The plumbers story

by Sjoerd Visser

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The Widow’s Offering (Mark 12:41-44)

41/5 Then he sat down opposite the offering box, and watched the crowd putting coins into it. Many rich people were throwing in large amounts. 42/6 And a poor widow came and put in two small copper coins,worth less than a penny. 43/7 He called his disciples and said to them, “I tell you the truth, this poor widow has put more into the offering box[than all the others. 44/8 For they all gave out of their wealth. But she, out of her poverty, put in what she had to live on, everything she had.”

A plumbing story

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We would like to start with a quotation: A plumbing story.

There is an old story that goes something like this: A man calls a plumber to his home to solve a problem with one of his pipes. The plumber looks around and listens for about 10 minutes, and then he grabs a pipe wrench and hits a pipe three or four times in the same place. The problem is quickly solved. The plumber then hands the man his bill, and the man is shocked to see that the invoice is for $200. The man objects, “How on earth can you charge $200 for simply banging on a pipe three or four times with a pipe wrench? I demand that you clarify this bill.” The plumber takes the invoice from the man, recalculates it, and hands it back. The invoice now reads:

Item one: Hitting the pipe with a pipe wrench–$2.00

Item two: Knowing to hit the pipe with the pipe wrench–$99

Item three: Knowing where and how to hit it–$99.

If you’ve ever had a plumbing problem, and you are not a plumber, you know that doing it yourself is probably the most expensive option available to you. It isn’t what you do, and you don’t do it enough to do it well.

The art of hitting the pipe with a pipe wrench resembles the diagnostic technique of medical percussion: Tapping several times on the body surface to determine underlying structures. Percussion was first described by the polymath Avicenna, the father of modern medicine. And like so many explorative diagnostic techniques, it can be done in a rather speculative way or in a more professional way. But for a layman, the methods used by professionals and amateurs could look the same. What then justifies that huge difference in payment between them? Was it knowledge, skill and craft or just good luck that the father of modern medicine or a professional plumber based his decisions on?

Probably both good luck and skills to evaluate beneficial events were initially needed. But lucky days do not last that long, so skills and craft learned by trial and error become more important in time. For this reason the tapping and listening skills had to be replicated in time, to be refined and distributed among peers. And with growing experience under many different circumstances, by way of trial and error, clever heuristic skills could be developed to become well established scientific techniques. Wisdom relying on recently empirically found facts, and not just based on from hearing say opinions found in empirically seen obsolete wisdom books.

The important empirical question becomes: Could you really hear a distinct pattern? Had you heard it before? When and where? How well do you tap? How well do you listen? Could you reproduce your findings? When doing percussion and encountering unexpected dullness in the right upper quadrant of the abdomen, physicians tap (probe) several times in that region before they would conclude that the patients liver or some other organ residing there was enlarged. They know that a normal liver is palpable after full inspiration just below the right costal margin. They learned to grasp the human anatomy and physiology. They know when and where to look for signs. But do astrologers

But do astrologers likewise know where to look for astrological signs? An amateur astrologer scanning a horoscope for significant astrological patterns might expect to have a hit with some incidental findings. He could get many like's on Astrology Forums with remarks like: I came just across some astrological pattern and I wonder about its meaning. Like-minded astrology fans could even fill long Astrodienst Forum threads with it. Just like the Hallelujah on religious forums when somebody returned to The Lord. Coincidence does not exist. It all came true.

But without any objective and rational means to evaluate your findings, it would only be some field-dependent astrological small talk. When the observation had a small sample size, here only one particular case, it would be impossible to jump to any conclusion. As one cannot generalise or judge on the basis of just one or a few convincing cases. Even if fits your favorite theory perfectly well. Just like you cannot conclude that a dice is false after only a few throws. That conclusion would only be reasonable when you approach more and more statistical significance for that argument after many similar observations with only a few throws left...

But ADB forum members could speculate on strange, but unique astrological encounters endlessly under the wrong supposition that chance does not exist in their particular field of knowledge. As it once happened to them and other Forum members in the way described so often before by important members in astrological community. This cannot be an irrelevant coincidence, as it brings so many sense to me.

See: Coming to Terms With Coincidence | Psychology Today:

The brain abhors randomness; it seeks patterns and craves control. But understanding the world as it really is—fundamentally random—can liberate and empower us.

But there are also field independent methods to calculate the expected risks involved with a 12 sided dice (regular dodecahedron). For the as well adored and prosecuted polymath, physician, gambler and astrologer Gerolamo Cardano binomial mathematics was such a basic tool.

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. ...

