8
Introduction
Questions To Ask of Statistics
5 Statistical Concepts


Polls and surveys are simply attempts to discover what
people think about a given topic.
These have limited value at the best of times.
• The most we can hope for is an accurate “snapshot” of how a
particular population feels at a given moment.
• They sometimes have predictive value for elections.
• They are occasionally useful for determining civil, provincial
and federal legislation.

While useful in a limited sense, in common use they are
virtually useless


Surveys of the scientific community can tell us what the majority of scientists think
about a subject.
• Caveats:
 This doesn’t mean that they’re right. Virtually every scientific theory has been
accepted by a majority before it’s overturned. Bear in mind that one of the big
arguments against Copernicus’ theory that the Earth revolved around the sun
was the fact that virtually every scientist of the time believed otherwise.
 To be truly representative, the survey should only involve experts in the field
under discussion. You don’t ask physicists to give their opinion about the
homeless issue or psychologists to discuss safe radiation levels. And as for
what celebrities and sports figure think about anything – who cares?
Surveys can help politicians decide what the public considers the most important
social issues and what they want done about it.
• Caveats:
 Just because a majority of the population believes something is important
doesn’t necessarily mean it is. As a result, many millions of dollars can be
spent “solving” issues that make little practical difference to the well-being of
society.
 Politicians are often in the position of making a particular social issue seem
more relevant than it is by bringing it to the attention of the press. As a result,
the general population can come to believe that a crisis exists when none
does, an example of this being marijuana.




Anecdotal evidence may indicate something that
should be looked at further, but it is not, itself,
evidence.
This comes up often when talking about gender
differences. For instance, a survey may indicate that a
vast majority of women enjoy shopping. Upon reading
this, some woman is bound to exclaim, “That’s not true!
I’m a woman and I hate shopping!”
This, however, does not disprove the survey any more
than the fact that I hate sports somehow disproves the
assertion that most men like sports.
Surveys and other statistics must be disproved from the
same level that they have been created:
• Showing that the study was flawed
• Showing that the interpretation was flawed
• Producing a similar study that contradicts the data
 It
is often said that “statistics can prove
anything.” This is not true of good
statistics, but most of what we see cannot
be called “good.”
 And even good statistics can have their
problems, especially in interpretation.



Tom Smith, director of the General Social Survey at the University of Chicago's National
Opinion Research Center.
• "All studies are possibly wrong, whether they're surveys, clinical trials, or
whatever."
David Murray, director of the Washington, D.C.-based Statistical Assessment Service.
• “The tide of bad statistics is rising. It's everywhere now. In politics. In polling. The
interpretation of public reaction. Physical sciences. It's the way you win arguments.
The way you make points. … It's like flying when it's really foggy and you tend to rely
on instruments rather than looking out the window. It's great, unless the radar is on
the fritz. Social scientists are captivated by the radar screen. They don't look out the
window anymore."
Joel Best, professor of sociology and criminal justice at the University of Delaware and
author of "Damned Lies and Statistics" (University of California Press, 2001)
• Most bad statistics are less the result of deliberate deception than incompetence,
confusion or self-serving selection of numbers that reaffirm one's beliefs.
• “A definition is everything. … Some studies have found 90% of workers are bullied in
the workplace. Others show 90% of students are bullied in schools. If you define
bully broadly enough as people being mean to you, it's amazing 10% of the
population has not been bullied."
• “Recently … scientists -- under increasing pressure to produce newsworthy results -have started marketing their results to the general public, bypassing the traditional
safeguards provided by peer reviewed journals. That's how you make your own work
more visible. That's how you get that next grant … Part of what's going on is we as a
society have an appreciation for science, and there's the sense we ought to get the
facts about one thing or another. … Activists have learned to package their claims as
facts by including numbers.”

