does putting on the sign cause the turbulence?

• Don’t confuse correlation with causation– Since the time that tobacco was introduced, life

expectancy has doubled, therefore smoking is good for your health.

Think about this…

• The number of ice cream Popsicles sold at the beach is highly related to the number of drownings (A lot of pops a lot of drownings). Does eating Popsicles cause people to drown?

• The cities that have the most churches also have the most bars. Does going to church drive people to drink?

Think about this…

• The per capita amount of milk consumed is moderately correlated to a country’s reported cancer cases. Meaning the more milk drunk, the more cancer reported. Should we be concerned that milk causes cancer?