Introduction 8 Questions To Ask of Statistics 5 Statistical
Concepts
Slide 2
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
Slide 3
Surveys of the scientific community can tell us what the
majority of scientists think about a subject. Caveats: This doesnt
mean that theyre right. Virtually every scientific theory has been
accepted by a majority before its 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 dont 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 doesnt 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.
Slide 4
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, Thats not true! Im 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
Slide 5
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.
Slide 6
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.
Slide 7
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.
Slide 8
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.
Slide 9
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 wasnt 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. Thats
4.48% of the total households From Bad statistics make me so
confused December 12, 2006Bad statistics make me so confused
Slide 10
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.Correlation does not imply
causation
Slide 11
Trauma counseling has been given a huge boost since the
Oklahoma bombing, the Columbine shootings, and the World Trade
Center attacks. Without such counseling, weve 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 long- term 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 loweron emotional distress than the flyers who
hadnt 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 dont 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.
Slide 12
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. Theres 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. Thats 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.
Slide 13
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]
Slide 14
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 CorpAHN 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.
Slide 15
Lets 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?
Slide 16
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
Slide 17
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
Slide 18
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
Slide 19
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, Wyeth- Ayerst, 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
Slide 20
Who Was Behind the Redefinition of "Obese" Case Western Reserve
University professor Paul Ernsberger describes how financially
conflicted researchers control the governments 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 Americas 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
Slide 21
Slide 22
Obese
Slide 23
Slide 24
Slide 25
Overweig ht
Slide 26
Slide 27
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.
Slide 28
1950195119521953195419551956195719581959 2481632641282565121024
1960196119621963196419651966196719681969
2,0484,0968,19216,38432,76865,53665.536131,072262,144524,288
1970197119721973197419751976197719781979 1.049 mil2.097 mil4.2
mil8.4 mil16.8 mil33.5 mil67.1 mil134.2 mil268.4 mil 1 536.9 mil
1980198119821983198419851986198719881989 1.1 bil2.2 bil4.3 bil8.6
bil 2 17.2 bil34.4 bil68.7 bil137.4 bil274.9 bil549.8 bil
1990199119921993199419951996199719981999 1.1 tril2.2 tril4.4
tril8.8 tril17.6 tril35.2 tril 1.Larger than the population of the
United States in that year. 2.Larger than the population of the
entire world.
Slide 29
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 isnt 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%
Slide 30
1. Where did the data come from? 2. 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? 7. Has there been a change in circumstance? 8.
Are the questions neutral?
Slide 31
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.
Slide 32
You always want to know who did the research that created the
data you're going to write about. If the person or publication cant
(or wont) 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. Youll 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,
dont 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 its just that the groups reading the
two papers have very different views from each other. Statistics
Every Writer Should KnowStatistics 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 UniversityThe Good, the Bad, and the Ugly
of Public Opinion Polls
Slide 33
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 couldnt stand up to such scrutiny. Statistics
Every Writer Should KnowStatistics Every Writer Should Know, by
Robert Niles
Slide 34
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 werent 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
KnowStatistics Every Writer Should Know, by Robert Niles
Slide 35
Zbigniew JaworowskiZbigniew Jaworowski, M.D., Ph.D.,
D.Sc.,(Chairman, Scientific Council of Central Laboratory for
Radiological Protection ) March 2007 Actual data points collected
showing distribution of particular substance over time in parts per
million.
Slide 36
Statistics Every Writer Should KnowStatistics Every Writer
Should Know, by Robert Niles Circled areas show data points chosen
to prove thesis of researcher that the substance has increased over
the years.
Slide 37
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 10-
year 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 age- dependent (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
KnowStatistics Every Writer Should Know, by Robert Niles
Slide 38
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:Eric Meyer When working on a
Milwaukee paper he would call the sheriffs 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
fender- benders 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 KnowStatistics Every Writer Should
Know, by Robert Niles
Slide 39
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 doesnt have to
be perfect to give us meaningful statistics, but it must be
consistent from one study to the next.
Slide 40
As we saw with the statistics about grown-up stay-at- home
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 wasnt 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 doesnt
necessarily mean theres more child-abuse merely that more children
(and peripheral adults) are willing to report it.
Slide 41
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 TodayBad Statistics: USA Today, by
John M. Grohol, Psy.D. March 16, 2006
Slide 42
The Mean The Median Percent Change Per Cent Increase Per Capita
Rate Margin of Error
Slide 43
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. EmployeeWage 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 Statistics Every Writer Should KnowStatistics Every
Writer Should Know, by Robert Niles
Slide 44
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 EmployeeWage
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 Statistics
Every Writer Should KnowStatistics Every Writer Should Know, by
Robert Niles
Slide 45
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? Theres
also another concept to consider: the per capita rate. Statistics
Every Writer Should KnowStatistics Every Writer Should Know, by
Robert Niles
Slide 46
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 its murder rate of 2.9%, while
Capital City has had an increase of 9.17%. Statistics Every Writer
Should KnowStatistics Every Writer Should Know, by Robert
Niles
Slide 47
Youll 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 Quimbys 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 dont forget that little bit
about 95 times out of 100. This means that for every 20 times you
run the poll, youll get one result completely different from the
norm Statistics Every Writer Should KnowStatistics Every Writer
Should Know, by Robert Niles