Robert, your results are NOT independent. They are different analyses of the same dataset, so the same outlier values may be causing the "anomalous" results in your different analyses. Your "effects" are also going to be correlated - the Moon is a common factor in all of them. And because they're not independent, you can't just multiply probabilities together. The only way you can look at multple effects is to do a multivariate analysis.

I haven't asked for your data, simply because I don't have time to look at them in detail right now. If I have time later, I'll let you know.

I'm still not convinced that the averages should be normally distributed. As I've suggested before, there is likely to be a long right-hand tail to the distributions. Plus, as aurora pointed out, because of the duration of weather patterns, your data are not independent. Have you tested your assumption of normality? How?

How were your random numbers distributed? If their distribution is not similar to your data, this comparison is worthless.

Hi everyone,

I've been reading some of the replies to R Tulip's claims, but not all of them, so humble apologies as appropriate. I have to agree that the statistics used by Robert have not and could result in fruitful results. I do think it's worth saying (as I know him as my friend) he does adhere generally to scholarly methodology.

Looking at the statistics side of things there are one or two points worth mentioning (if not already)

The original question addressed I believe was whether the daily data correlates with a cyclical phenomena of period 29? And could the identification of this correlation be amenable via statistics ?

First, I understand that Robert has grouped the daily observation R( i ) with observation R (i+29m), for m=1,2 3 ... thus forming 29 groups.

If the above is correct, then adding the rainfalls in each group, could, because of the central limit theorem result in approximately normal variates. If the original daily data are variates with finite means and standard deviation then the normal distribution should be assumed. However there are only 29 of them, so the statistical power will not be very good.

A better way (if one believed that an explanation could ever likely to be consistent with science) is to model the daily data with terms such as Day effect, (1-29), as well as regressive terms and non-normal error terms.

has not found convincing evidence of a 29 cycle - and his statistical techniques should be tightened up significantly. Also, correlation is not causation (as Robert has earlier implied). This error must wait until after good statistical tests have been made.

My emphasis above. You're right in general, but rainfall data are often highly skewed (days and days with no rain at all, and a couple of days of complete deluge). I would be reluctant to just assume normality without testing it.

Yes, it should be tested, not just assumed as I had said, but let's remember, Robert is (if I understand the methodology correctly) adding approximately 300 variates to form each of the 29 final numbers. Also, as each of original 300 numbers are separated by 29 days, the autocorrelation should be negligible. I would be surprised if the Normal distribution was not a good approximation. I did however do a QQ-plot on the 29 numbers and found rough agreement with the Normal. Not perfect, but not bad for a sample of 29. However, the roughness of the agreement does, as people have pointed out, affect the levels of significance that he has claimed, Overall it is not strong evidence of a cyclical pattern.

I understand also he used the Binomial distribution to obtain the significance levels. I'm not sure why - it would have been simpler to use the Normal. Maybe I've missed something. Of course, it would be better to model the daily rainfall, and test for cyclicity another way. Robert's statistical methodology lacks power and only has approximate levels of significance.

Peter

The random numbers were generated by replacing the Moon-Planet column described in #3 with =rand()*12-6, where rand() gives a random number between 0 and 1. This gives a column of random numbers from -6 to +6 where the empirical data gave the angle between moon and planet (with +-6 =180 and 0=0 degrees). The random numbers typically generate a standard deviation spread of 3.5 SD, whereas the real data has spread of 5 SD, a readily observable difference. If the angle between moon and planet had no effect on rainfall, the chart from this random comparator would look the same as the chart of the real data. However, there is massive evidence of regularity in the empirical data. For example, the Uranus-Moon data, which for some reason seems to be the strongest example, basically gives a straight line for the 29 points along the mean except for a massive spike up (above average rain) at U-M=10 days and a big spike down at U-M= 4 days. John, I really appreciate your help and advice, and was not asking you to do more, but I remain bemused that others are so indifferent to what is a significant scientific claim. If others had the fortitude to examine my claims, they could see for themselves that the results are independent, and not caused by the same outliers, and that this method does produce a normal distribution in the absence of planetary effects. I remain of the view that the Moon-Uranus result has chance probability of one in one hundred and fifty, so demands investigation.

