Evolving Excellence

Fun With Statistics, Carbon Footprint Edition

In this issue of Fun With Statistics we'll tackle that new consumer term du jour, the "carbon footprint."  Most of us know by now that the carbon footprint is the amount of carbon dioxide and other greenhouse gases that are created when a product is created, shipped, stored, and eventually used.   But is it a reliable gauge?  Yes and no.

There are three primary issues, the first being how the number is calculated.  Depending on who is doing the calculation and their perspective on the product, the number may not include the entire supply chain.

Several studies of milk's carbon footprint are under way in the U.S. Each has come up with a different number, largely because each is counting things differently.

A recent study by National Dairy Holdings, a Dallas-based dairy, found that the carbon footprint of a gallon of its milk in a plastic jug is either 6.19 pounds or 7.59 pounds. The difference rests in what kind of cases the jugs are placed in during transport from the milk-processing plant to the distribution center. Plastic cases, because they take more energy to produce, yield more carbon-dioxide emissions than do cardboard ones.

But National Dairy Holdings' study doesn't count all the emissions created by a gallon of milk. It includes those from the cows themselves (more than half of the total), from the processing of the milk and from the transport of the milk to a distribution center. It doesn't count the emissions earlier in the process: growing the cows' feed. Nor does it count the emissions later in the process: transporting the milk from the distribution center to the store and refrigerating it there.

But the second, and perhaps more annoying problem, is what to do after the analysis is complete and a number is agreed upon.

When New Belgium Brewing Co. set out last year to compute the carbon footprint of a six-pack of its Fat Tire Amber Ale, it figured it would find transportation was the biggest problem. That's the emission source New Belgium thinks about most often. The microbrewer, based in Fort Collins, Colo., has been expanding into more states, necessitating more trucking of its beer.

When the numbers came in this summer, they showed that a six-pack's carbon footprint was about seven pounds. The real surprise was where the bulk of that number came from: the refrigeration of the beer at stores. Transportation came in fourth, behind manufacturing the glass bottles and producing the barley and malt. "It seems that in every [carbon-footprint study] I've come across, people are surprised," says Jennifer Orgolini, New Belgium's sustainability director.

A third significant issue is the difference between like products, or how the term "product" is used.  If the "product" is "car" then there's a problem similar to what Toyota discovered.

Sometimes, the differences between models can be substantial. For one overview of how cars stack up, consider a new computer model paid for by Toyota Motor Corp. that computes the lifetime carbon footprints of about 400 auto models from multiple manufacturers.

To narrow things down, consider a handful of Toyota's own models. The Prius, a hybrid gasoline-and-electric car that averages 42 miles per gallon, has a lifetime carbon footprint of 44 metric tons, according to the updated computer model done for Toyota by Kreider & Associates, a consultant based in Boulder, Colo. The Corolla, a small sedan with a conventional gasoline engine rated at 29 miles per gallon, has a footprint of 64 tons. The Camry, a larger car rated at 23 miles per gallon, has a footprint of 95 tons. And the 4Runner, an SUV rated at 16 miles per gallon, has a footprint of 118 tons.

That's probably to be expected, and definitely something to be aware of.  The carbon footprint is emerging as an important metric, but it is critical that we be aware of some of the nuances of the calculation. 

And that's today's Fun With Statistics. 

Fun With Statistics, Overhead Edition

In this edition of Fun With Statistics we tackle the quandary of published overhead or administrative costs.  We commonly use administrative overhead statistics as a measure of organizational efficiency.  For example, when investing in a mutual fund we'll often take a look at the expense costs to determine how much bang the investment gets for the management expense required.  In that case it's a pretty clear-cut calculation... total return versus the expense.  But that's not always the case.

One common argument for nationalized health care is that current government health care programs such as Medicare have very low administrative costs compared to private plans.  That may be true, but is it the whole story?  Let's take a look at a recent article from The Washington Post which was also discussed here, which follows a similar blog post referencing a New York Times article from last December.  The sub-head from the WaPo article basically gives you the answer:

Medicare pays most claims without review.

