Re: Pattern matching with statistics
- From: junk5@xxxxxxxxxxxxxxxx
- Date: 24 Feb 2006 02:39:35 -0800
If I have a set of random data, which could be the result of rolling a
6 sided die 1,000 times, and the die is favored to rolls 2 numbers more
often than the others, how do I analyze the data to determine which
numbers it favors without knowing in advance that it favors any of the
numbers?
A simple approach to this involves performing a Chi^2 hypothesis test.
Your null hypothesis would be that the distribution underlying your
sample is the same as the 'fair' distribution. So, in the case where
you have samples drawn by throwing a single 6-sided dice, your null
hypothesis would be that there is no difference between the
distribution underlying the samples and the discrete uniform
distribution for 6 values (i.e. the numbers 1-6 each have probability
1/6). By choosing an appropriate significance level, you can then work
out if it is likely or unlikely that the two distributions are the
same.
So this will tell you if it's likely that some numbers are favoured
over others, but it won't tell you which ones. You cannot just look for
the most common number(s) in the sample, as you need to know which ones
are statistically significantly more common. You might want to think
carefully about whether this is what you want or if the answer obtained
from Chi^2 will solve your problem.
Normally the gamblers fallacy ... [snip]
I think you're misusing this term here. The Gamblers Fallacy is the
phenomenon that you see in gamblers where they think that an event that
in reality has a fixed probability is more or less likely if that event
has recently occurred. In you example, you seem to be talking about
"sampling without replacement". In this kind of sampling, it is events
that have not happened yet that become more probable (and eventually
inevitable when there is only one item left to be sampled).
Lets say for this example that the machine is programmed to never
produce the same number twice, until it has randomly generated every
other possible number. Is there a way to predict this is happening by
looking at the data?
I'm not sure exactly what you mean here. Here's some possibilities:
i) You have a sample of data, you know the order in which each datum
was generated, you know the data should have been generated by sampling
without replacement and you want to know if the data was indeed
generated in that way.
ii) You have a sample of data, you *don't* know the order in which each
datum was generated, you know the data should have been generated by
sampling without replacement and you want to know if the data was
indeed generated in that way.
In case i) it should be very simple to rule out sampling without
replacement if you know the range of values that can be sampled and
have a large sample. If you see the same number twice before all
possible numbers have been sampled, then sampling without replacement
cannot be happening. You will need to think carefully about the case
where you only have a small sample though.
In case ii) you may also be able to rule out sampling without
replacement by considering the probability of a given value occurring
in the size of sample that you have.
.
- References:
- Pattern matching with statistics
- From: virtualadepts
- Pattern matching with statistics
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