Revsmile (Peter) is correct in observing that the data are normal, but he has not looked closely enough at the data to judge the statistical power, although I fully acknowledge that replication with other datasets is essential for anything approaching proof. Australian Bureau of Meteorology has all rain data available for A$194, but I cannot afford this.
The 27 years of data is sufficient to normalize this skew. Hence the fact that the biggest rain day is only 1% of total.
Peter and I discussed this autocorrelation problem, which JohnW also cites from Aurora, namely the fact that on the model of a random walk a rainy day is more likely to be followed by more rain than is a dry day. He correctly identifies that the grouping of 10003 days into 29 groups of 345 data points with each data point one month apart is sufficient to normalize any autocorrelation because rain clumping rarely lasts a month. However, Peter has not looked closely enough at the data to judge the strength of the evidence or power of the method. I previously acknowledged that the binomial method does not apply, and have not used it other than for an early illustration since recognized as incorrect. Peter seems to have wrongly inferred that the significance levels are derived from binomial method, whereas I clearly explained at #27 that they derive from the normal distribution. My reason for posting here is partly to tighten my statistics, with all constructive criticism highly welcome.

Robert,

If we form the first group of 345 observations, each one separated by 29 days, and then form the second group in the same way, everyone of the daily observations in the second group will be consecutive with an observation in the first group.

Will then the grouped data variates 1 and 2 be independent? Will they be normal?

I realize that I am questioning now my earlier claim that they were normal, but with this correlation amongst the data in different groups, the speed of convergence to the normal could be an issue.

We also know that the original data is highly skewed, probably non-stationary and autocorrelated. How good will the normal distribution and the assumption of independence be?

You seem to be using the same data for different planet-moon angles. Why are these different analyses independent? The groups would be related to each other, wouldn't they? If this is the case, you cannot keep searching thru the results, and when an unusual value pops up, claim to have an accurate significance level for it.

Also, if you are going to use mathematical terms such as "random walk", define it please, or use an accepted definition. I don't think a random walk is a good model for the daily data. In a random walk, the variance of each daily variate grows without bound.

Finally, is it your hypothesis that there is a 29 day cycle in the data? Is that it? If so, why look at any other moon-planet groupings? Why not just look at the correlation with the moon ?

Peter

This is helpful, but does not affect the problem at hand. The point is that the data may be dependent (ie the result for one of the 29 groups may relate to the result for the previous and subsequent groups), but this is irrelevant to the existence of large spikes in the data. For example, plugging the 29 data groups listed at Planets and Rain para 5 into a chart will show two non-random features – (i) a tendency for most points to be closer than average to the preceding point, and (ii) two big spikes. Feature (i) is caused by autocorrelation, while it appears that (ii) can only be caused (subject to verification) by the planetary effect.

The reason the different planetary analyses are independent is that the positions of the planets are independent – hence there is very little overlap in the data points producing the different significant results. Thank you for the clarification on use of random walk, I was familiar with its use in the context of Nile River height analysis and had not understood it necessarily involved boundless growth.

My hypothesis is not just a 29 day cycle but a planetary effect, with the base point of the lunar cycles shifting with each planet. I have already referred at Planets and Rain to the sun-moon cycle with its highly significant anomaly in rain level at the first quarter. I have now done an additional analysis using just the position of the moon against the zodiac, and while the variance appears to be less, with only two points close to standard deviation = 2, the autocorrelation was much stronger, with high and low rain during several common three day periods.

The 29 data points for the lunar zodiac cycle are: 1308.6;1517;1201.4;1141.2;1332;992.6;1035.8;1091.8 ;1232.6;1397.8;1240.2;908.4;911;948.6;1157.1;1520. 8;1389.4;974.8;1328;1179;957.8;1327;1078.6;859.1;9 07.8;935.5;1185.4;1045.6;1027.8;
And for the sun moon cycle:
1280.4;1285;1288.2;873.8;850;1096.8;969.8;1541;162 0.8;1233.4;905.4;977.8;1258;1093.8;1223.4;975.6;86 5;1293;1066.8;1257.6;922.6;1200.7;1188.4;925.8;103 4.4;1120.8;1047.5;1326.6;1410.3;

Robert,

I take it that you are saying that the presence of our moon has had, and continues to have effects on earth, and that some of these effects may be cyclical due to the orbit of the moon. A lot of things here on Earth have a cyclic nature and have periods around a month. I'm not sure how for how many, the moon's gravitational effects would be a promising direction in searching for an explanation for the cycles. There would be some perhaps. Rain is not proven, by agreement. You might care to offer some other phenomena for your theory to address.

