SHENANIGANS:

1. SHENANIGANS: When Statistics Go Wrong NMH Upward Bound Summer Academy 2014

2. “There are three kinds of lies: lies, damned lies, and statistics.” –Statesman Benjamin Disraeli • Statistics is not just about the calculations. It is about analyzing and interpreting data. You need to be able to answer the question, What does this data mean? • And on the other hand, you need to be able to recognize data that is being misused, misinterpreted, or misconstrued. • You can also avoid this if you do any of your own surveys! Maybe…

3. BAD SAMPLES • Recap: A selection of some members of a population used to make inferences about the whole population. • A Sample can be biased, which means “not representative of the population from which it has been obtained.” • How? • The sample was a voluntary response sample • Internet surveys • Very small samples (small n studies) • Republicans of Pocatello, ID

4. BAD GRAPHS • Sometimes, graphs published to convince their interpreters of a point are purposefully constructed to make the situation look better or worse than it actually is – distortion of reality

5. BAD PICTOGRAMS • Some objects commonly used to depict data include three-dimensional object such as moneybags, stacks of coins, army tanks (for military expenditures), barrels (for oil production), and houses (for home construction). • When drawing such objects, one can create false impressions that distort differences.

6. BAD PERCENTAGES • Misleading or unclear percentages are sometimes used in Statistics. • If you are taking 100% of some quantity, you are taking it ALL. • Continental Airlines versus the New York Times • “We had a 100% increase in rainfall this year compared to last year” • Know how to do percent calculations! • Percentage of an amount • Fraction  Percentage • Decimal  Percentage • Decimal  Percentage

7. BAD (or LOADED) QUESTIONS • Questions that are intentionally worded to elicit a desired response • National Election Survey 2004: • “Should the president have the line-item veto to eliminate government waste?” 97% responded ‘yes’ • “Should the president have the line-item veto or not?” 57% responded yes • The gun example

8. ORDER OF QUESTIONS • Questions that are (usually unintentionally) loaded by such factors as the order of the items being considered. • From a poll conducted in Germany: • Would you say that traffic contributes more or less to air pollution than industry? • Would you say that industry contributed more or less to air pollution than traffic? • For the first question, 45% blamed traffic and 27% blamed industry. • For the second question, 24% blamed traffic and 57% blamed industry.

9. SELF-INTEREST STUDY • Studies are sometimes sponsored by parties with interests to promote. • Kiwi Brands, a shoe polish manufacturer, printed in some newspapers: “According to a nationwide survey of 250 hiring professionals, scuffed shoes was the most common reason for a male job seeker’s failure to make a good first impression.” • Be wary of situations where the sponsor can enjoy monetary gain from convincing people that their statistics are true • Doctors and pharmaceutical companies

10. PRECISE NUMBERS • Numbers can be really precise but not accurate! • “There are now 103,215,027 households in the United States.” • What if a new household started in the last 30 seconds? That number is not accurate! • Precision versus accuracy Precise but not accurate Accurate but not precise Accurate and precise

11. PARTIAL PICTURES • A statistic may not always show you the whole “picture” of a situation. • In 2003 a car company published the commercial message that said “90% of all our cars sold in this country in the last ten years are still on the road.” What they didn’t mention was that 90% of the cars sold by that company in the last ten years were sold in the last three years, so most of the cars on the road were quite new.

12. PRACTICE FOR HOMEWORK • Use critical thinking to develop an alternative conclusion: • A study showed that homeowners tend to live longer than those who do not live in their own homes. Conclusion: Owning a home creates inner peace and harmony that causes people to be in better health and live longer. • In a study of cold symptoms, every one of the study subjects with a cold was found to be improved two weeks after taking ginger pills. Conclusion: ginger pills cure colds. 2. After the 2000 national census, the Poughkeepsie journal ran this front-page headline: “281,421,906 in America.” What’s wrong with this headline? 3. a) What is 26% of 950? b) Convert 5% to an equivalent decimal. c) Convert 0.01 to an equivalent percentage. d) Convert the fraction 527/1200 to an equivalent percentage. Express the answer in the nearest tenth of a percent.