Often statistics are nothing more than pure guesses. Joel Best
quotes Mitch Snyder, the activist for the homeless, who said
his estimate of 2-3 million homeless people was based on
getting on the phone and talking to a lot of people. Such
guesses are problematic both because activists tend to guess
high and because, once reported, the numbers take on a life
of their own. Best says:
• People lose track of the estimate's original source, but they
assume the number must be correct because it appears
everywhere -- in news reports, politicians' speeches, articles in
scholarly journals and law reviews, and so on. Over time, as
people repeat the number, they may begin to change its meaning,
embellish the statistic. . . After a newsmagazine story reported
"researchers suggest that up to 200,000 people exhibit a stalker's
traits," other news reports picked up the "suggested" figure and
confidently repeated that there were 200,000 people being
stalked.
 In
1985, the gay newspaper, The
Washington Blade reported that “as many
as 3,000 gay youths kill themselves a
year.”
 This is a pretty good trick, considering
only about 2,000 youth commit suicide
per year.


An Ad Age article on time-shifted viewing stated: “40 percent of TV
viewing is now being done via some sort of time-shifting, a much
larger percentage than had previously been thought.”
This statistic comes from a Nelson Media Research study which
says, “40% of broadcast viewing in households with DVRs is
time shifted.”
• Cable viewing wasn’t part of the study.
• Only homes with DVRs were counted. But according to a May 2006
study, only 11.2% of households had a DVR.


So what the NMR study really shows is that 40% of the TV viewing
in 11.2% of homes happens on a time-shifted basis.
That’s 4.48% of the total households
From Bad statistics make me so confused… December 12, 2006


A study from the University of Pennsylvania Medical Center,
published in the May 13, 1999 issue of Nature magazine, found that
young children who sleep with the light on are much more likely to
develop myopia in later life.
A later study at Ohio State University did not find any link between
infants sleeping with the light on and developing myopia.
However, they did find something else:
• There was a strong link between parental myopia and the
development of child myopia, and …
• Myopic parents were more likely to leave a light on in their
children's bedroom.
From “Correlation does not imply causation,” Wikipedia.

Trauma counseling has been given a huge boost since the Oklahoma bombing, the
Columbine shootings, and the World Trade Center attacks. Without such counseling,
we’ve been told, the mental damage can be “widespread and devastating.”
• Professor Yvonne McEwan, advisor to the U.S. government after the Oklahoma City
bombing, said the booming profession [psychology] was at best useless and at worst
highly destructive to victims seeking help: “Professional counseling is largely a
waste of time and does more to boost the ego of the counselor than to help the
victim….” “The rights of the victims are being sacrificed to keep counselors in jobs.”
• In 1996, a team of psychiatrists at Whitechurch hospital in Cardiff, Wales, who
monitored the recoveries of 110 burn victims, found, “Victims who are made to talk
about the pain and shock of their accidents are three times more likely to suffer longterm problems than those who receive no counseling.”
• A Boston study on the long-term effects of aviation crash survivors found that “The
psychological well-being of airplane crash survivors compared to air travelers who
have never been involved in any type of aviation accident or crash was much better
on all the levels measured. The crash survivors scored lower…on emotional distress
than the flyers who hadn’t been in an accident...Among the survivors who did not
want or need counseling immediately following the crash, many appeared to be the
least troubled by the crash experience and reported the least amount of distress
among the survivors.”
• An editorial in the October 2000, British Medical Journal noted several studies
showing that Debriefing Psychology methods don’t help and, in fact, may harm.
Justin Kenardy, an associate professor in clinical psychology, cited studies that
questioned the validity and workability of psychological trauma counseling.





According to the American Census Bureau, the percentage of people ages 18 to 34 who
live at home with their family increased from 12.5 million to 18.6 million since 1970, a
jump of 48%.
This statistic has been reported regularly along with articles and editorials bemoaning
the number of people refusing to go out and get places of their own.
There’s even a movie about it called Failure to Launch.
However:
• In 1970, the U.S. Census Bureau reports there were approximately 204 million
Americans.
• In 2006, the estimate is approximately 297 million Americans.
• That’s an approximate 32% increase in population.
• This means there has only been been a 16% increase in the number of people
between the ages of 18 to 34 living at home.
Not so dramatic. But along with this, we must also consider the background situation.
• In 1970 the United States was in the middle of the Vietnam War, which meant a great
many men between the ages of 18-34 were not living at home because they were in
the army.
• As a result, the 1970 numbers may have been artificially lower than they otherwise
would have been.
 Consider
a report by three environmentalist
authors back in 1988 in Journal of the
American Medical Association (JAMA),
analyzing male-female birth ratios between
1970 and 1990. The authors found male
births declining, and blamed man-made
chemicals. Yet public data going back to
1940 showed gender ratios are always
changing, for no obvious reason. Years that
disproved their thesis were simply sliced
out.
[Fumento Science Journals]