According to my calculations, the effect of Uranus's gravity here on earth is 1/ 49 millionth that from the moon. The moon's does not appear to be that large to start with, so for Uranus, we're not even talking tenuous.

Many events are critically dependent on the inputs, so that inputs with an energy below a certain threshold do not excite the output no matter how many of the inputs are received. It is only when the threshold is reached, that the event occurs. See activation energy in chemical reactions, or electron orbital jumps.

The cycles in the gravity from outer planets are so miniscule that they could just fail to register on any large class of events here on earth.

There are different sorts of "random walks", you have to be specific in your model. If you use others results, it has to be appropriate to your own model.

The "original" random walk was the drunkard's walk--but clearly on the surface of the earth a drunkard is not going to get farther than 20,000 km away from where they start!

Those sort of limits modify your statistics. But I like to point out that the most probably position is the origin, but the most probably distance from the origin grows without bound, over time. That's not really a paradox, when you think about it. And a random walk in two dimensions is different from a "walk" in three.

Have you looked at other possible causes of the still-debated cycle? Have you checked the pollution levels during the time period? What about heat-island effects creating additional rainfall? What about airflight schedules causing additional flight at certain times, which increase the number of contrails which might effect climate? These simple, earth-bound, mundane explanations are certainly more viable then a multi-planet harmonic created over 5 billion years.

__________________
I was just sitting here contemplating the immortal words of Socrates who said, "I drank what?"

"Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot." --Carl Sagan "Pale Blue Dot"

At http://www.abc.net.au/rn/backgroundb...06/1794986.htm, Richard Dawkins comments “Our eyes see the world through a narrow slit in the electromagnetic spectrum. Visible light is a chink of brightness in the vast dark spectrum from radio waves at the long end to gamma rays at the short end. Quite how narrow is hard to appreciate, and a challenge to convey. Imagine a gigantic black burkha with a vision slit of approximately the standard width, say about 1-inch. If the length of black cloth above the slit represents the shortwave end of the invisible spectrum, and if the length of black cloth below the slit represents the long-wave portion of the invisible spectrum, how long would the burkha have to be in order to accommodate a 1-inch slit to the same scale? It's hard to represent it sensibly without invoking logarithmic scales, so huge are the lengths we are dealing with.”

My hypothesis suggests that planetary tides have a similarly hard to intuit reality, and that the sceptical suggestion that they have zero effect is based more on the emotional view, as maksutov said at Planets and Rain, that the possibility is almost obscene.

Based on standard tidal range of 0.6 metres in the open ocean, the daily planetary tidal contributions in nanometers are as follows.

Mercury 148
Venus 23,072
Mars 436
Jupiter 2,790
Saturn 95
Uranus 1.37
Neptune 0.46
Pluto 0.00002
Moon 455,906,882
Sun 144,066,575

On the model of the suggestion from the good Dr Dawkins that such difficult data is more easily understood on a logarithmic scale, we have
Mercury 5.00
Venus 10.05
Mars 6.08
Jupiter 7.93
Saturn 4.55
Uranus 0.31
Neptune -0.79
Pluto -10.91
Moon 19.94
Sun 18.79

I posit that this logarithmic presentation helps to see relative effects, considering that these effects have occurred more than one trillion times (ie every day), so their relative impact is more likely to be logarithmic than arithmetic. Of course that does not explain why far Uranus, with a log tide only 5% of that of Jupiter, has such a significant effect on the Sydney rain cycle.

A rather meagre stream made the Grand Canyon of the Colorado River. This illustration of the power of permanence is more relevant to the case at hand than events which are critically dependent on inputs with energy above a threshold. Planetary effects are more like the butterfly effect posited by Dr Lorenz, as cited at Planets and Rain

Certainly? That is a big call given that you have done no empirical study. These may well be true, illustrating that my observations are not proofs, and that testing against other datasets is needed. When I get other datasets or check the predictions at Planets and Rain I will let you know.

This makes it sound like cause and effect. All your analysis could show is a correlation. A correlation is not cause and effect - as any first year science or statistics textbook would make clear.

Secondly, the word "significant" is not correct statistically because - if I understand your methodology- you have not accounted for correlation between groups. The word is also misleading if it's used in its non-statistical meaning. Why not use the word "great" or "awesome" They would be equally meaningless.

