#### Re: Box/auto distribution 1938

Tim O'Connor

Larry

Ok, you have 120 trains, 7000 cars, 2400 box cars right? Or 20 box
cars per train (on average)?

Here's a simple, straightforward probability calculation --

Let's say 4 out of 100 box cars is owned by SP or T&NO. (I checked my 1940
ORER, the two combined owned 27,740 box, automobile & furniture cars.)

So what is the random chance of a 20 box car freight train with ZERO
SP/TNO box cars?

It's just .96**20 or .44 -- a 44% random chance. Or in other words, with the
SP/TNO owning 4% of the fleet, a 20 box car train has a 56% chance that it will
have -at least one- SP/TNO box car. (It could have 2 or more of course.)

The statistic that we have been discussing is "expectation" -- what is the
"expected" (or average number) of SP box cars. G-N says it is 0.8 (.04*20),
but in your data set of 120 trains it is 1.6 (200/120). Now recall that
probability of at least 1 car -- 56%. The population -difference- between the
observed and expected number in your sample (of 4.5% of freight trains) is
less than 1 car per train. This is why I said it -could- be explained by
random chance, especially since the data set is so small. We both agree
that the recession of 1938 also could skew the data.

Yes, it is highly frustrating to us because we have so little data. We can
certainly learn a lot from conductor's reports -- about cargos, destinations,
composition of individual freight trains, all kinds of operational stuff that
is wonderful to know. I have an SP conductor's book, and it's great. But I'm
just not so comfortable with trying to extrapolate a lot about distribution
of box cars in the USA from a small number of these books. I know Dave and
Tim Gilbert used a lot of other sources.

Tim O'Connor

The 201 SP cars represent 15.4% of all non-UP boxcars, whereas according to the G-N hypothesis it should be 3.3%. The expected number of cars is 44 according to G-N. That sounds like SP dominance to me, but of course it could be due to "random luck". That would make the many discussions on this list of the presumed anomaly pointless. Perhaps someone more statistically gifted than I am can tell us how likely the dominance is due to the luck of the draw.

Best wishes,
Larry Ostresh
Laramie, Wyoming

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