Canada's Obesity Problem Could Lower Children's Life Expectancy
March 28, 2007 11:40 a.m. EST
Danielle Godard - All Headline News Staff WriterOttawa, ON (AHN) –
A House of Commons committee on health made the shocking revelation Tuesday that Canada's
children will likely die sooner than their parents due to childhood obesity, while smoking and
drinking deaths have now been outranked by obesity as the number-one Canadian killer.
Committee chair Rob Merrifield said he was shocked by the study, which said 26 per cent of
Canadians between the ages of two and 17 are overweight or obese.
In 1978, overweight children only accounted for 15 per cent.
Smoking and drinking deaths have now been outranked by obesity as the number-one Canadian
killer.
Overall, the report found the proportion of children aged 2-5 who were overweight or obese
has stayed virtually the same from 1978 to 2004. However, the proportion of overweight
children aged 6-11 doubled while the rate was up 14 per cent to 29 per cent for children
aged 12-17.
AHN Media Corp, March 28, 2007

Toronto Sun, March 28, 2007. “Battle with blubber.”
•
The situtation has reached epidemic proportions as obesity rates among children have risen
almost threefold between 1978 and 2004.


Let’s do some math.
From the AHN Media Corp. story:
Committee chair Rob Merrifield said he was shocked by the study, which said 26 per cent of
Canadians between the ages of two and 17 are overweight or obese.
In 1978, overweight children only accounted for 15 per cent.

Using the percent change formula: Subtract old value from new value and divide by
new value, multiply by 100.
•
•
•
•

1978: 15% of children overweight
2007: 26% of children overweight
((26-15)/15)X100 = 73.333
That’ s a 73% increase.
From the Toronto Sun story:
The situation has reached epidemic proportions as obesity rates among children have risen
almost threefold between 1978 and 2004.
• A “threefold” increase would be 200%
• Where is the discrepancy coming from?
 Some
more analysis:
Overall, the report found the proportion of
children aged 2-5 who were overweight or
obese has stayed virtually the same from 1978 to
2004. However, the proportion of overweight
children aged 6-11 doubled while the rate was
up 14 per cent to 29 per cent for children aged
12-17.
 Ages 6-11 increased by 100%
 Ages 12-17 increased by 29%
 What happened to the other 79%?
“Obesity Scandal,” Health Care News, May 1, 2005






In March 2004, Tommy Thompson, then Secretary of the U.S. Department of Health and
Human Services, joined representatives of the Centers for Disease Control (CDC) and
National Institutes of Health at a joint news conference warning, "Americans need to
understand that overweight and obesity are literally killing us."
At the news conference, the CDC released a study concluding obesity is now the second
leading cause, behind tobacco, of preventable, premature death in America. The report
attributed some 400,000 deaths per year to obesity.
Almost immediately, the study came under heavy criticism. The May 2004 issue of Science
magazine fired the first volley, reporting that CDC scientists who had cast doubt upon the
reliability of the 400,000 figure (one called it "loosey-goosey") were ignored.
"I am worried that the scientific credibility of CDC likely could be damaged by the
manner in which this paper and valid, credible, and repeated scientific questions about
its methodology have been handled," Terry Pechacek, associate director for science in
the CDC's Office on Smoking and Health, told the Wall Street Journal last year.
"I would never clear this paper if I had been given the opportunity to provide a formal
review," said Pechacek.
The Journal conducted its own review of CDC documents and reported in November 2004 that
the 400,000 figure was inflated by approximately 20 percent because of a statistical error.
“Obesity Scandal,” Health Care News, May 1, 2005




