Moon Madness

There are fisher-folk who gauge the right time to go fishing with a quite terrifying exactitude. They eagle-eye watch and measure past and current weather, the barometric pressure, the type of water and even, I have heard tell, the phase of the moon. Then, with the precision of a crouched tiger, they pounce, fully tackled up, onto the right place at the right time (unlike next-door's cat, which has on several occasions pounced onto a small artfully constructed pile of dry brambles).

At least this is their plan; I assume this works for them.

Personally, I prefer the "I fancy going fishing today" approach. My ideal fishing conditions are therefore; "Whatever they happen to be when I decide to go out for a dangle." Obviously, with such a lassaiz-faire approach I never catch anything.

It occurs to me to run an experiment on one of the above exactnesses. Since 2005 I have recorded fishing trips with some precision, that is, the date, the venue, the fish caught and on what (mostly) they were caught. That is about it. Nevertheless, it is possible to extract another variable with decent accuracy, that is, the phase of the moon, by calculating it from the date. I can total up how many fish were caught during each moon-phase and ascertain if there appears to be any kind of correlation. In June 2019 I constructed this page and was then defeated by a coding error I could not work out. Picking it up again 12 months later necessitated some tedious critical problem solving, which eventually led to a duplicated variable, three file calls away from this page...buggrit...that being fixed...

If excited by this prospect, do jump right to the summaryYou'll be sorry....

Proper experimental protocol requires a number of things, especially when people are involved, as people (curse them) are riddled with cognitive biases, false memories and vested interests. Proper protocol requires:

  1. A Hypothesis; i.e. I postulate that there is some relationship between 'X' and 'Y'.
  2. Randomisation; of the subjects, the times, the data. If it can be randomised, it should be. No randomisation = 'no effect'.
  3. A Control Condition; i.e. to show that 'doing nothing' does not have the same result as 'doing the thing'.
  4. An Underlying Mechanism; is desirable; some sensible credible idea about how 'X' might be affecting 'Y'.
  5. Falsifiability; is very desirable; i.e. the ability to show a hypothesis is false. If a hypothesis cannot be shown as false, it is generally not possible to show it is true.

So, some exposition on the preceding:

A Hypothesis: This must be formulated before one starts and it needs to be testable in some way. Post hoc hypotheses are not valid, as they are literally fitting a theory to the data. Essentially, this is looking at data and deciding that some natural or random variation means that there is an effect, then fitting the hypothesis to it. This is no more valid than fitting a hypothesis to the number that comes up when you roll a dice.

One might propose "There is some positive relationship between each phase of the moon and the number of fish caught by JAA.". OK, this is technically eight hypotheses. A moment's rational thought will show that this is not the way to go...

I did some research. Well, we can call it 'research'. Quite a lot of folk seem to think the full and/or the new moon phases are most efficacious for fishing. So the two hypotheses to be tested here are:

"There is some positive relationship between the new moon and the number of fish caught by JAA."
"There is some positive relationship between the full moon and the number of fish caught by JAA."

Randomisation: Using data collated 'for funsies' 'whenever I happened to be fishing' adds a certain amount of randomisation (with respect to the moon's phases) especially as, perforce, my fishing was and is mostly at week-ends. I certainly was not considering the phase of the moon as a factor in any kind of deliberation, or in fact engaging in any kind of deliberations at all. So, although the reader will have to take the author's word for it (as this is technically 'anecdotal'), for this page, it is reasonably fair.

Essentially my fishing trips timings were dictated by a combination of whim and mostly only being free at week-ends. Kinda random.

Control Condition: this verifies that 'doing nothing' does not have the same outcome as 'doing the testable thing'. In other words a non-manipulated condition, kept in the same conditions as the experiment, but with no experimental manipulation applied. In this instance, this suggests that catch rates would need to be evaluated with 'no moon present'. Which is tricky.

