Menus Subscribe Search

Follow us


We Are Accused of Over-cheerfulness

• April 24, 2009 • 11:15 PM

Letters to the editor: OK, bucko, step outside and say we’re afraid of population growth. Go ahead. See what happens.

Whoever told you to mail me a free copy of Miller-McCune certainly had their insider information right. I’ve spent most of the day reading almost all the great articles. I love your compassion, optimism, realism, worldwide perspective and data-based and solution-based approach. I intend to subscribe tomorrow.

I do have a disappointment, however, and I think I understand your reasoning. You do not wish to emphasize the dangers of population growth because it does not lead to any cheerful solutions.

Colleen Shaddox points out (“Simply Rwandan,” March-April) that Rwanda, the size of Vermont, has a “rapidly growing population of 10 million,” and also that “Rwanda has always been a country of large families.” Almost certainly the population will exceed 20 million before many decades, right? It is not at all realistic to assume that most of the additional 10 million will be bankers, tourist guides, software programmers and high-tech technicians. We can assume that there will therefore be intense pressures for land — for cows and farming. Yes, I appreciate that all the articles end up on an upbeat note. But wouldn’t effective steps toward family planning make Rwanda’s future much brighter?

I live in Guatemala, Central America, and the resistance to family planning is very similar. In my lifetime, the population has doubled twice and will likely double again to about 25 million in the next 30 years. Probably not coincidentally, we have had a long, bloody, evil and horrible civil war. We are now beset by drug running, organized crime, family violence and violence against women, environmental degradation and massive under-employment. Would family planning have completely prevented the suffering? Of course not. But population growth will eventually have to end. Humans can make the choices — or let tragedy make the choices for us.

Paul E. Munsell, Ph.D.
Guatemala City, Guatemala

For Those of You Who Paid Attention in Statistics Class…
Can we ever prevent the imprisonment of innocent people?

Following up on Steve Weinberg’s article (“Innocent Until Reported Guilty,” October 2008) and the subsequent commentary, let me offer a sad but sober dose of mathematical reality. The conclusion is that so long as only a very small minority of people commit crimes and the criminal justice system is fair (“fair” meaning that all people are equally subject to investigation) there will always be a very large proportion of innocent people convicted.

Now the supporting argument, made by way of an example:

Suppose there are 10,000 true criminals in the United States annually. I don’t know how many there really are, but let’s assume 10,000 for the example.

Second, let’s assume that the criminal justice system is 99.9 percent accurate. By “system” I mean the entire system, starting with investigation and prosecution and ending with punishment. I know that 99.9 percent may be Pollyannaish, but, again, let’s accept it for the example. This means that the probability of a guilty person being caught and successfully tried, convicted and punished is 99.9 percent and the probability of an innocent person being convicted is but 0.1 percent.

Now let us ask and answer the key question: If a person is found guilty of a crime, what is the probability that s/he is guilty?

This probability is a ratio that has, in its numerator the number of guilty people successfully punished = .999 x 10,000 = 9,990. In the denominator is the number of guilty people being punished plus the number of innocent ones being punished. We already have the guilty part of this (9,990). The innocent part is .001 times the number of innocent people in the U.S., or .001 x 300,000,000 = 300,000.

So the answer to the question is:

9,990/(9,990+300,000) = 9,990/309,990 = 3%

Or, expressed another way, 97 percent of those in prison, under the circumstances of this example, would be innocent. Of course if the true number of criminals is 100,000, then the proportion of innocents is “only” 70 percent. It is amazing that so few horror stories are being told.

Howard Wainer
Professor of Statistics
The Wharton School
of the University of Pennsylvania

A question from the editor: We’d like to double-check some of your reasoning with you. You create a fraction with the number of people successfully punished in your example in the numerator (in this case, 9,990) and in the denominator, you use 300,000,000 as the number of innocent people in the U.S.

We were wondering, for your example to be valid, wouldn’t you have to place a number of “charged” innocent people in the denominator, and not the entire U.S. population?

A response from Wainer: Thank you for taking the time to read and think about my example. No, the denominator is as I have specified it. The figure 99.9 percent represents the probability of getting it right of the whole process — this means initial investigation, charging, prosecuting, convicting and imprisoning.

So it assumes that at the beginning of any investigation, everyone is under consideration (although a large proportion may be eliminated quickly). This assumption may not be true — it may be that some groups of people (the usual suspects) are always considered, and some never are. I was proceeding under the democratic assumption that initially at least we are all equal under the law.

Note, by the way, that the same arithmetic is informative in evaluating medical testing. Each year in the U.S., 186,000 women are diagnosed, correctly, with breast cancer. Mammograms identify breast cancers correctly 85 percent of the time. But 33.5 million women each year have a mammogram and when there is no cancer it only identifies such with 90 percent accuracy. Thus if you have a mammogram and it results in a positive (you have cancer) result, the probability that you have cancer is:

186,000/(186,000+3.35 million) = 4%

So if you have a mammogram and it says you are cancer free, believe it. If it says you have cancer, don’t believe it.

The only way to fix this matches your question — reduce the denominator. Women less than 50 (probably less than 60) without family history of cancer should not have mammograms.

An editor’s challenge: We still suspect that professor Wainer knows his statistics cold but scored less well in Assumption Making 101. If you know we’re right or wrong, go online at Miller-McCune.com and tell us why. Our comments section awaits your brilliance.

Miller-McCune welcomes letters to the editor, sent via e-mail to theeditor@miller-mccune.com; via the comment sections of our Web site, Miller-McCune.com; or by standard mail to The Editor, 804 Anacapa St., Santa Barbara, CA 93101. Letters published in the print magazine may be condensed for space reasons.

Sign up for our free e-newsletter.

Are you on Facebook? Become our fan.