That phrase is probably creating a gleam in the eye of some nefarious people, hopefully not our readers.

A critical aspect of the problem is that Medicare, the health program for the elderly and the disabled, automatically pays the vast majority of the bills it receives from companies that possess federally issued supplier numbers. Computer and audit systems now in place to detect problems generally focus on overbilling and unorthodox medical treatment rather than fraud, scholars say.

No focus on fraud.  Ok... how about an example of how big this problem is.

All it took to bilk the federal government out of $105 million was a laptop computer.

From her Mediterranean-style townhouse, a high school dropout named Rita Campos Ramirez orchestrated what prosecutors call the largest health-care fraud by one person. Over nearly four years, she electronically submitted more than 140,000 Medicare claims for unnecessary equipment and services. She used the proceeds to finance big-ticket purchases, including two condominiums and a Mercedez-Benz...

Law enforcement authorities estimate that health-care fraud costs taxpayers more than $60 billion each year.

So administrative costs are low, but fraud costs over $60 b-b-billion.  Cato puts it more eloquently:

So Medicare’s approach to paying claims is not unlike, say, shoveling money out the door?

Officials who oversee the Medicare program say they are vigilant despite time pressure and limited resources. Employees review fewer than 5 percent of the nearly 1 billion claims filed each year…This year, CMS is working to finalize a rule that would prevent convicted felons from obtaining Medicare billing numbers.

But the important thing here is that Medicare is keeping administrative costs down, and passing the savings on to you, the taxpayer.

Tongue-in-cheek, presumably.  Or perhaps more appropriately the taxpayer is getting some other appliance in some other orifice. 

So next time you hear some statistic lauding low administrative cost, be it in government or the private sector, make sure you also look at the other side of the story.  Where is the value to the customer?

Fun With Statistics, Percentile Problems Edition

In this edition of Fun With Statistics we'll tackle a statistical nuance that has bugged me for a long time: percentiles with populations that change over time.  This has a direct application to product line aging versus profitability calculations that many companies use for life cycle and discontinuation analyses, where they commonly make errors that cost a lot of dollars.  Leave it to our friend Russell Roberts at Cafe Hayek to provide an understandable example of the problem: income percentiles.

I apologize in advance for quoting so much of his post, but that's the only way to do it justice.

As I have written here before, looking at slices of the population over time is a very misleading indicator of what happens to particular families over time, particularly when family composition is changing. Arnold Kling makes the same point and does it superbly:

In his new book Unequal Democracy, Larry Bartels writes (p.7),

families at the 20th percentile experienced declining real incomes in 20 of the 58 years...by comparison, families at the 95th percentile have experienced only one decline of 3% or more in their real incomes since 1951.

I have a nit to pick, which is that Census department percentiles are not families.

Now he dives into explaining the statistical fallacy. 

Suppose that we start out with 20 families, and the 4th-lowest family (the 20th percentile) has an income of $10,000, while the 3rd family has an income of $9500. Next year, suppose that everyone's family income rises by 2 percent, but we add a new family at the bottom of the income distribution, with an income of $6000. As a result, the new 20th percentile is now somewhere between the income of the original 3rd family (now the 4th family out of 21) and the original 4th family (now the 5th family). The income of the 20th percentile goes down, even though the income of every family has gone up.

Next, consider what happens when you have millions of families, and you add lots of new families each year. Because new families (immigrants and young families) tend to join the income escalator at the bottom, it should be no surprise that the bottom percentile shows declines more frequently than the top percentile.

Also take into account the impact of the flood of immigrants, who primarily move into low-paying agricultural jobs, and the impact that has on the lowest 10% percentile.  Would you expect to see upward movement?  Roberts then points out one more anomaly that can create radical shifts in income.

Another issue that people raise with Census data is that the basic unit is the household. If a household breaks into two households, due to divorce, average household income plunges by 50 percent, even though nobody's income has changed. Trends in household income tend to look worse than trends in income per person.

After which he provides considerable statistics on income by percentile, population changes, and the change in the number of households over the past several decades.  The bottom line?

