"If a high percentage of your growing base (new users not cyclical) consists of upgrade buyers buying every 3 to 4 years (cyclical), you might interpret that this chart suggests a rather large upgrade cycle is pending, with some assumptions."
I fully agree that many of the buyers who bought in 1998-99 will be, and have been, upgrading systems. This is, after all, why sales have not gone to zero, why bladerack systems are replacing Sparcstations as servers, and so on.
But this has nothing whatsoever to do with attempting to read patterns that aren't statistically significant into charts. And if your theory is correct, why the 2-year cycle? (Answer: there are many other, more fundamental reasons, not based on chart analysis.)
"Also, if you think the odds of an upgrade buyer buying is being equated to the outcome odds of flipping a coin (essentially your words), you could be confusing a few things that are basic principles of statistics: "
No, I am implying that much the same patterns of "some up, some down" cycles will happen with coin tosses. For this particular 8-year sequence, the fact that "odd years" had "3 up, 1 down" and "even years" had "2 up, 2 down" is no more significant that if 8 coins had been tossed randomly, placed in 8 boxes blindly, then four of the boxes had been marked "odd" and four marked "even" and then the boxes opened. "Look, the odd boxes had 3 heads and 1 tail but the even boxes had 2 heads and 2 tails. This must mean something."
Now do you understand the coin-flipping point, and the related null hypothesis?
"RE: "Poisson distribution"
"You're talking about a distribution pattern within a cycle (which is completely different than discussing economic patterns that stretch between the cycles).
Take another look, the distribution under an individual graph looks more like a Gaussian distribution than a Poisson distribution. Mean > 30 . . . "
No, the Poisson applies when one asks questions about _small numbers_ and the fluctuations are some expected value. If there is no correlation between up and down and odd or even, which is our working null hypothesis until disproven, then the expected result is "2 up and 2 down" for either the odd years or the even years. Of course, nature will not be so kind as to conveniently make this come out to the "expected" number, so we get things like the Poisson distribution.
There are two ways to do this calculation: straight permutations and combinations, as in hands of poker, or with Poisson's distribution.
I'll do the calculation for the Poisson, understanding that we're bounded on the upside to a maximum of "4" (we can see only a maximum of 4 ups or 4 downs in either the odd or even year sets).
Given that we expect, based on probability calculations, to see m of something, where m is some relatively small number, what's the chance that we'll see s, where s could be 0, or 1, or 2, etc.?
(Side note: Poisson was motivated by studies of how many soldiers in a regiment were kicked do death by their horses in any given year. Same calculation applies to clicks of a Geiger counter, when the number is small, rings of a telephone, and so on. None of these things follows the law of large numbers, because the numbers aren't large.)
Suppose there is no underlying correlation between odd years and up or down trends, or between even years and up or down trends. Then in any given 8-year sequence consisting of 4 odd years and 4 years we would _expect_ to see the odd years to show 2 ups and 2 downs and the even years to show the same. However, sometimes we will see 0 up and 4 down, 1 up and 3 down, 2 up and 2 down, 3 up and 1 down, 4 up and 0 down. How many of each of these outcomes we will typically see is given by the Poisson distribution.
If m is the expected number, and s is the number actually observed, then
P(s;m) = exp (- m) m ^ s / s!
So, if we expect to see m = 2, then the probability of seeing s = 3 is given by
P (3;2) = exp (- 2) 2 ^ 3 / 3!
= .18
Approximately. The Poisson is more general than we need here, because it admits the possibility of there being 5 ups, 6 ups, etc., (5 clicks, 6 clicks, etc.), which there can't be in our 4 odd years/4 even years example. But it's still the way to look at the problem.
"Regarding the pattern between cyles, if you don't believe in small economic cycles, the following might annoy you even further, but might possibly interest others: "
Don't misrepresent what I said. I said the correlation you claimed to have seen in the ups and downs in the odd and even years was not statistically significant. Period.
"there were large economic downturns in 1819, 1937, 1957, 1873, 1893, 1914, and 1930 - or respectively, 18, 20, 16, 20, 21, 16 years.
"Our last large economic downturn was (I think) around 1983 (whenever the auto industry went bust and almost took down the rest of the country), and loosely add 18 years to this and you get a very chilling 2001. Some think there are also political cycles too - approximately every 15 years (i.e. 15 years for the next party, which is 30 years for the next cycle) - Robert McElvaine's 80's book contained a prediction that a liberal epoch was due in the 1990s and Arthur Schlesinger made a prediction in 1949 that the next conservative epoch will begin around 1978. We could very well be stuck with Bush until 2008. "
I sure hope you're not a believer in Kondratieff Waves, Elliot Wave Theory, Robert Prechter, and all that nonsense.
If so, you're lost.
--Tim May |