One might divide the fishing trips and their catches into eight random piles and see how that looks, as long as one states one's hypothesis first. However, one would have to take many, indeed all possible such groupings, then look at the likelyhood of any actual catch rate with respect to the moon-phases, with respect to how often it might emerge by chance...if only there was some kind of test for this analysis of variances...

Underlying Mechanism: With no proposed underlying mechanism, one cannot take an apparent correlation and move from ['A is coincidental with B'] to ['A causes B'], and then possibly move from a hypothesis to a theory. Becuse, with two correlated variables it could be the case that:

'A' may cause 'C', which in turn causes 'B'.
'C' may cause 'A' and 'B'.
'B' may cause 'A'.
'A' may cause 'B'.
There may be an 'X'. It just is not possible to say...

Anyhoo...an underlying mechanism? No idea. Something...something...something tidal? *waves hands in mysterious way*

A quick look at tidal forces. It is the case that the Great Lakes in Canada rise and fall less than 5cm as a result of the moon's gravity. Lake Superior is 11,000 Cubic Km and let us allot this fine body of water a generous 5cm 'tide'. Pete's Upper Pond is 100 m × 40 m × 1.5 m = 6000 Cubic Metres. As a working estimate, the tide on Pete's Upper Pond is around:

(6,000 / 11,000 × 109) × 5 cm = 2.72 × 10-11 m

To give this some perspective, 1.2 × 10-10 meters is the diameter of one oxygen atom. So our 'tide' to which we ascribe an effect on fish catches is in fact smaller than the diameter of one oxygen atom (by ten times) on a one acre pond. I would suggest this is not a factor...

I poked around the interweb and found three more possibles. The first is that light level at night might make a difference to catches. I assume 'if it is not cloudy' and the impact during the day would be 'negligible'. The second, which I quite like, is that insect hatches are known to be linked to moon phases and the fish are reacting to these. This seems worth exploring. The third is that the moon affects weather and this in turn affects the fish. This seems feasible, but would need careful examination, as weather is also at the behest of many other (confounding) factors, some of which are global and some of which will be local (e.g. the orientation of the venue and its topology).

Tidal reaches of rivers might be a different kettle of, er, fish and I would even find it plausible that a still water near the sea, such that the local water table might rise and fall due to tidal forces (albeit 'out of phase'), could possibly change its character in sync. with moon phases. I would not rule out a full moon with clear skies affecting the behaviour of sight hunting predators, for obvious reasons.

The potential insect hatch mechanism is interesting. I found this: "THE RELATIONSHIP BETWEEN LUNAR PHASES AND THE EMERGENCE OF THE ADULT BROOD OF INSECTS" (NOWINSZKY, PETRÁNYI & PUSKÁS. 2010), which clearly shows that the moon's phase affects insect hatches. From the abstract:

"We have found that the emergence of the adult brood of several Macrolepidoptera and Coleoptera species is associated with a special lunar phase, most often with the Last Quarter.

Do not get too excited...to make something of this, one must first postulate the fish are easier to catch when insects are hatching, or are harder to catch as they are pre-occupied with emergers, which can also happen. Pick only one...

Falsifiability: This is important. It is very desirable that the null hypothesis can be tested, that is, a possible outcome can be identified that conflicts with predictions deduced from the hypothesis. In this case, this would be to design an experiment to show that the full and new moon phases do not affect catches. If this cannot be done, then the hypotheses cannot be meaningfully tested and a meaningful conclusion cannot be drawn from basic observation.

