This is close to the right idea... Here's a gedanken experiment: have a
1 dB difference in power on even vs odd minutes over a single contest at
a major station. Execute a non-parametric permutation test where the
statistic tested is the difference between the total score for even
minutes and the total score for odd minutes. The station would have to
ensure a 1 dB difference between P_out_even_minute and P_out_odd_minute
on all bands. This will yield a p-value for the difference, where the
p-value is defined as the probability that the difference occurs by
random chance. Thus the lower the p-value, the smaller the probability
that the difference is de to random chance. This way, we can test the 1
dB hypothesis with all other parameters held constant because there is
no physical reason for the score of all the even minutes and all the odd
minutes to be different. The problem could even be made band specific:
on what band or bands is a 1 dB difference most likely detectable in the
score?
This is a great gedanken experiment because it holds everything constant
*except* P_out. It would require a fair bit of effort at a big
multi-multi contest station to get the best, most definitive data set.
Alas, no major contester in their right mind would do this because they
are in it to maximize their score, not to experiment with 1 dB.
Regardless, this is about the only way the problem can be approached
while isolating all other variables.
Kim N5OP
On 5/19/2022 12:47 PM, Michael Tope wrote:
On 5/19/2022 8:43 AM, Kim Elmore wrote:
My test worked, so I'll try again...
To everyone that has commented: Thank you very much! This discussion
is fabulous!
I concede the point that statistically, there is likely to be score
improvements with 1 dB power increase and certainly 2 dB. These are
best described as statistical improvements and I suspect that the
data set has to be moderately large to detect a "significant"
difference, that is for a statistic to have much power. Thus a DXer,
who is not a contester (there are such things) probably won't notice
a significant improvement in how long it takes to break through a
pile-up with a power increase of 1 dB. Over a long run, a contester
will be able to see a score increase at with a 1 dB power increase.
A smaller data set (possibly much smaller) will show statistical
score improvements given a 2 dB increase, significant at some
arbitrary p-value.
Perhaps this is what you are getting at, Kim, but unless an operator
is switching between power levels on some fairly short time interval,
so as to create two otherwise identical data sets, I don't see how you
can get any meaningful statistics when looking at small differences in
power. Comparing previous contests or within a single contest against
another nearby station running a slightly different power still leaves
you with a lot of uncontrolled variables.
I tend to skepticism when someone says they can notice a significant
improvement given a *single* contest assuming everything else
(including the operator) is held constant. It will take several
contests to see a *statistical* improvement but I'll now bet it's
there. Fewer contests will be required for a 2 dB increase. I prefer
resampling (i.e. a permutation test) to parametric statistics simply
because parametric test assumptions are almost always violated,
leading to unknown degradations of the test's validity.
You could test this hypothesis by taking some public logs and dividing
them in two by making one log out of even minute entries and another
log out of odd minute entries and comparing the scores (QSOs, QSO
points, mults, total score, etc). That would give you some feel for
how sensitive a test would be that interleaved Pout vs Pout + NdB with
similar dwell intervals. If the score difference between odd and even
minutes in the control logs (i.e. constant power logs) was
consistently less than 10%, then the power difference in the
interleaved power difference logs would have to show a score
difference significantly greater than 10% to be considered
statistically significant.
73, Mike W4EF
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