Fun With Statistics - Veneer of Verisimilitude Edition

By Kevin Meyer

It's been a long while, probably over a year, since I've done a Fun With Statistics post, but the WSJ gave me the perfect opportunity to dive into a pet peeve: calculation precision.  Those engineers among us know what I mean having had the concept of significant figures drilled into us in class after class.  Unfortunately much of the world is not so enlightened.

The underlying premise of Charles Forelle's article is the EPA fuel economy calculation that adds or removes cars from the Cash for Clunkers program, where 0.0001 miles per gallon was a discriminating result.  As Forelle puts it,

After all, 0.0001 miles is about six inches, and, if you could count it, a car getting around 18 miles to the gallon would consume about half a drop of fuel in that distance. Such precision is futile when dealing with essentially unknowable quantities derived from rough real-world experiments and seasoned with debatable assumptions.

No kidding, but such is politics.  Oops, sorry.  I don't want to be branded an "evil-monger" or "un-American" or get added onto a White House "fishy information" spam list.  Strange how protesting was patriotic only a few months ago.  But where was I...

Oh yes, significant figures.  For the non-numerical among you,

The principle is simple: When combining measured numbers, the final answer is only as precise the least-precise piece of data that went into it; you can't just add a tail of decimal places, even if they show up on the calculator. So a room that's 2.5 meters (two significant digits) by 3.87 meters (three) has an area of 9.7 square meters, though the two numbers multiply to 9.675.

So how about another abuse of the decimal:

Still, decimal places lend the aura of authority and the veneer of verisimilitude. So the modern world is awash in squishy numbers wearing the many-figured garb of faux precision.

The state of Montana reported three weeks ago that its unemployment rate for June "increased 0.1% to 6.4%." Did it? Maybe. The unemployment data come from the federal Current Population Survey, which interviews tens of thousands of people across the nation but only 1,200 in Montana -- too few for a precise figure. The rate is derived from a statistical model.

Barbara Wagner, a state economist, admits the figure isn't precise. But, she says, "it is still our best guess at the exact rate."

Now that's a line to remember!  I think I'll try that in my next financial review!  "It's my best guess at the exact rate."

And finally, for those of you that are curious, as admittedly was I:

ver-i-si-mil-i-tude [ver-uh-si-mil-i-tood]  - something, as an assertion, having merely the appearance of truth.

I'm biting my tongue...

Comments

[Mark]

With measurement error, a "drop" of 0.1% might actually be an increase, right? Or it's just common cause variation in a stable unemployment system.

"Understanding Variation" by Donald Wheeler should be required reading for any college graduate, or even high school graduate. Or at least required reading for our blog readers!!

[Jeff Holloway]

Here's my favorite statistic....."Kills 99.9% of germs on contact" did someone really count exactly 1000 germs in a petri dish, drop in a solution, and then find just 1 live one to get this percentage? And why aren't they working on something to kill that monster germ?

[Bill Waddell]

To relate this to manufacturing directly, MRP systems are lot sized based, and lot sizing is based on some variation of EOQ. I am not picking on the author if this article - all EOQ theory is pretty much the same.

Consider the inputs to this formula - almost all of them unknown and some unknowable. Everyone has to resort to very rough estimates ... some number plus or minus 30% or more ... then mulitiply and divide and square root those rough estimates to calculate lot sizes to the single unit, and then use those numbers to drive their factories. Inventory levels, tootal costs, customer service levels, floor space consumption are all functions of manufacturing lot sizes. The illusion of precision is breathtaking when it spits out of a computer running ERP. But it is all built on this very flimsy statistical house of cards.

Basic EOQ Formula

EOQ = (√ ((2 X Annual Usage in Units X Order Cost) ÷ (Annual Carrying Cost Per Unit))

Annual Usage.
Expressed in units, this is generally the easiest part of the equation. You simply input your forecasted annual usage.

Order Cost.
In manufacturing, the order cost would include the time to initiate the work order, time associated with picking and issuing components excluding time associated with counting and handling specific quantities, all production scheduling time, machine set up time, and inspection time. Production scrap directly associated with the machine setup should also be included in order cost as would be any tooling that is discarded after each production run.

Carrying cost.
Also called Holding cost, carrying cost is the cost associated with having inventory on hand. It is primarily made up of the costs associated with the inventory investment and storage cost. For the purpose of the EOQ calculation, if the cost does not change based upon the quantity of inventory on hand it should not be included in carrying cost. In the EOQ formula, carrying cost is represented as the annual cost per average on hand inventory unit. Below are the primary components of carrying cost.

Interest. If you had to borrow money to pay for your inventory, the interest rate would be part of the carrying cost. If you did not borrow on the inventory, but have loans on other capital items, you can use the interest rate on those loans since a reduction in inventory would free up money that could be used to pay these loans. If by some miracle you are debt free you would need to determine how much you could make if the money was invested.

Insurance. Since insurance costs are directly related to the total value of the inventory, you would include this as part of carrying cost.

Taxes. If you are required to pay any taxes on the value of your inventory they would also be included.

Storage Costs. Mistakes in calculating storage costs are common in EOQ implementations. Generally companies take all costs associated with the warehouse and divide it by the average inventory to determine a storage cost percentage for the EOQ calculation. This tends to include costs that are not directly affected by the inventory levels and does not compensate for storage characteristics. Carrying costs for the purpose of the EOQ calculation should only include costs that are variable based upon inventory levels.

From Optimizing Economic Order Quantity (EOQ)
By Dave Piasecki
http://www.inventoryops.com/economic_order_quantity.htm

[Martin B]

I am of an age to have used slide rules in my youth. They certainly taught one significant figures. You couldn't read off much beyond three or four figures, unlike today's calculators.

Old professor's joke: Ask a student to multiply 2 times 2 on his slide rule and he'll tell you *squinting at slide rule* "It's three point nine, nine, er... oh, make it four."

[Tim McMahon]

Nice post. Unfortunately I run into poor use of mathematics and statistics often. While it is great that people use data to make decisions they don't understand that bad data or poor interpretation of the data is as bad as no data. My favorite is when people compare two scenarios by averages of disimiliar population sizes. Claiming that a difference in numbers is significant. Just as bad as taking one or two data points to draw conclusions.