Re: Box/auto distribution 1938
Tim O'Connor
Larry
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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. GN 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 nonUP boxcars, whereas according to the GN hypothesis it should be 3.3%. The expected number of cars is 44 according to GN. 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. 
