Quote:
Originally Posted by aurora
No, it isn't.
If the distribution is normal, about 99.5% of the observations would fall within +/- 3 SD of the mean.
You've got daily data for 24 years? About 8700 days? And the best evidence you have is just slightly over 3 standard deviations?
Get thee to an introductory statistics course.
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Thank you for bearing with me on this discussion. Following Aurora’s kind suggestion, I have looked again at reference material at
http://en.wikipedia.org/wiki/Standar...stributed_data
The null hypothesis is that Moon-planet cycles have no effect on terrestrial rain. Aggregating the 27 years of data into 29 groups of 345 days, one group for each day of each monthly Moon planet cycle, should therefore produce a normal distribution. (The actual gamma distribution of rainfall should be normalised by this aggregation process). We are looking at 29 data groups, not 10,000. The confidence intervals under the central limit theorem show that on average, one group of 345 days in every 29 will be more than ~1.67 standard deviations (SD) from the mean. Similarly, the chance that one of the 29 groups is more than two SD above average is 29/44 = 2/3 = 66%, while the chance that one group is more than 3.07 SD above average (the biggest finding in the sample) is 29/795 = 1/27 = 3.65%. This means it would take 27 random samples of dates grouped according to this method to find one result of this size. Statisticians may be able to help me consider whether both tails of the distribution should be included here – I assume not. I tested 7 samples, and found a number of significant results.
Restating the likelihoods of other Moon Planet findings listed at #13 which were above 2SD from mean, we have:
1. Uranus Rainiest Day SD = 3.07: Likelihood 3.65%
2. Uranus Driest Day SD = -2.76: Likelihood 18.8%
3. Venus Rainiest Day: SD = 2.81: Likelihood 15.7%
4. Neptune Driest Day: SD = -2.37: Likelihood 43%
5. Sun Rainiest Day SD = 2.39: Likelihood 41% (note this was adjacent to the second rainiest day with SD = 1.98)
6. Saturn Driest Day: SD = -2.13: Likelihood 58%
Correct me if I am wrong, but I would expect the products of these results would give combined probability: ie the likelihood of both the Uranus Rainest Day and Uranus Driest day occurring by chance would be 3.65% x 18.8% = 0.686%. Combining all six results above in this way give a result with likelihood of one in 9000. Significant.
I previously discussed the amplification issues in terms of the Lorenz observations of weather cycles in complex systems: see
Science and Astrology
Science and Astrology (paras 10-15) and
Science and Astrology