Uses and Misuses of Statistics
Use vs. Misuse

 Describe data
 Compare two or more
data sets
 Determine if a
relationship exists
between variables
 Test hypotheses
 Make estimates about
population
characteristics
 Sell products that don’t
work properly
 Attempt to prove
something true that is
really not true
 Grab our attention by
evoking fear, shock and
outrage
Describing Misuse

 “There are three types of lies – lies, damn lies, and
statistics”
 “Figures don’t lie, but liars figure”
Suspect Samples

 Using very small samples
“three out of four dentists recommend Crest
toothpaste”
 If only four dentists were surveyed, that could just
be chance. The result could be quite different if 100
were surveyed
Volunteer Samples

 It is important to know how the subjects were
selected
 Studies using volunteers have a built in bias because
1. Particular socioeconomic background (unemployed)
2. Spending time in another environment (college
students and retirees)
3. Generalizing results to both men and women
4. Opinion polls that require phone or mailed response
Convenience Samples

 When intact groups are used for a sample, they may
not be representative of the entire population
(classroom)
 When all customers within a certain time frame are
used for a sample, they may not be representative of
the entire population (time)
Ambiguous Averages

 There are four commonly used terms that are loosely
called averages. (mean, median, mode, and midrange)
 Depending on the data set, these can vary greatly
Changing the Subject

 Statistical distortion can occur when different values
are used to represent the same data.
 For example, a politician might say “During my
administration, expenditures increased a mere 3%”
While someone running for the same position might
say “during my opponent’s administration,
expenditures increased a whopping $6,000,000”
Detached Statistics

 A claim that used detached statistics is one in which
no comparison is made.
 For example, “our brand of crackers has one-third
fewer calories”… than what?
Implied Connections

 Many claims attempt to imply connections between
variables that may not actually exist.
 For example:
“Eating fish may help to reduce your cholesterol”
“Studies suggest that using our exercise machine will
reduce your weight”
“Taking calcium will lower blood pressure in some
people”
Misleading Graphs

Faulty Survey
Questions

 Survey questions can be phrased in ways the
influence the way people answer them
 For example: a survey question like “Do you think
the Union School District should build a new football
stadium?”
If it were phrased “Do you favor increasing
school taxes so that the Union School District can
build a new football stadium?”
So are statistics good?

 Yes, when used properly….
 It’s like a car. If you use it to get to where you need
to go, then it’s good. If you use it to run over people
you don’t like, not so good…
Biased or Unbiased?
Why?

1. Eight citizens are asked their opinions about what
trash should be collected.
2. A phone-in survey is taken by a radio station to see
how many listeners enjoy jazz in the morning.
3. Every fortieth student who enters the school is
asked to name their favorite sport.
4. Ten students are randomly selected to participate in
a survey about home computer usage.
Biased or Unbiased?
Why?

5.
Each math class randomly selects two students do
represent their class on an advisory panel being
assembled by the principal.
6.
A shirt manufacturer wants to check quality control
of their products. The plant manager decides to check
every 5th shirt inspected by Inspector D. There are 15
inspectors in the plant.
7.
A survey is conducted at the local shopping mall
about household products used on a daily basis.
For example

 http://www.youtube.com/watch?v=FP6ZP0DM1po
 http://www.politifact.com/