About those definitions…
Beginning in 1942, the Metropolitan Life Insurance Company developed height and
weight tables for its insureds, taking into account gender and frame size. The
tables, widely used to identify "desirable" body weight, were revised upwards
in 1959 and 1983.
The federal government adopted the BMI in the 1990s as a guideline to help
doctors determine when to address medically their patients' overweight or obese
status. Initially, the BMI tables used by the federal government labeled men as
overweight if they scored 28 or above, and women at 27 and above. In 1998,
the National Institutes of Health lowered the overweight score to 25 for both
men and women.
Under the 1999 Metropolitan Life tables, a 5'3" woman with a large frame and a
weight of 151 pounds was not considered overweight. Under the revised BMI,
however, she has a BMI score of 27, solidly in the overweight column.
“Obesity Scandal,” Health Care News, May 1, 2005





This decision [to redefine “overweight” and “obese”] was made by a National
Institutes of Health obesity panel chaired by Xavier Pi-Sunyer, one of the most
influential obesity researchers in the country.
Over the years, Pi-Sunyer has received support from virtually every leading
weight-loss company, including Novartis, Sanofi-Aventis, Ortho-McNeil, WyethAyerst, Knoll, Weight Watchers, and Roche. He has served on the advisory boards of
Wyeth-Ayerst, Knoll, Abbott, Johnson & Johnson, and McNeil Nutritionals.
He once headed up the Weight Watchers Foundation and is currently a board
member of that organization.
Pi-Sunyer gave the "obesity overview" presentation on behalf of Knoll, maker
of the weight-loss drug Meridia, at a 1996 FDA advisory panel hearing on the
drug.
He has also been paid to sign his name to ghost-written journal articles used
to promote the dangerous weight-loss combination known as "fen-phen."
“Obesity Scandal,” Health Care News, May 1, 2005


Who Was Behind the Redefinition of "Obese"
Case Western Reserve University professor Paul Ernsberger describes
how financially conflicted researchers control the government’s
pronouncements on obesity:
• "Medical beliefs about obesity are shaped by expert panels that are highly
selective in the data they consider. Experts included on government consensus
panels have been disproportionately drawn from the ranks of diet clinic
directors, which might explain the congruence between panel
recommendations and the economic interests of the diet industry. In short,
economic factors encourage a systematic exaggeration of the health risks
of obesity."
• Many of America’s most influential obesity experts receive significant
financial support from the $46 billion weight-loss industry. These experts
help drive obesity hype by churning out a steady stream of studies, alarmist
public pronouncements, and treatment guidelines.
“Obesity Scandal,” Health Care News, May 1, 2005
Obese
Obese
Obese
Overweig
ht
Overweigh
t
 When
doing his thesis in 1995, a graduate
student grabbed media attention with his
statistics that the number of children killed by
gunfire had doubled each year since 1950.
 This statistic was picked up an re-printed in
various publications.
 Following is a chart showing what these figures
would mean.
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
2
4
8
16
32
64
128
256
512
1024
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
2,048
4,096
8,192
16,384
32,768
65,536
65.536
131,072
262,144
524,288
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1.049 mil
2.097 mil
4.2 mil
8.4 mil
16.8 mil
33.5 mil
67.1 mil
134.2 mil
268.4 mil1
536.9 mil
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1.1 bil
2.2 bil
4.3 bil
8.6 bil 2
17.2 bil
34.4 bil
68.7 bil
137.4 bil
274.9 bil
549.8 bil
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
1.1 tril
2.2 tril
4.4 tril
8.8 tril
17.6 tril
35.2 tril
1.
Larger than the population of the United States in that year.
2.
Larger than the population of the entire world.
 The
student had misread a 1994 report by the
Children's Defense Fund that found the number
of American children killed each year by guns
had doubled since 1950 – not doubled every
year since 1950. In other words, it had
increased 100%, not 17.6 trillion %.
 Even this statistic isn’t as alarming as it might
appear at first since the population has
increased 73% since 1950, meaning that in 44
years there has been a 27% increase in the
number of children killed by guns – not 100%
Where did the data come from?
Have the data been peer-reviewed?
3.
How were the data collected?
4.
Are the comparisons appropriate?
5.
Are the numbers in context?
6.
Are the definitions valid?
Has there been a change in circumstance?
8.
Are the questions neutral?
1.
2.
7.
A
study, and a report about a study are not the
same thing.
 If it is a report, does it cite the original study so
you can find it? Best of all is when a web site
links directly to the orignal study.
 A study may say something very different from
what the report on the study is claiming.
 This discrepancy is often the result of conscious
manipulation, but it is also commonly the result
of poor and lazy reporting.
You always want to know who did the research that created the data you're going to
write about.
If the person or publication can’t (or won’t) tell you where the data comes from, that
should be your first hint that you need to be very skeptical about what you are being
told.
Even if your data have an identifiable source, remember that many organizations
produce their own data in order to promote their own agendas. You’ll want to know if
this possibility exists in order to watch for it.
Just because a report comes from a group with a vested interest in its results doesn't
guarantee the report is a sham. Sometimes, because they have more expertise on the
subject they can bring a more sophisticated understanding to the research. But you should
always be extra skeptical when looking at research generated by people with a
political agenda. At the least, they have plenty of incentive NOT to tell you about data
they found that contradict their organization's position.
Some, perhaps most, data produced for public consumption is collected by amateurs
– even when done by large organizations. Newspaper polls, for instance, don’t tell you what
the population at large believes about a particular subject – merely what its readers
believe (and at that, only those readers who responded, which may over-represent a
particular side of the debate).