So over the last half-century, the number of households has increased at a much faster rate than the number of people, mainly because of divorce. That totally contaminates the comparison of percentiles over time and makes it appear that people are falling behind or standing still when in, fact, particular families are seeing their standard of living rise. Arnold calls a nitpick. I call it a massive structural flaw.

"Massive structural flaw" indeed.  But at least it makes for a lot of misinformation, easily shaped by whichever political bias you subscribe to.

But the lesson here can be applied to the business world as well.  Think about your individual products and product families, and their contribution margin to the overall bottom line.  Presumably newer high-margin products are always entering the picture, creating the inverse scenario to the population/income scenario above.  As a product or product family ages, it's margin goes down, but how about total cash contribution which is driven by volume?  Are you analyzing the percentiles correctly?

Fun With Statistics, Lazy Women Doctors Edition

How's that for a title for this edition of Fun With Statistics?  But before I receive a bunch of comments that I have the power to simply discard, let's learn a bit more.  First off, some background.

Various studies have projected a shortfall of anywhere from 50,000 to 100,000 physicians in the U.S. relative to demand by 2020, and the Institute of Medicine, a federal advisory body, just reported that in a mere three years senior citizens will be facing a health-care workforce that is "too small and woefully unprepared."

So... what does that have to do with women?

This looming shortage is forcing into the open a controversy that has been cautiously debated in hospitals and medical practices for some time: Are women doctors part of the problem? It's not the abilities of female doctors that are in question. It's that study after study has found women doctors tend to work 20% to 25% fewer hours than their male counterparts.

And now I'll get myself off the hook.  The women aren't lazy, they simply value balance in their lives.

Women doctors in the U.S. work less—47 hours per week on average, versus 53 for men. They also see about 10% fewer patients and tend to take more time off early in their careers. "It's pretty much an even bet that within a year or two of entering practice they will go on maternity leave," says Phillip Miller, a vice-president of the medical recruiting firm Merritt, Hawkins & Associates. "Then they are going to want more flexible hours."

This does create some advantages.

On the plus side, women are willing to take on lower-paying specialties that male doctors are moving away from, such as primary care, pediatrics, and obstetrics. Since 1996 there has been a 40% jump in the number of women choosing primary care, offsetting the 16% decline in men entering the field. A lighter workload also has its advantages. "Lots of studies show that doctors who work fewer hours have less burnout," says Dr. Joseph Flaherty, dean of University of Illinois College of Medicine. "There is a strong association between long hours and medical errors."

But the real lesson is for the future, when both men and women will be looking for balance... and how that will impact statistics.  As you look at your workforce and consider the level as well as the succession plans I'm sure you already have in place (right...?), do you account for an increasing desire for balance?  Or are you driving them hard?  If so, you may be surprised by how your workforce has to grow over the next few years just to accomplish the same tasks. 

Of course the other option is to focus on lean manufacturing and lean enterprise methods to reduce the number of tasks to balance with the load your employees are willing to take on.

Fun With Statistics, Bachelor Edition

In this edition of Fun With Statistics we'll take on the perennial question: why are there so few eligible bachelors?  Of course this was never a problem for me, but for some reason the angst of women to locate eligible bachelors also didn't seem to create any positive fortune.  I guess I simply wasn't eligible... enough.

Tyler Cowen over at Marginal Revolution discusses the Eligible Bachelor Paradox.

The pool of appealing men shrinks as many are married off and taken out of the game, leaving a disproportionate number of men who are notably imperfect (perhaps they are short, socially awkward, underemployed). And at the same time, you get a pool of women weighted toward the attractive, desirable "strong bidders."

Game theory helps explain the conundrum.

Game theory predicts, and empirical studies of auctions bear out, that auctions will often be won by "weak" bidders, who know that they can be outbid and so bid more aggressively, while the "strong" bidders will hold out for a really great deal. You can find a technical discussion of this here.

And how does this work?

Where have all the most appealing men gone? Married young, most of them—and sometimes to women whose most salient characteristic was not their beauty, or passion, or intellect, but their decisiveness.