This is where things start to become problematical - to make such an experiment, one has to account for all of what academics like to call 'confounding factors'. That is, those things (which are independent variables) that also might affect the catch rate (the dependent variable of interest) irrespective of the phase of the moon (the independent variable of interest). There are plenty of 'confounding factors'; here are just some I can think of:

• Distance of the moon from the earth.
• The moon's presession, both nodal and apsdial.
• Variance in baits used and their effectiveness.
• Venues' stocking levels.
• Angling pressure on the venue(s).
• JAA's intentions on the day.
• JAA's competence on the day (varies wildly).
• The method and tackle in use.
• Time spent actually fishing on the day.
• The weather on the day or immediately preceeding.
• Water temperature.
• Air temperature.
• Relative humidity.
• Light levels.
• Dissolved oxygen.
• Air pressure.
• Wind speed and direction
• Whether one thinks the phase of the moon matters.
• Whether JAA himself is influenced by the moon; i.e. I am justanotherwere-angler.
• Luck

With some confidence it can be stated that I have not eliminated these factors. In fact there are so many confounding factors, it would be impossible for anyone to quantify all these factors and design a control experiment to eliminate the phase of the moon as a factor, in order to argue the hypotheses are falsifiable. On this basis alone, this is pseudoscience at best.

[The Austrian philosopher and scientist Karl Popper (1902-1994) introduced the concept of falsifiability in his writings on the demarcation problem, which explored the difficulty of separating science from pseudo-science, i.e. the ability to prove one's hypothesis is false. If one cannot prove something is false, it is not generally possible to prove it is true. This defence is the first refuge of the charlatan. Of course one cannot prove there is no yeti. Of course it is possible there is. It is also possible all the molecules in the hostess's underwear will simultaneously leap three feet to the right, something that is about the same level of 'possible'. It is not clever to conflate 'possible' and 'likely'. It is downright snidey to do it in order to take money from people. But I digress...]

In any event, as I have some 500+ records of fishing trips, I will still take a look at the data.

Methodology

As previously alluded to, in each record I mostly note the species and quantity of fish caught during any one trip. However, if a species is numerous and/or I cannot be hedgehogged, then I simply note, e.g. 'perch = lots'. I might, on the same trip note 'roach = 5', or gudgeon = 'lots', or 'bronze bream = 7'. Or all four of those during the same trip. This means if one wished to calculate the number of fish per trip to determine an average catch, one of several options might be considered:

Option 1: For each record with a 'lots' entry, simply ignore this entry, while still counting the fish that were counted (as it were). This will consistently under-report fish numbers, specifically when the catch was high. Probably not ideal.
Option 2: Completely discount any record where 'lots' were recorded for any species. Reduces the sample size. Skews data set towards small catches.
Option 3: Include all records and use 'some number of fish' for each of the 'lots' instances, e.g. '5' or '10'. This looks like the best option.

An engine was developed to examine each fishing record, count the number of fish, work out the moon's phase for said record, then add the record's 'number of fish' to a running total for each phase. Then, the engine divides the number of fish for each phase by the number of trips taken during that phase to produce a mean catch. Additionally the totals for 'all of the fish' and the 'mean fish count per fishing trip' are calculated.

This 'engine' and any modifications to it were verified against two years' records (2005 & 2006), for which I 'mandraulically' produced verified counts for: 'fishing trip records', 'number of fish', the number of records with 'lots' instances and number of 'lots' instances.

The outputs are be an average number of fish caught per trip during each phase. So any relationship must be based on any statistically significant difference between the means of the samples for each phase and the overall mean. Which is awkward. One could perform a horrifying statistical analysis to establish whether any such result is sufficiently unlikely to be significant that one might reject the null hypotheses and say with a numerical confidence, that the results support the hypotheses. This is done by looking at all the possible average values from the overall samples and establishing if the variance of the averages is significantly outside the likely variance in these average counts...in short an analysis of variance. Or 'ANOVA'. I both lack the tool to do the analysis and the will to extract and enter all the data in an appropriate form. In short, 'not currently hedgehogged'...

...I am, as it is my experiment, going to side with Rutherford, who more-or-less said, that if one needs statistics to see an effect, then one ought to design a better experiment. So the output will be an easy-to-read table of 'each of eight phases of the moon' vs. 'number of fish', mean number of fish per phase and notation indicating the deviation from the overall mean catch rate.