Thirdly, while you make a good point about long term minute erosion causing the grand canyon, it is only an analogy. You have earlier implied that the small effects of the outer planets ( 10 orders or magnitude less than the moon's gravity) will somehow - because they have been around a long time - have an observable effect here on earth. I don't agree that this follows.

A result with highs and lows of the order observed in the Moon-Uranus data is seen only once in 150 (0.66%) random sets. Autocorrelation makes no contribution to this anomaly. My test of 8 datasets found several other significant statistical anomalies. These unusual results are validly described as statistically significant. I have discussed correlation between groups in observing that the independent motion of each planet makes the datasets independent, and that outliers have only a small contribution to the results. Are you just trying to wish the results away because you find them unsettling?

IF there really is a correlation, you need to explain why it exists for the Uranus set and not for any of the other planets that you acknowledge should be a much bigger influence.

Can you do that?

That doesn't make any sense at all. "Random" usually implies that a particular distribution is being used. What might be significant on the basis of one random distribution may not be significant on the basis of another.

You could however resort to the Chebychev Theorem for general results (if you didn't know much about the distribution that you are working with. (It's pretty easy: Prob { observation >= k sds from mean }<= 1/k^2. This could be used to estimate significance.

Again, could you refrain from claiming that correlation implies causality? If Event A causes both Event B and Event C , then B and C will be correlated, however they need not be causally related.

You know very well that I do not find these results unsettling. I don't even find them to be "results". What I do find unsettling however is the naive use of probabilistic arguments to claim some sort of significance.

Rgds

Peter

The aim here has been to find a dataset which would show objective planetary correlations with events on earth. The method is empirical, but the underlying goal is astrological, seeking to validate a theory of planetary influence. Results are promising but not conclusive, and indicate high value in testing against other data.

Astrology has drifted far from empirical moorings. However, its wide popular appeal and the firm conviction of its adherents justify scientific exploration of a possible underlying causal basis without prejudice. Given that planetary effects are so weak, human phenomena have largely proven too complex as a subject of objective tests for planetary correlations. My hypothesis is that weather events are more amenable to empirical study. Rain data is studied here, but temperature, humidity and pressure records would be equally worth a look.

The reasoning in this planet rain study is inductive, searching for anomalies in observed data. Deductive logic is required for proof, so this inductive observation proves nothing. Questions from BAUT have asked what deductive basis might support the findings. I have offered speculations drawing on the theory of complex systems, notably regarding entrainment of tidal rhythms. I believe this framework is coherent and possible. I personally find it elegant and persuasive, but recognise that my scientific case is as yet far from compelling.

The Moon-Uranus cycle is emphasized because its results are most unlikely out of the eight lunar-planetary cycles examined for this study. In percentage terms, total rain was 56% above average on the dates 10 days before Moon-Uranus conjunction and 50% below average on the dates 4 days before conjunction for this cycle. I believe this result has probability of 0.7%, but my statistical method is disputed.

Looking again at other moon-planet cycles in Sydney rain records from 1980-2007, the following interesting results appear:
* Moon–Lunar Node: rain is 33% above average from 7 to 10 days after conjunction and 16% below average from 2 to 6 days after conjunction
* Moon-Sun: rain is 28% above average on days 8-10 (first quarter to gibbous) and 17% below average on days 4-7 (crescent to first quarter)
* Moon-Jupiter: rain 18% below average in the week after conjunction and 16% above average in the second week after conjunction
* Moon-Venus: rain 23% above average from 9 to 12 days after conjunction and 22% below average the four days around conjunction
* Moon–Neptune: rain 24% below average from 4 to 2 days after conjunction and 16% above average from 2 to 6 days after conjunction.

These results are entirely independent of each other because the second planet in each test is totally independent of the others. The largest single rain date (327mm) had less than 1% of the total rain for the sample, and only five dates had more than 0.5% of the total, so outliers are not responsible for the findings. Autocorrelation (rain clumping) does not affect variance because each of the 29 groups of 345 rain dates includes days which are all about one month apart. Proving causality in these correlations would require a much tighter deductive argument. Additional corroborating data, especially longer time series for the same site, would also support the hypothesis. I would welcome any suggestions or help for publication or discussion of this study.

Robert Tulip