Transcript Misuse of Statistics - Lynn Public Schools

Probability & Statistics
Misuse of Statistics
Misuse of Statistics
Although statistics can be used as a
valuable tool to study many different
aspects of the world we live in, be careful.
Many individuals, businesses, and
advertising firms misuse statistics to their
own advantage.
Misuse of Statistics
When examining statistical information, consider
the following:
•
Was the sample used to gather the statistical
data unbiased and of sufficient size?
•
Is the statistical statement ambiguous, could
it be interpreted in more than one way?
Misuse of Statistics
Example: Misleading Statistics
An advertisement says, “Fly Speedway Airlines and
Save 20%”.
•
•
Here there is not enough information given.
The “Save 20%” could be off the original ticket
price, the ticket price when you buy two tickets or of
another airline’s ticket price.
Misuse of Statistics
Example: Misleading Statistics
A help wanted ad read,” Salesperson wanted for Ryan’s
Furniture Store. Average Salary: $32,000.”
•
•
The word “average” can be very misleading.
If most of the salespeople earn $20,000 to $25,000
and the owner earns $76,000, this “average salary”
is not a fair representation.
Misuse of Statistics
Graphs can also be misleading, consider the
following situation:
We never really know what goes on behind closed doors
regarding trades in professional sports.
One (fairly unreliable) source reported that there were
secret trade talks that took place between the Boston
Celtics and the Los Angeles Lakers after the 2009-10
basketball season.
The value of Celtics' guard, Paul Pierce was the topic at
hand.
Misuse of Statistics
Los Angeles Lakers General Manager:
Excerpt from the report sent to the Boston Celtics.
“Paul Pierce is not worth much in a trade. His numbers
are decreasing quickly and he will soon not be worth any
salary.”
Misuse of Statistics
Boston Celtics General Manager:
Excerpt from the report sent to the Los Angeles Lakers.
“Paul Pierce has consistently been one of the top players
in the league and his numbers show that he will
continue to be a big money player.”
Misuse of Statistics
Both graphs of Paul Pierce's stats (from the
previous two slides) were based on exactly the
same numbers.
Neither of the General Managers lied about the
stats and both graphs were completely accurate.
Misuse of Statistics
The difference between the two graphs is simply the
scales used.
The Lakers used a scale of 2 on the y-axis (average
points per game) and put the data on a broken graph
starting with 18 points and going up to 28 points (a
range of 10 points)
The Celtics used a scale of 10 on the y-axis and showed
point averages from 0 to 50 points per game (a range of
50 points).
Does one of the graphs violate the area principle?
Misuse of Statistics
The difference between the two graphs is simply the
scales used.
This broken graph does not start at
zero and uses a scale of 2 on the
frequency axis
This graph starts at zero and uses a
scale of 10 on the frequency axis.
Does one of the graphs violate the area principle?
Misuse of Statistics
Charts and Graphs
Charts and graphs can also be misleading.
•
Even though the data is displayed correctly,
adjusting the vertical scale of a graph can
give a different impression.
•
A circle graph can be misleading if the sum of
the parts of the graphs does not add up to
100%.
Misuse of Statistics
Here’s another example of misleading graphs:
While each graph presents identical information,
the vertical scales have been altered.
Which graph makes Stock A look better?
Misuse of Statistics
In general, individuals, businesses, and advertising agencies will
misuse statistics to make themselves, their products, or their
clients appear to be better than others.
For a graph to show data to look like there
has been significant change:
* Usually a
broken graph
Use a small scale and a small range.
For a graph to show data to look like there
has been very little change:
Use a large scale and a large range.
Misuse of Statistics
Example: The following chart shows the percent of the U.S.
population that was age 65 and over for the years 1970, 1980,
1990, 2000, and 2010, where the column labeled year refers to the
number of years since 1970.
A. Create a graph that would make it
look like the population of elderly U.S.
residents has remained stable over the
past 40 years.
B. Create a graph that would make it
look like the population of elderly U.S.
residents has shown significant increase
in the past 40 years.