Decisiveness?  Tyler questions the validity of the argument.

I view the real world auction as being held -- at least if you wish -- continuously rather than at discrete times.  So the "strong bidding women" can always cave and settle for a "lesser man" after an optimal amount of waiting, yet many don't.  The distinction between period-by-period happiness and overall lifetime happiness also shapes the market.  As smart single women mature, their lives get better and better.  "Settling" becomes psychologically harder, even if it would make some of the "settlers" happy in the longer run.  So settling doesn't happen; decisiveness become harder to conjure up at the same time that its long-run value is increasing, or in other words behavioral economics is very much at work here.

Of course this post was written, directly and indirectly, by a couple of guys.  Last time I tried to figure out the the vagarities of the female brain I got into some serious trouble.

Fun With Statistics, Fad Edition

In this edition of Fun With Statistics, we ask you to be careful of fads, especially those driven by popular passion.  We all want to be environmentally sensitive; it's simply a good thing to do.  Whether or not you agree that global warming is caused by humans, reducing pollutants and green house gases is still a noble objective.  Didn't Greenland really used to be green?  Hmm...

But how about ethanol fuel and bamboo products?  Ethanol is touted as a great replacement for petroleum-based fuel, although as we pointed out last December there is still a debate whether it is a net positive or negative from an energy output standpoint when processing energy is taken into account.  Now some people are wondering about how ethanol production will affect global warming.

A study published in the latest issue of Science finds that corn-based ethanol, a type of biofuel pushed heavily in the U.S., will nearly double the output of greenhouse-gas emissions instead of reducing them by about one-fifth by some estimates. A separate paper in Science concludes that clearing native habitats to grow crops for biofuel generally will lead to more carbon emissions.

That's on top of some of the other indirect effects.

The findings are the latest to take aim at biofuels, which have already been blamed for pushing up prices of corn and other food crops, as well as straining water supplies.

Have you noticed how popular bamboo products are?  On the surface there's a good reason.  Take bamboo t-shirts for example.

Bamboo naturally grows at a fast rate even when you don't place any fertilization, chemicals or pesticides on them. This means that there is always an ample amount of bamboo available to make the shirts. Another great thing about these are that they are antibacterial because of properties in the plant. They are also antifungal and do not hold sweat as other cotton t-shirts can. This means that you won't have to wash it as much as a cotton shirts which saves on energy.

But, as you probably suspected, there is another side of the story.  A side that isn't exactly eco-friendly.

The not so eco-friendly part and the biggest part is in the way that they are made. The t-shirts are made using the bamboo but the process is highly pollutant and harmful to the workers manufacturing the shirts. They use a hydrolysis alkalization process to soak the bamboo leaves and shoots in sodium hydroxide and carbon disulfide. It is then placed in a bleaching solution in which it goes through many phases before it is complete. All of these chemicals give off a harmful vapor that could result in health problems for the individuals working.

That doesn't sound all that great.  Bottom line: dig into a manufacturing or business fad.  Is the popularly-accepted benefit based on reality?  All reality?

Fun With Statistics, Ethanol Edition

In this edition of Fun With Statistics we'll consider the question of "using more to use less."  Earlier this week President Bush signed the new energy bill, which includes a host of incentives and regulations in an attempt to reduce the U.S. dependence on foreign oil.  I won't go into the political and even logical aspects of the various components to the bill.  Except for one.

Biofuel, predominantly corn-based ethanol, has become a hot commodity lately.  Supposedly the cure-all for our energy ills, but few are looking at the side effect of our new use for corn.  Such as the tortilla crisis in Mexico, where the price of that food staple is skyrocketing out of reach of the common folk.  We've said it before, and we'll say it again, fooling around with the free market is like pushing on a balloon... there will be an opposite reaction somewhere, and often we can't predict where.

But there's another aspect of ethanol that is being hotly debated in the scientific community, especially in the last year or so: does ethanol production actually create a net surplus of energy?  Planting, harvesting, and processing corn into ethanol takes energy, and therefore is the energy balance negative or positive.