Follow us on Twitter.

Add our news to your site.

Miller-McCune Readers
Our readers react to our articles. Sometimes, they even overreact.

More From Miller-McCune Readers

A weekly roundup of the best of Pacific Standard and PSmag.com, delivered straight to your inbox.

Recent Posts

October 24 • 4:00 PM

We Need to Normalize Drug Use in Our Society

After the disastrous misconceptions of the 20th century, we’re returning to the idea that drugs are an ordinary part of life experience and no more cause addiction than do other behaviors. This is rational and welcome.


October 24 • 2:00 PM

A Letter to the Next Attorney General: Fix Presidential Pardons

More than two years ago, a series showed that white applicants were far more likely to receive clemency than comparable applicants who were black. Since then, the government has spent hundreds of thousands of dollars on a study, but the pardons system remains unchanged.


October 24 • 12:00 PM

What Makes You So Smart, Middle School Math Teacher?

Noah Davis talks to Vern Williams about what makes middle school—yes, middle school—so great.


October 24 • 10:00 AM

Why DNA Is One of Humanity’s Greatest Inventions

How we’ve co-opted our genetic material to change our world.


October 24 • 8:00 AM

What Do Clowns Think of Clowns?

Three major players weigh in on the current state of the clown.


October 24 • 7:13 AM

There Is No Surge in Illegal Immigration

The overall rate of illegal immigration has actually decreased significantly in the last 10 years. The time is ripe for immigration reform.


October 24 • 6:15 AM

Politicians Really Aren’t Better Decision Makers

Politicians took part in a classic choice experiment but failed to do better than the rest of us.


October 24 • 5:00 AM

Why We Gossip: It’s Really All About Ourselves

New research from the Netherlands finds stories we hear about others help us determine how we’re doing.


October 24 • 2:00 AM

Congratulations, Your City Is Dying!

Don’t take population numbers at face value.


October 23 • 4:00 PM

Of Course Marijuana Addiction Exists

The polarized legalization debate leads to exaggerated claims and denials about pot’s potential harms. The truth lies somewhere in between.


October 23 • 2:00 PM

American Companies Are Getting Way Too Cozy With the National Security Agency

Newly released documents describe “contractual relationships” between the NSA and U.S. companies, as well as undercover operatives.


October 23 • 12:00 PM

The Man Who’s Quantifying New York City

Noah Davis talks to the proprietor of I Quant NY. His methodology: a little something called “addition.”


October 23 • 11:02 AM

Earliest High-Altitude Settlements Found in Peru

Discovery suggests humans adapted to high altitude faster than previously thought.


October 23 • 10:00 AM

The Psychology of Bribery and Corruption

An FBI agent offered up confidential information about a political operative’s enemy in exchange for cash—and they both got caught. What were they thinking?


October 23 • 8:00 AM

Ebola News Gives Me a Guilty Thrill. Am I Crazy?

What it means to feel a little excited about the prospect of a horrific event.


October 23 • 7:04 AM

Why Don’t Men Read Romance Novels?

A lot of men just don’t read fiction, and if they do, structural misogyny drives them away from the genre.


October 23 • 6:00 AM

Why Do Americans Pray?

It depends on how you ask.


October 23 • 4:00 AM

Musicians Are Better Multitaskers

New research from Canada finds trained musicians more efficiently switch from one mental task to another.


October 22 • 4:00 PM

The Last Thing the Women’s Movement Needs Is a Heroic Male Takeover

Is the United Nations’ #HeForShe campaign helping feminism?


October 22 • 2:00 PM

Turning Public Education Into Private Profits

Baker Mitchell is a politically connected North Carolina businessman who celebrates the power of the free market. Every year, millions of public education dollars flow through Mitchell’s chain of four non-profit charter schools to for-profit companies he controls.


October 22 • 12:00 PM

Will the End of a Tax Loophole Kill Off Irish Business and Force Google and Apple to Pay Up?

U.S. technology giants have constructed international offices in Dublin in order to take advantage of favorable tax policies that are now changing. But Ireland might have enough other draws to keep them there even when costs climb.


October 22 • 10:00 AM

Veterans in the Ivory Tower

Why there aren’t enough veterans at America’s top schools—and what some people are trying to do to change that.


October 22 • 8:00 AM

Our Language Prejudices Don’t Make No Sense

We should embrace the fact that there’s no single recipe for English. Making fun of people for replacing “ask” with “aks,” or for frequently using double negatives just makes you look like the unsophisticated one.


October 22 • 7:04 AM

My Politicians Are Better Looking Than Yours

A new study finds we judge the cover by the book—or at least the party.


October 22 • 6:00 AM

How We Form Our Routines

Whether it’s a morning cup of coffee or a glass of warm milk before bed, we all have our habitual processions. The way they become engrained, though, varies from person to person.


Follow us


Politicians Really Aren’t Better Decision Makers

Politicians took part in a classic choice experiment but failed to do better than the rest of us.

Earliest High-Altitude Settlements Found in Peru

Discovery suggests humans adapted to high altitude faster than previously thought.

My Politicians Are Better Looking Than Yours

A new study finds we judge the cover by the book—or at least the party.

That Cigarette Would Make a Great Water Filter

Clean out the ashtray, add some aluminum oxide, and you've (almost) got yourself a low-cost way to remove arsenic from drinking water.

Love and Hate in Israel and Palestine

Psychologists find that parties to a conflict think they're motivated by love while their enemies are motivated by hate.

The Big One

One company, Amazon, controls 67 percent of the e-book market in the United States—down from 90 percent five years ago. September/October 2014 new-big-one-5

Copyright © 2014 by Pacific Standard and The Miller-McCune Center for Research, Media, and Public Policy. All Rights Reserved.