"Correlated" implied to me a comparison across multiple cars. It's a relationship (in this case) between two indicators "0-60 time" and "5-60 time" across cars. It doesn't work for one pair of values, like the 0-60 and 5-60 times for one car. It's an aggregate representation of how the two variables are related to each other across many instances (either a whole bunch of runs of the same car or a single pair of runs for multiple cars). As we usually don't get a whole lot of repeats of 0-60 and 5-60 runs for the same car, I had those times across a variety of different cars in mind. Now if you envision those two distributions (one for 0-60 and another for 5-60) of values gathered from a wide range of cars, it would be likely that some cars would occupy the same or nearly-the-same location on both variables (say, the highest 0-60 and the highest 5-60) while other cars might occupy substantially different locations (say 25th percentile for 0-60 but 75th percentile for 5-50). The correlation between the two variables, (that is, 0-60 time and 5-60 time) will be higher the more cars there are that were tested whose scores are in similar positions on the two distributions. If every car tested had its 0-60 score on the same exact spot on the 0-60 distribution as its 5-60 score on the 5-60 distribution, the correlation between 0-50 times and 5-60 times would be perfect (that is, 1.0). If the scores on the two distributions bore no correspondence beyond what you'd expect purely by chance, you'd have no correlation (that is, 0.0). Correlations can come about causally in one of three ways, either Variable A causes Variable B, Variable B causes Variable A, or one or more other variables (let's just call those, collectively, C) causes both Variable A and Variable B. For this situation, the likely factors determining any observed correlation between Variable A (let that be 0-60 time) and variable B (5-60 time) are effective power and weight. By "effective power" I mean something that takes gearing into consideration over the speed range in question, in additional to the total horsepower. Weight is pretty straightforward. Cars that have more power and less weight can accelerate faster, and will, all else being equal. Cars with more weight and/or less power will accelerate less quickly, all else being equal. Thus, it is no surprise that two measures of acceleration will be substantially correlated. They're being caused by the same antecedent variables. And the more variability there is in the variables being examined, the larger the correlation will be. If you take cars that typically get 0-60 times between 4.5 and 4.6 seconds, for example, the correlation between 0-60 times and 5-60 times can't be all that large because one of the variables (doesn't matter which one) has such a small range. On the other hand, if you take cars with 0-60 times ranging from 3.5 seconds to 6.5 seconds and 5-60 times with a comparable range from highest to lowest, the possible correlation can be substantially higher. another way to think about correlation is the extent that the two time "vary together" as you focus your attention from car to car. In fact, there's a thing called a covariance that is closely related to a correlation coefficient. Thinking about how two variables covary makes it easier to understand that in order to covary, the variables have to vary. If either one of them is invariant, the correlation has to be zero. if either or both are nearly invariant, the correlation will be near zero. If both vary substantially, the correlation may be (but isn't necessarily a whole lot higher than zero.
What I've called "effective power" may well be influenced by normal vs forced aspiration. In fact, it certainly is. A turbo on full boost will result in more power than with essentially zero boost. That will certainly attenuate the correlation between 0-60 and 5-60 times, which is your point. That point is entirely correct. But I still think the correlation would be substantial between the two times (although I don't have data at hand, of course). First, the percentage change in horsepower under full and minimal boost won't be vast. I'm guessing we're talking something considerably less than a 50% horsepower increase between a turbo and non-turbo version. In addition, that horsepower difference isn't in effect for the entire run. Once the turbo spools up, the latter part of the 5-60 run benefits from it. But still, your point has merit that the presence of the turbo from the get-go in one case and only later in the other (especially with launch control) is not trivial. But to the extent that either 0-60 or 5-60 time is an indicator of the capacity of the car to accelerate (which is the real variable of interest in day-to-day driving), I think either metric provides useful, although not identical information about the same underlying determining factors, l.e. the engine and the vehicle weight.
Another point worth noting is that correlation isn't the same as agreement. Two variables can never have the same value but can agree perfectly. Let's take a simple example. Imagine that you give a bunch of kids a set of blocks shaped kind of like a deck of cards. You ask the kids to make a pile of the blocks. Under condition 1 they can pile the blocks so that the broadest surface is no the table, and every subsequent block on top of it is in the same orientation. In the second condition, the blocks have to be piled so that their smallest edge is on the surface of the table and every subsequent block has to go small-edge-to-small edge, on top of that. So the two variables are "flat-side-to-flat-side score" and "small-edge-to-small-edge score." Let's call them Variable 1 and Variable 2 for now. I doubt that, for any given kid, the value of Variable 1 would equal Variable 2. It's so much easier to get more blocks into a stable pile when they're laying flat that Variable 1 should be consistently higher than variable 2. But if the kids were a really good pile-maker, a so-so pile maker, and a not-so-good pile maker, they may make the best, next-best, and worst piles no matter which type of pile you were talking about. So, the best kid would "win" with the best score on Variable 1 and the best score on Variable 2. The worst pile-maker would have the lowest score for Variable 1 and for Variable 2. The third kid would be in between those extremes for each variable. The correlation you'd obtain between Variable 1 and Variable 2 would essentially be perfect, even though for any kid, the Variable 1 score and the same kid's Variable 2 score would never be the same. what's important is not a match or mismatch but that for each variable, that kid scored in the same relative position compared to the other two kids.
I realize this is kind of technical but I think it may explain why when I said that 0-60 and 5-60 times would be substantially correlated, that may have been less than obvious. I've computed hundreds, if not thousand, of correlation coefficients on both real and simulated data and it can be surprising how little "apparent" similarity two variables need to have in order to be substantially correlated, assuming you have a sufficient amount of data. I was thinking of how these times would compare when looking over a broad spectrum of automobiles of varying performance capabilities. I think you were probably thinking about the fact that, for several cars that come to mind, the 0-60 and 5-60 times look pretty different. I think we're both right in that regard. Both those can be true at the same time. We were really referring to different things in the way we were using the word "correlation."
Sorry for the long winded and off topic reply. I just got on a roll there. I like sifting through the details of complex topics. Pleas don't view any of this as criticism or even disagreement. I really do think we're on the same page here. It just took me a while to understand the reasons for our apparent disagreement.