•
For instance: Readers’ polls on gun control conducted by The Star and The Sun would likely
produce widely divergent results. In both cases there would be no question of anyone “fudging”
the figures – it’s just that the groups reading the two papers have very different views from each
other.
Statistics Every Writer Should Know, by Robert Niles
See also: The Good, the Bad, and the Ugly of Public Opinion Polls, Russell D. Renka, Professor of Political Science, Southeast Missouri State University



Have the data been peer-reviewed? Major studies that appear
in journals like the New England Journal of Medicine undergo a
process called "peer review" before they are published. That
means that professionals - doctors, statisticians, etc. - have
looked at the study before it was published and concluded
that the study's authors pretty much followed the rules of
good scientific research and didn't torture their data to
make the numbers conform to their conclusions.
Always ask if research was formally peer reviewed. If it was, you
know that the data you'll be looking at are at least minimally
reliable.
And if it wasn't peer-reviewed, ask why. It may be that the
research just wasn't interesting to enough people to warrant
peer review. Or it could mean that the authors of the research
knew it couldn’t stand up to such scrutiny.
Statistics Every Writer Should Know, by Robert Niles





This one is very important, especially if the data were not peer-reviewed. If the
data come from a survey, for example, you want to know that the people who
responded to the survey were selected at random and weren’t part of one
particular group (unless that group is what the survey was about).
In 1997, the Orlando Sentinel released the results of a call-in poll in which more
than 90 percent of those people who responded said that Orlando's NBA team,
the Orlando Magic, shouldn't re-sign its center, Shaquille O'Neal, for the amount
of money he was asking. The results of that poll were widely reported as
evidence that Shaq wasn't wanted in Orlando, and in fact, O'Neal signed with the
Los Angeles Lakers a few days later.
This is what statisticians call a "self-selected sample." For all we know, two or
three people who got laid off that morning and were ticked off at the idea of
someone earning $100 million to play basketball could have flooded the
Sentinel's phone lines, making it appear as though the people of Orlando
despised Shaq.
Another problem with data is "cherry-picking." For example, in epidemiological
studies (which means no new data was collected, old data was simply examined
in a different way) looking at illnesses in areas surrounding toxic-waste dumps,
power lines, high school cafeterias, etc. it is all too easy for a lazy researcher to
draw the boundaries of the area he or she is looking at to include several extra
cases of the illness in question and exclude many healthy individuals in the
same area.
When in doubt, plot the subjects of a study on map and look for yourself to see if
the boundaries make sense.
Statistics Every Writer Should Know, by Robert Niles
Actual data points collected showing distribution
of particular substance over time in parts per
million.
Zbigniew Jaworowski, M.D., Ph.D., D.Sc.,(Chairman, Scientific Council of Central Laboratory for Radiological Protection ) March 2007
Circled areas show data points chosen to prove
thesis of researcher – that the substance has
increased over the years.
Statistics Every Writer Should Know, by Robert Niles






