Probability and Statistics “Critical Thinking”

Flawed statistics  Statistics are often misused and flawed either because of: (1) Evil intent on the part of dishonest people, or… (2) Unintentional errors on the part of people who don’t know any better

Types of errors  Misleading graphs  Biased questions  Biased (non-random) sample, such as voluntary response  Sample size too small  Mistaking correlation for causality  Allowing survey participants to “self- report”

Types of errors – Biased questions  Effect of the wording of a question: “Should the President have the line item veto to eliminate waste?” 97% yes “Should the President have the line item veto, or not?” 57% yes

Types of errors – Biased questions  Effect of the order of questions: “Would you say that traffic contributes more or less to air pollution than industry?” 45% blamed traffic; 27% blamed industry “Would you say that industry contributes more or less to air pollution than traffic?” 24% blamed traffic; 57% blamed industry

Types of errors – Small sample size  You must be sure to survey a large enough number of people to represent the population.  The more people you survey, the more accurate your results will be.  For example, if you survey 20 people in the U.S. and ask who they will be voting for there will be a + or - 20% “margin of error.” If you ask 1000 people, there will be a + or – 3% margin of error.

Types of errors – Correlation/Causality  Just because two variables seem to have an effect on each other doesn’t mean that they do.  Example – People who sleep 6 hours a night live longer than people who sleep 8 hours or more  Will simply sleeping for less time cause me to live longer or could there be another explanation?

Types of errors – Self-reporting  Suppose in a survey you ask 100 people if they wash their hands after using the bathroom and 80% say yes. Do you think that statistic is reliable? Why or why not?  Suppose you ask 100 women at random how much they weigh and their mean weight is 117 pounds. Do you think that statistic is reliable? Why or why not?

Classwork / Homework  Pages (all evens or odds)