Cornell University ecology Professor David Pimentel, however, sides with Patzek, calling production of ethanol "subsidized food burning."  "The USDA isn't looking at factors like the energy it takes to maintain farm machinery and irrigate fields in their analysis," he said, adding that the agency's ethanol report contains overly optimistic assumptions about the efficiency of farming practices. "The bottom line is that we're using far more energy in making ethanol than we're getting out."

Up until two or three years ago it was almost indisputably negative, with production and conversion energy required running between 35% and 65% greater than the ethanol energy created.  But ethanol plants have become far more efficient and the relative value of the crude energy required versus the refined energy gained has by most estimates created a net positive.  But controversy still exists.

"His figures (regarding energy consumed in fertilizer production) are accurate for older nitrogen fertilizer plants, but newer plants use only half the energy of those that were built 35 years ago," he said. He also cited the increasing popularity of no-till farming methods, which can reduce a corn farm's diesel usage by 75 percent. "With hydrogen fuel, people are willing to say, '25 years from now it will be good.' Why can't we also be forward-looking when it comes to ethanol?"

Some scientists claim that when all inputs are identified and added to the equation, it is still negative.  Others, in that same and remarkably balanced article, have data showing it is even more positive.  Interestingly enough, both claims are peer-reviewed and published in journals.  Others are concerned about the "collateral damage," such as the additional fertilizer required (which requires energy to make, by the way) running off and polluting the environment.

Patzek's report also highlights the potential environmental hazards of ethanol production. "When you dump nitrogen fertilizer on corn fields, it runs away as surface water, into the Mississippi River and Gulf of Mexico," he said. The excess nitrogen introduced into the water causes out-of-control algae growth, creating an oxygen-poor "dead zone" where other marine plants and animals cannot survive. And while ethanol produces fewer carbon monoxide emissions than regular gasoline, some researchers have found that ethanol releases high levels of nitrogen oxide, one of the principal ingredients of smog, when burned.

But perhaps the most interesting concept, and one that will ring a bell with our lean-oriented readers, is the one of value.  And just as manufacturing value isn't related to price alone, ethanol value isn't related to energy content alone.  We aren't trying to just create another source of energy, we're trying to create another source of portable energy.  Portability has inherent value.

Other contributors to the debate argue that ethanol's net energy balance should not be the sole consideration when policymakers are evaluating its usefulness -- factors like the fuel's portability and lower carbon monoxide emissions need to be considered as well. "So what if we have to spend 2 BTUs for each BTU of alcohol fuel produced?" reads an editorial in the Offgrid Online energy newsletter. "Since we are after a portable fuel, we might be willing to spend more energy to get it."

Although a negative 2:1 ratio makes you wonder if we should be looking at other solutions.

Patzek thinks lawmakers and environmental activists need to push ethanol aside and concentrate on more sustainable solutions like improving the efficiency of fuel cells and hybrid electric cars or harnessing solar energy for use in transport. If they don't, he predicts economics will eventually force the issue.

Some day, perhaps.

Fun With Statistics, Convenient Scapegoat Edition

In this edition of Fun With Statistics we take on the lure of the convenient scapegoat.  Let's start with an example that is all the rage these days... global warming. 

By now pretty much everyone agrees that some level of warming is occuring, and the more agitated like to pin the blame on humans.  One only has to ponder the fact that Greenland used to be... green... and only a few centuries ago, to create some actual thought along those lines.  Then when you consider that an average volcano eruption throws more particulate and greenhouse gases into the air than a couple years of human activity and you really start to wonder.  And don't get me started on cow flatulence.  Which is why more and more scientists believe that the warming is simply part of a much larger cycle operating in geologic time, with some looking at data that appears to show the warming stopped a couple years ago.  Who really knows?

Of course that doesn't mean we should stop trying to reduce emissions and pollution.  That is simply being a good steward of the Earth.  What is interesting is how market forces are now driving green initiatives faster than regulatory forces.