Researchers like to do something called a "regression," a process that
compares one thing to another to see if they are statistically related. They will
call such a relationship a "correlation." Always remember that a correlation
DOES NOT mean causation.
A study might find that an increase in the local birth rate was correlated with the
annual migration of storks over the town. This does not mean that the storks
brought the babies. Or that the babies brought the storks.
Statisticians call this sort of thing a "spurious correlation," which is a fancy term
for "total coincidence."
People who want something from others often use regression studies to try to
support their cause. They'll say something along the lines of "a study shows that
a new police policy that we want led to a 20 percent drop in crime over a 10year period in (some city)."
That might be true, but the drop in crime could be due to something other than
that new policy. What if, say, the average age of those cities' residents increased
significantly over that 10 year period? Since crime is believed to be agedependent (meaning the more young men you have in an area, the more crime
you have), the aging of the population could potentially be the cause of the drop
in crime.
The policy change and the drop in crime might have been correlated. But that
does not mean that one caused the other.
Statistics Every Writer Should Know, by Robert Niles
Be aware of numbers taken out of context. Again, data that are
"cherry picked" to look interesting might mean something else
entirely once it is placed in a different context.
Consider the following example from Eric Meyer, a professional
reporter now working at the University of Illinois:


•
•
•
•
•
When working on a Milwaukee paper he would call the sheriff’s department
whenever it snowed heavily and ask how many fender-benders there had
been.
Inevitably, we'd have a lede that said something like,’A fierce winter storm
dumped 8 inches of snow on Milwaukee, snarled rush-hour traffic and
caused 28 fender-benders on county freeways.”
One day Eric called the sheriff's department to ask how many fenderbenders were reported on clear, sunny days.
The answer was 48.
Eric comments: “[It] made me wonder whether in the future we'd run stories
saying, ‘A fierce winter snowstorm prevented 20 fender-benders on county
freeways today.’ There may or may not have been more accidents per mile
traveled in the snow, but clearly there were fewer accidents when it snowed
than when it did not.”
Statistics Every Writer Should Know, by Robert Niles
As Joel Best said earlier, ““A definition is everything.”
Homeless statistics are notoriously difficult for
several reasons.


•
•

One of which being that it is intrinsically difficult to count
people with no fixed address.
Another being that there is no set definition of “homeless.” Is
someone homeless who stays with a friend?
Another problem arises when definitions change. A
definition doesn’t have to be perfect to give us
meaningful statistics, but it must be consistent from
one study to the next.



As we saw with the statistics about grown-up stay-athome children, the circumstances in 1970 could well
have produced below average numbers.
In the late 1970s in Toronto there was a 300%
increase in prostitution arrests. This wasn’t the result
of an influx of prostitutes, but of a change in the law
concerning prostitution.
The ability and willingness to report various crimes
can result in an artificial increase in statistics. A
dramatic increase in child-abuse statistics between
1950 and 2007 doesn’t necessarily mean there’s more
child-abuse – merely that more children (and
peripheral adults) are willing to report it.
The answers to surveys can often be manipulated by wording
the question in such a way as to induce a prevalence towards a
certain answer from the respondent. Consider these two
questions, both asking about support for the war:

•
•
Do you support the attempt by the United States to bring freedom
and democracy to other places in the world?
Do you support the unprovoked military action by the United
States?
Another way to do this is to precede the question by
information that supports the "desired" answer.

•
•
"Given the increasing burden of taxes on middle-class families, do
you support cuts in income tax?"
"Considering the rising federal budget deficit and the desperate
need for more revenue, do you support cuts in income tax?"
Bad Statistics: USA Today, by John M. Grohol, Psy.D. March 16, 2006
The Mean
 The Median
 Percent Change
 Per Cent Increase
 Per Capita Rate
 Margin of Error





