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Old 02-23-2007, 10:52 AM   #50
YellowJacket
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Join Date: Jan 2005
Location: Richmond, VA
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Alright, professional statistician with a degree in engineering weighing in here...

As an engineer, I agree completely w/ Jim's points regarding the factors that could influence these results, and that when you're talking about a 1-2% gain on 4 runs, anything--even the temperature of the room from previous runs, time since you opened the garage door, or wind could come into play here!

However, as a statistician, I'd say that just because you can't model these other factors into your test doesn't mean you can't get reliable and significant results. In all probability, there is SOME correlation between output and presence of the snorkel. It's silly to say that a thousand other factors to which output is sensitive could be screwing with your test, but that the snorkel has no impact. Which is it? Is HP so sensitive that any chance can result in a different reading (in which case the snorkel qualifies as a change!), or do items like the snorkel have no impact, in which case we can discount the snorkel AND a thousand other variables. I think it's the former. But back to my point -- the fact that you can't account for all the external variables is fine, as long as you can randomize them across your trials.

If you want a decent but simple test, run this 10 times (in my line of work we'd have a couple million data points, but obviously we have to comprimise here). Each time, flip a coin, heads=snorkel; tails=no snorkel. Then model your runs using a regression w/ 2 independent variables predicting HP -- iteration # (1-10), and an indicator for the snorkel being present. Try to minimize changes, but if you think of something halfway through that you have to change (your wife calls you in for dinner and you take a 1 hour break between iterations 3 and 4), just add indicators for these events in your model. Assume everything else is random -- alternator draw, etc., because once you account for time, you've accounted for most of your unknowns implicitly.

Jim -- would the results of something like this satisfy you? Not that the increase is exactly 5.xxxx HP, but that there is an increase in the order of magnitude of 2%?
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