But once we perceive a potential cause of a problem, it soon becomes a convenient scapegoat.  Global warming, human-created or not, has become such an entity.  A few days ago the "Warm List" began making the email rounds... a list of problems that are being blamed on global warming, with hyperlinks to the original new stories.  At last count it was over 600, ranging from the Minneapolis bridge collapse to the tick population moving northward in Sweden.

However the point of this Edition is closer to home.  How many of us take the easy way out in our operations instead of taking the time to really identify and then decimate the root cause?  I know of one company that used to blame every conceivable problem on "material variability."  Processes out of control, quality defects, the resulting long cycle times and high work order costs, the inability to set defined delivery dates... all due to material variability.  I bet high employee turnover was also attributed to that misconception.  Stacks of NCMR's, hoards of people that did nothing except process exception documentation, offsite storage to hold all the paperwork.  Dang material variability!

Costs were astronomical.  Almost as high as the initial effort that would have been required to systematically find and nail the root cause, creating more robust and stable processes.  Except that effort to deal with the supposed material variability was never-ending, while the effort required to do some root cause analysis would presumably only be required once per issue.

While looking around to find your constraint "Herbie" how about also keeping an eye out for convenient scapegoats.   

Fun With Statistics, Compensation Edition

Many of us have long been struggling with helping employees understand the confluence of benefits and compensation.  Straight wages are the most obvious form of compensation, but those of us that get to experience the exciting employer side of things also realize the cost, and value, of benefits as health care, insurance, and other costs rise.  Some employers completely shield employees from those rising costs, in which case the employees are oblivious to their "total compensation" while most share or pass on the increases.

Both a former employer as well as my current company have tried to educate employees as to the value of their total benefits package by creating personalized annual statements, usually with a nice fat bar graph showing how benefits are worth 30-50% above straight wages.  Unfortunately the message doesn't seem to get across, which explains the popular perception of "stagnant wages."  Our friend Steve Conover over at The Skeptical Optimist has a couple of posts on the subject.  In the first he takes on the stagnant wage myth itself.

Here's how the BLS describes their compensation data: "The Employer Costs for Employee Compensation product is a quarterly survey that shows the employers' average hourly cost for total compensation and its components."  I charted the BLS numbers, and calculated the change in real compensation for the six years from Q4 1999 to Q4 2005.  A pleasant surprise: real compensation per hour has been the opposite of "stagnant"; in fact, it grew by 6.7% in the 2000-2005 interval.  That's better growth than any six-year period in the last twenty years, including 1995-2000.

He then goes on a bit of a well-deserved rant on how the presidential candidates, especially from one side, are blathering about the myth and the moderators and press aren't calling them on it.  However he really gets interesting in a follow-on post asking Do Employee Benefits Benefit Employees?  What the heck kind of question is that, you ask?  Let's let Steve describe his quandary.

In the three days since I posted the article below this one, I've had to revise my opinion about employee benefits.  Specifically, I've had to revise downward my estimate of the number of people who actually consider them beneficial to employees.

Benefits apparently aren't benefits to those whose political talking points get more difficult if employee benefits are assumed to benefit employees.  If the cost of health insurance increases, and a company pays part or all of the increase, guess what: that doesn't "benefit" the employee; sure, it cushioned the blow, or even eliminated it, but somehow that's not good enough to be classified a "benefit."  (Makes one wonder how many employers realize that any extra money they'd pay out for health insurance cost increases would not be considered of "benefit" to their employees.) 

Whatever.  In my judgment, employee benefits benefit employees, just as money wages do.  Compensation (pretax) is the sum of the two, and real compensation (pretax) has increased significantly since the business-cycle-peak year of 2000.  And, because everyone's income tax rates went down since 2000, the after-tax effects would have to be even larger; too bad the BLS doesn't publish after-tax numbers. 

I've been called an "idiot" for that thought process.