This is one of the more
common statistics you will
see.
To compute a mean, add up all
the values in a set of data and
then divide that sum by the
number of values in the
dataset.
The chart shows how it works.
But notice, only three of the
nine workers at WWW Co.
make the mean or more, while
the other six workers don't
make even half of it.
Another way to look at
average salaries is the
Median.
Statistics Every Writer Should Know, by Robert Niles
Employee
Wage
CEO
$100,000
Manager
$50,000
Manager
$50,000
Factory Worker
$15,000
Factory Worker
$15,000
Factory Worker
$15,000
Factory Worker
$15,000
Trainee
$9,000
Trainee
$9,000
Total
$278,000
Mean
$30,889
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The median is the exact
middle. You basically line
the numbers up by value,
and then find the middle
number
In this case, that would
be one of the factory
workers with $15,000
Statistics Every Writer Should Know, by Robert Niles
Employee
Wage
CEO
$100,000
Manager
$50,000
Manager
$50,000
Factory Worker
$15,000
Factory Worker
$15,000
Factory Worker
$15,000
Factory Worker
$15,000
Trainee
$9,000
Trainee
$9,000
Total
$278,000
Median
$15,000
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Percent changes are useful to help people understand changes in a
value over time.
Simply subtract the old value from the new value, then divide by the
old value. Multiply the result by 100 and slap a % sign on it. That's
your percent change.
Let's say Springfield had 50 murders last year, as did Capital City. On
the face of it, the crime rate is the same for both cities Let's go back
and look at the number of murders in those towns in previous years, so
we can determine a percent change.
Five years ago, Capital City had 42 murders while Springfield had just
29.
Subtract the old value from the new one for each city and then divide
by the old values.
• Capital City: (50-42)/42 X 100 = 19% increase
• Springfield: (50-29)/29 X 100 = 72.4% increase
So Springfield has obviously had a far greater increase in crime.
Or has it? There’s also another concept to consider: the per capita rate.
Statistics Every Writer Should Know, by Robert Niles
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This year Springfield has 800,000 people, while five years ago it had 450,000
This year Capital City has 600,000 people, while five years ago it had 550,000
The fact that Springfield grew so much more than Capital City over the past five
years could help explain why the number of murders in Springfield increased by so
much over the same period.
To find out if one city really is more dangerous than another, you need to determine
a per capita murder rate. That is, the number of murders for each person in town.
To find that rate, simply divide the number of murders by the total population of the
city then multiply by 100,000 to get the number of murders per 100,000 people.
• Springfield today: (50/800,000)X100,000 = 6.25 murders per 100,000.
• Springfield 5 years ago: (29/450,000)X100,000 = 6.44 murders per 100,000.
• Capital City today: (50/600,000)X100,000 = 8.33 murders per 100,000
• Capital City 5 years ago: (42/550,000)X100,000 = 7.63 murders per 100,000
Percent Change: Subtract old value from new value, divide by the old value, and
multiply by 100.
• Springfield: (6.25 - 6.44)/6.44 X 100 = -2.9%
• Capital City: (8.33 – 7.63)/7.63 X 100 = 9.17%
So Springfield has had a decline in it’s murder rate of 2.9%, while Capital
City has had an increase of 9.17%.
Statistics Every Writer Should Know, by Robert Niles

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You’ll notice that polls done by reputable agencies come with a
disclaimer that generally reads something like: “Margin of error plus or
minus 4 percentage points, 95 times out 100.”
This means that if you repeated this poll 100 times, then 95 times it would
come out within plus or minus 4 percentage points of the number
reported.
This is a very important concept to remember during election polls, and
one which the newspapers most commonly ignore.
For example, consider the pre-election polls for Quimby and Sideshow
Bob, both of whom are running for mayor:
• A poll on March 22 shows Quimby with 54% and Sideshow Bob with 46%.
• A poll on April 2 shows Quimby with 50% and Sideshow Bob with 50%.
• Although most newspapers would report that Quimby’s support has slipped,
this is not really the case – the difference between the two polls is within the
margin of error. A poll conducted the next day may show Quimby with 58% and
Sideshow Bob with 42%, and it would still not mean that there had been any
change.

And don’t forget that little bit about “95 times out of 100.” This means that
for every 20 times you run the poll, you’ll get one result completely
different from the norm
Statistics Every Writer Should Know, by Robert Niles