These are: 'new', 'waxing crescent', 'first quarter', 'waxing gibbous', 'full', 'waning gibbous', 'last quarter' and 'waning crescent'. By a lucky coincidence, these are also the outputs of a 'php' algorithm that derives the phase of the moon from the dates in question.

I took the trouble to verify this algorithm by calculating the moon's phase for a sample of dates from each year in the data then verifiying theem against a number of reputable 'moon phase' caculating web-pages.

The current moon phase is: 'waning_gibbous'. Here's a picture:  A moon phase

For reference:

A moon phase   'New'
A moon phase   'Waxing Crescent'
A moon phase   'First Quarter'
A moon phase   'Waxing Gibbous'
A moon phase   'Full'
A moon phase   'Waning Gibbous'
A moon phase   'Last Quarter'
A moon phase   'Waning Crescent'

So, 'one piece of coding with considerable de-bugging' later...

Option 1 - All Fishing Records, Discounting Instances of 'Lots'

Summary

The number of records parsed is: 1157. Should be unvarying, allows a simple cross-check against file-count.
Number of fishing trips processed: 645.
The total number of 'multiple uncounted catches' instances was: 404.
The total sample size (N) for this option: 645.
The total number of counted fish caught is: 3185.

Moon Phase Trips Fish Mean No. Fish +/-
New Moon A moon phase 71 318 4.5 -0.5
Waxing Crescent A moon phase 74 303 4.1 -0.8
First Quarter A moon phase 86 544 6.3 +1.4
Waxing Gibbous A moon phase 75 488 6.5 +1.6
Full Moon A moon phase 90 486 5.4 +0.5
Waning Gibbous A moon phase 75 294 3.9 -1.0
Last Quarter A moon phase 91 415 4.6 -0.4
Waning Crescent A moon phase 83 337 4.1 -0.9
Totals 645 3185 4.94

*modifies code* ...*verifies code*

Option 2: Discount Any Fishing Record with Any Instance of 'Lots'

Summary

The total number of records parsed is: 1157.
Number of fishing trips processed: 645.
The total number of records with at least one 'multiple uncounted catch' is: 211.
The total sample size (N) is therefore: (645 - 211) = 434.
The total number of counted fish caught is: 2585.

Moon Phase Trips Fish Mean No. Fish +/-
New Moon A moon phase 53 295 5.6 -0.4
Waxing Crescent A moon phase 51 247 4.8 -1.1
First Quarter A moon phase 60 351 5.9 -0.1
Waxing Gibbous A moon phase 45 402 8.9 +3.0
Full Moon A moon phase 57 404 7.1 +1.1
Waning Gibbous A moon phase 51 255 5.0 -1.0
Last Quarter A moon phase 63 355 5.6 -0.3
Waning Crescent A moon phase 54 276 5.1 -0.8
Totals 434 2585 5.96

*modifies code* ...*verifies code*

Option 3: All fishing Records, All 'Lots' Instances Counted as 5 Fish

Summary

The number of records parsed is: 1157.
The total sample size (N), i.e. all fishing trips: 645.
The total number of 'multiple uncounted catches' instances is: 404.
The total number of counted fish caught is: 5205 ('lots' = × 5).

Moon Phase Trips Fish Mean No. Fish +/-
New Moon A moon phase 71 493 6.9 -1.1
Waxing Crescent A moon phase 74 528 7.1 -0.9
First Quarter A moon phase 86 774 9.0 +0.9
Waxing Gibbous A moon phase 75 753 10.0 +2.0
Full Moon A moon phase 90 766 8.5 +0.4
Waning Gibbous A moon phase 75 579 7.7 -0.3
Last Quarter A moon phase 91 720 7.9 -0.2
Waning Crescent A moon phase 83 592 7.1 -0.9
Totals 645 5205 8.07
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Results and Discussion

Scanning the first three options' results does suggest prima facie that something is going on. The mean catch per trip does seem to be above average for Waxing Gibbous and New phases.

Option 1: The sample consists of all fishing records, but skews the catch data away from large catches.