I guess that forces me to join the idiot club as well.  As a final note, I've always been intrigued with how some benefits are critically valuable for some and not others and how some benefits become attached to employee compensation and others don't.  Employers don't provide car insurance, so why are they should they provide health insurance?  Sure, healthy employees make for good employees, so there is a business interest.  But in supporting that business interest do we add far greater unnecessary complexity with regards to health care portability?  Similarly many employers are experimenting with "opt-out" forms of 401k enrollment to help "encourage" employees to save for retirement, but we run into a wall with young kids more interested in where the weekend's beer money will come from than in what they'll be living off of in fifty years. 

Fun With Statistics, Prostate Edition

In this edition of Fun With Statistics we'll explore why it is important to really read every word, and understand the sequence of data analysis, in a statistical argument.  With a hat tip to Donald Luskin at The Conspiracy to Keep You Poor and Stupid, there's a bit of controversy over Rudy Giuliani's recent comments on healthcare.  First, Rudy's comment:

My chance of surviving prostate cancer ¬ and thank God I was cured of it ¬ in the United States? Eighty-two percent," says Rudy Giuliani in a new radio ad attacking Democratic plans for universal health care. "My chances of surviving prostate cancer in England? Only 44 percent, under socialized medicine.

Of course that throws the lefties into a tizzy, as it flies in the face of their theory that the government, apparently including the DMV, is more effective than private enterprise.  So the uniquitous Paul Krugman weighs in.

Mr. Giuliani got his numbers from a recent article in City Journal, a publication of the conservative Manhattan Institute. The author gave no source for his numbers on five-year survival rates ¬ the probability that someone diagnosed with prostate cancer would still be alive five years after the diagnosis. And they’re just wrong. You see, the actual survival rate in Britain is 74.4 percent.

Now before we get started on the actual statistics, Krugman plays classic Krugman by himself not giving the source of his numbers.  Go figure.  But as the City Journal then opines, Krugman simply doesn't understand statistical analysis chains.

Let me be very clear about why the Giuliani campaign is correct: the percentage of people diagnosed with prostate cancer who die from it is much higher in Britain than in the United States. The Organisation for Economic Co-operation and Development reports on both the incidence of prostate cancer in member nations and the number of resultant deaths. According to OECD data published in 2000, 49 Britons per 100,000 were diagnosed with prostate cancer, and 28 per 100,000 died of it. This means that 57 percent of Britons diagnosed with prostate cancer died of it; and, consequently, that just 43 percent survived. Economist John Goodman, in Lives at Risk, arrives at precisely the same conclusion: “In the United States, slightly less than one in five people diagnosed with prostate cancer dies of the disease. In the United Kingdom, 57 percent die.” None of this is surprising: in the UK, only about 40 percent of cancer patients see an oncologist, and historically, the government has been reluctant to fund new (and often better) cancer drugs.

The root of the misunderstanding is the sequence of analysis.

So why do the critics think that Britain’s survival rates are as high as America’s? The main reason is that they are citing overall mortality rates, which are indeed, as Ezra Klein writes, similar across various countries. That is, the percentage of all Americans who die from prostate cancer is similar to the percentage of all Britons who do. But this misses the point, since a much higher percentage of Americans than Britons are diagnosed with prostate cancer in the first place. If you are a patient already diagnosed with prostate cancer, like Rudy Giuliani, your chances of survival—as Giuliani correctly said—are far higher in the United States.

When looking at statistics, understanding the data population is critical.  Are you analyzing the overall population or a subgroup?  When comparing statistics are you comparing the same populations?  Krugman is becoming famous for this error... or intentionally using it as some contend.  As an aside, a comment on his own article provides another interesting statistical sidelight.

More than 70,000 Britons will have treatment abroad this year – a figure that is forecast to rise to almost 200,000 by the end of the decade. Patients needing major heart surgery, hip operations and cataracts are using the internet to book operations to be carried out thousands of miles away. Research by the Treatment Abroad website shows that Britons have travelled to 112 foreign hospitals, based in 48 countries, to find safe, affordable treatment.  Yep, that the equivalent of say 350,000 U.S. citizens seeking medical care abroad... now.

Great... now I have to figure out how that plays into things... another subpopulation.  Sigh...