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					                 CO SCI 58
Asking the Right Questions
Statistics are evidence expressed as
 Often just educated guesses or estimates because of
 difficulties in collecting data
   Lack of truthfulness
   Failure to report events
   Physical barriers to observing events
Clues for Evaluating Statistics
1. How were the statistics obtained?
2. What type of calculation was used?
3. Do the statistics prove the conclusion or something
4. Compare the necessary statistical evidence with what
   is actually provided.
5. Form your own conclusion from the statistics and ask
   “Is there missing information?”
Confusing Averages
There are three different calculations that might be
 called an “average”:
Mean: Add all of the values and divide the total by the
 number of values
Median: List all of the values from highest to lowest and
 find the one in the middle
Mode: Find the value that appears most frequently
 An Average is an Average?
                        Program                      Downloads
These are the number    Panicware                     3,783,443
  of downloads of
                        Safeguard                       729,719
  popup ad window
  blocker programs      Ultimate Popup                  694,945
  from    Killer
                        Ad Smasher                      134,699

See what a difference   Pop Up and                        3,564
                        Spyware Ad blocker
  there is in the
  “averages”?           Mean                          1,069,274
                        Median                          694,945
                        Mode                 None (no repeats)
Pay close attention to the wording of the statistics and the
  wording of the conclusion to see whether they are
  referring to the same thing.

The financial problems of our public schools are highly
  overrated. In 1992-93, an average $6,100 was spent on every
  public school student in the United States. Furthermore,
  full-time public school teachers make an average $34,027
  per year according to the American Federation of Teachers.
  This salary is not at all bad, compared to the 1990 median
  income of $34,400 of families in the U. S.. It isn’t
  insufficient funding or ill-paid teachers that are killing the
  educational system; it is, instead, the lack of well-trained
  teachers thanks to grossly lax colleges of education.
The conclusion is:
The educational system is being killed by the lack of well-
  trained teachers thanks to grossly lax colleges of
Average $6,100 spent on each student 1992-1993
Teachers make average $34,027 (median of 1990 was $34,400)
 Is anything proven about the quality of teacher training?
 What kind of average is $6,100?
 A median is not a great way to compare salaries and why
  was 1990 used instead of 1992-93?
What further information do you need
before you can judge the impact of the
 Our new police chief John Neu is not doing his job. The fact
 is that Torrance is becoming a more dangerous place to
 live. According to the latest statistics, the number of
 crimes went from 1,471 to 1,537. That’s a 4.5% increase.
 During the same time period, other South Bay cities
 became safer. Manhattan Beach had 47 less crimes than
 the year before and Hawthorne had 86 fewer crimes.
What’s Missing?
This argument that the Torrance police chief isn’t
  doing his job is based on statistics about the crime
  rate. You might want to know:

1. What was the pattern for crime in previous years
   in Torrance? Maybe the current year was unusual
   for some reason.
2. How many total crimes were there in Manhattan
   Beach and Hawthorne?
3. How did other local cities compare?
4. What kind of crimes increased? Was it homicide,
   rape, assault or auto theft?
The details:

1. Torrance had extremely low crime numbers in
   2004 and 2005.
2. Manhattan Beach went from 356 in 2005 to 309 in
   2006 (-13%). Hawthorne went from 2,406 to 2,320
3. Crime in Rancho Palos Verdes increased by 13%.
   Rolling Hills increased by 75%. Lawndale
   decreased by 2.7%. Lomita was unchanged.
4. There was a spike in the number of aggravated
   assaults in Torrance in 2006. Burglary and auto
   theft rose a little. Rape and robbery decreased.
Source: Altman, Larry. “South Bay Crime Report.” Daily Breeze. Sun. 11
    March 2007. Page A1.
As Compared to….?
Another form of missing information is the lack of relevant
 Americans belief in the value of international education
 was not shaken after the Sept. 11 terrorist attacks. A recent
 poll (March 2002) showed that 77% of the public supported
 international course requirements in college.

More information about the poll at:
The Relevant Comparison
How does 77% support compare to previous years? It was
  actually the same as the April 2000 survey.
Among other things, you might also be curious about:
 Who was “the public” surveyed? Did they have college-age
 How were the survey questions worded? Would so many
  have been favorable if the students were going to the
  middle east to study?
 Who is ACE? Do they have a reason to push international
What’s Wrong with the Statistics?
Marriage drives men to drink and the problem seems to be
 getting worse. Married men are twice as likely as bachelors
 to become alcoholics, as evidenced by the fact that 66% of
 all male alcoholics are married. In addition, the problem
 has increased over the past 10 years, suggesting that
 marriage is becoming increasingly stressful to the average
 male. Statistics collected by the state of Michigan show
 that there were over 15,000 married male alcoholics in
 1998, compared with only 12,000 in 1988.
The Relevant Comparison
 Concludes that marriage causes men to become alcoholic.
  All you can really conclude is that more (two thirds) of
  alcoholics are married.
 How were people categorized as alcoholic? By asking
  them straight out?
 The statistics are misleading. Need to know:
    The percentage of married men who are alcoholic versus the
     percentage of single men who are.
    The percentage of men who were alcoholics in 1998 vs. 1988. There
     could be more men.

   End of lecture

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