Number of fishing Records (N): 643
Total Number of fish caught: 3175
Mean catch rate per trip = 4.94 (quite what '0.94' of a fish is, I'm not sure...)
New Moon mean catch rate per trip: -0.6 less than overall mean
Full Moon mean catch rate per trip: +0.5 more than overall mean

Option 2: The sample consists of all fishing trip record with multiple catch records discounted. This skews the data by removing predominantly larger catches. Lower sample sizes are generally worse than large ones. There are fewer fish overall but the sample size has dropped considerably, so a higher mean is not unexpected.

Number of fishing Records (N): 432
Total Number of fish caught: 2574
Mean catch rate per trip = 5.96
New Moon mean catch rate per trip: -0.5 less than overall mean
Full Moon mean catch rate per trip: +1.3 more than overall mean

Option 3: The sample consists of all fishing records and is arguably the least skewed data set, with a 'reasonable' average 'lots' catch set as '×5' fish.

Number of fishing Records (N): 643
Total Number of fish caught: 5175
Mean catch rate per trip = 8.05
New Moon mean catch rate per trip: -1.2 less than overall mean
Full Moon mean catch rate per trip: +0.6 more than overall mean

If the last option is taken as the 'best data', then it looks as if there is some weak support for the hypothesis concerning the full moon. It also might look as if there is a pattern emerging, with fish catches in the First Quarter, Waxing Gibbous and Full Moon being above the mean. However, there are eight phases here, the common descriptive ones. If the data was repeatedly randomly scattered into eight piles, on average four would above the mean and four below and a 5/3 split would be a quite common occurrence. With a single data set it is the case that the 5/3 split in Option 3 above is not necessarily significant.

For interest, if, for Option 3, the 'number of fish' assigned to a multiple catch is changed to '1 per' or '10 per' the new and full moons phases stay stubbornly below and above the mean, respectively.

Running an ANOVA is still an option and if this showed the variance in the means is statistically significant (p < .05), one might be tempted to think this 'proves' the hypothesis. No it would not. In the first place, one only supports a hypothesis. In the second, the inference of a statistically significant ANOVA output is really more like;

"If proper experimental protocols have been observed, data appropriately randomised, the sample size is significant, samples were all taken under the same conditions and all confounding factors are eliminated or accounted for, then is it likely that there is only a 5% (or one chance in 20) chance of getting this result if the null hypothesis is true".

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Summary

It does, at first glance, look as if something may be going on in the run up to the full moon and an ANOVA might provide an indication of statistical significance. However, even if this were the case, it still does not satisfy the conditions required for good and meaningful science.

There is a hypothesis, but no falsifiability, an inability to run a control, the randomisation is pseudo-randomisation in this context, there are numerous confounding factors, some of which are cognitive biases, to ever be able to assign any effect to just the phase of the moon. Further there is no credible underlying theoretical mechanism at this point, although insect hatching is promising and feasible and disassembling the data further and looking at those phases when insect hatches are greatest might be suggestive. I may yet do that.

Then there is 'repeatability'. That is, even if the statistical analysis of my data showed a significant skew, the experiment would still need repeating with another data set. In simple terms, a significant level of p < .05, means that there is a 1 in 20 possibility that this result is a fluke. A repeated result with the same level of confidence raises this to 1 in 400, and a third result raises this to 1 in 8000. One significant result is almost meaningless in the real world. Especially when people are part of the independent (and confounding) variable set.

I am aware some people swear by such things. There is much magical thinking...is the belief that unrelated events are causally connected despite the absence of any plausible causal link between them... in angling, this is part of its charm, but that does not mean it actually works. In the same vein, self-report catch rates of something with so many confounding variables, along with the affects of confirmation biasThe tendency to search for, interpret, focus on and remember information in a way that confirms one's preconceptions., rosy retrospection...refers to the psychological phenomenon of people sometimes judging the past disproportionately more positively than they judge the present., illusion of control biasThe tendency to overestimate one's degree of influence over other external events., illusory correlation biasInaccurately perceiving a relationship between two unrelated events., salience biasThe tendency to focus on items that are more prominent or emotionally striking and ignore those that are unremarkable, even though this difference is often irrelevant by objective standards. ...and so on, reduce such evidence to 'anecdotal' that is 'anecdotes' or stories.

If you try and fish mostly during a full moon, then most of your fish will be caught during the full moon.

"Well, you know, some people believe that they're Napoleon. That's fine. Beliefs are neat. Cherish them, but don't share them like they're the truth." ~~  Bill Hicks ~~ 

The only certainty is, that if one is by the water then there is a chance. Fishing rituals, much like the rituals of padding up and twiddling your bat, feel good and perhaps reduce uncertainty as 'that time before when you did it' you made runs...but proper footwork, a clear mind and a straight bat is far more efficacious...on average.

In any event, I find that neither of my hypotheses are supported by the above analysis.

Moon madness, pfft *waves hand dismissively*

"One cannot do science with independent variables held constant or allowed to vary without measurement. Astronomy did not progress by only observing dependent variables. It was the measurement and correlation of both that led to progress. Relying on anecdotes, no matter how numerous, fails to specify any value of the independent variable, or the intentional state of an animal. The plural of 'anecdote' is not 'data.'" ~~  Irwin S. Bernstein ~~ 

(The interested reader may care to note that exactly the same issues dog the notion of 'HNV Theory'; firstly this is a hypothesis [not a theory], and secondly, cannot ever be properly supported by fishing data, as there is the same preponderance of confounding factors as for moon-phase and catch-rate correlations. The almost embarrassing ease with which carp can be caught on a cut white sandwich loaf, also holes the HNV hypothesis below the waterline.)

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Post Hoc...

A final point. I had this bright idea in March 2019 and abandoned the original engine due to an annoying (already alluded to) code error in July 2019 or so. I fixed it, got it working and verified during May 2020. So the above tables only cover 2005-2019, that is, before I ever thought of this or saw any verified output. The below table covers 13th May 2005 to 3rd December 2020. It will be interesting to see how the numbers change as I fish on. In June 2020 I hypothesised the average catch rates for each phase will tend towards similar numbers. If my fishing behaviour changes and I start to fish tidal rivers and/or the sea a significant amount, then I will have to factor that in later.

For this, the 'Option 3' conditions (above) are used; that is, each instance of 'lots' of a fish is counted as '5 fish', as this seems the best way to get the data as solid as possible.

Another good reason to keep this running is that there is a cycle of moon phases, the 'Metonic cycle', after which the phases of the moon recur on the same day of the year. This takes 19 years, so if this last table runs for the next three years, any skew caused by the phases of the moon not being evenly distributed on week-ends, which is the bulk of the samples, may even out.

Today, is the 3rd December 2020.

The current moon phase is: 'waning_gibbous'. Here's a picture:  A moon phase

Summary

The number of records parsed is: 1261.
The total sample size (N), i.e. all fishing trips: 677.
The total number of 'multiple uncounted catches' instances is: 409.
The total number of counted fish caught is: 5558 ('lots' = × 5).

Moon Phase Trips Fish Mean No. Fish +/-
New Moon A moon phase 76 517 6.8 -1.4
Waxing Crescent A moon phase 79 618 7.8 -0.4
First Quarter A moon phase 92 809 8.8 +0.6
Waxing Gibbous A moon phase 77 803 10.4 +2.2
Full Moon A moon phase 93 838 9.0 +0.8
Waning Gibbous A moon phase 79 589 7.5 -0.8
Last Quarter A moon phase 96 756 7.9 -0.3
Waning Crescent A moon phase 85 628 7.4 -0.8
Totals 677 5558 8.21

So the above table has the figures from 13th May 2005 (the incept date for the diary) to 3rd December 2020.

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Can you say; "Regression to the mean"?

Can you say; "Waxing Gibbous?"

JAA