The coefficient a in the term of a x^b y^c is known as the binomial coefficient or (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle.

We mentioned Cardano in our quantitative study on 79 art critics: Geronimo Cardano and the Book on Games of Chance.

Gerolamo (or Girolamo,or Geronimo Cardano (Italian:[d.e.r.lamo kar.dano]; French: J'erome Cardan; Latin: Hieronymus Cardanus; 24 September 1501 - 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler. He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the Western world. He wrote more than 200 works on science.

Recently the physicist Michael Brooks wrote an interesting book about Cardano: The Quantum Astrologer's Handbook:

The Quantum Astrologer's Handbook: A History of the Renaissance Mathematics That Birthed Imaginary Numbers, Probability, and the New Physics of the Universe Paperback – April 6, 2021

So, I would propose we should first study his ideas about our quantum reality. Ideas that were based on the triangle of Pascal and the thinking of other mathematical giants like Pythagoras: Four is all, but 1+2+3+4 sum as 10/1, a new beginning in the not yet ended sixth day.

How to use and abuse the binomial distribution to do small scale astrology research

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A simple binomial calculator as shown below is very handy for probability questions like: I have seen 12 charts of plumbers. Four of them have Mercury in Scorpio. Do we have a case for astrology? [Of course providing a single case for that argument would not be that convincing, as we deal with astrological patterns that should be visible in the empirical reality. On the many exceptions on the rule professional gamblers like Cardano could not rely in the future]

Of course the answer depends on the found and expected values. If this astrological finding would also be quite common in other professions, we would not have a case for astrology. Statisticians would say that the event might as well occur in any random sample. And this is typically the case with scores near the expected mean. But most astrologers have little knowledge of the sampling error that is involved with the many deviations around an expected mean value.

Suppose astrologers expected the following ideal values when studying 12 horoscopes.

But they ended with the following scores when studying the plumbers.

When getting values of zero, two, three or four as times as expected, when on average one case could be expected under 12 plumbers, most statisticians would not be impressed. Even though the relative differences might look impressive. The problem is that the effect size of your first throw with a six sided dice, is also six times higher than expected. As you found one case against 1/6 expected. But that would not let you reasonably conclude that the risks of the other five possibilities should be much lower. That would be a thinking error. The point is that you cannot see all possibilities in a small sampling experiment. And to effectively deal with this fact, you have to use the laws of statistics, if you like it or not.

A quick glance at the binomial distribution on the right would tell you that the risk of aselectively getting 4 out of 12 cases of Mercury in Scorpio is 1,19 % and that of the risk of getting 4 or more out of 12 is 1,19 + 0,19% is 1,38% (The 1-Cum value refers to >3, which equals to the risk of 4 and beyond). So this could be a case for astrology.

As the found value of 4 out of 12, against only one expected (effect size 4) differs more than usual from the expected values 0 to 3, being on average found in 98,62 % of cases (Cum. table). Values of 4 and more would thus be statistically significant, as they lie outside the 95% range of values around the mean that scientists regard as to be expected by chance.

But this finding could also be a case of selective attention. Noticing and discussing only what strikes you, but neglecting the many evident other usual events that did not fit your theory. Then your presented case would not be different from a randomly chosen sample, but a case of cherry-picking: Presenting a particular case that is not representative of the whole.

An irrational astrological assumption could be that plumbers solve problems with underground water pipes, so no wonder plumbers have more often Mercury in Scorpio might seem a valid symbolic explanation. But when a much larger study could not confirm that assumed to be logical association, that symbolic explanation would have no value anymore.

One question remains thus paramount when dealing with unlikely events: Could you or another astrology researcher repeat this finding? For that reason, more data would be required. Of course not in the form of more comments and likes on Facebook, Twitter, Tiktok or Telegram, but real data from another preferably a-selectively chosen sample of plumbers.

TikTok - trends start here. On a device or on the web, viewers can watch and discover millions of personalized short videos. Download the app to get started.

Actually the TikTok app has now become a tool of the Chinese Government to manipulate the masses in an easy way:

Censorship by TikTok affects material published by people on the Chinese social media platform TikTok. There is evidence that TikTok has down-weighted the posts of political dissidents, LGBTQ+ people, disabled people, and certain African-American hashtags. TikTok's explanations for this vary, ranging from attempting to protect users from bullying to algorithmic mistakes.

But let us go back to empirically found facts instead of the locally found popular opinions. When another researcher would do three more observations of plumbers with a negative result (having an expected risk of 77%, use n= 3 and p=1/12 in the calculator), the resulting score of 4 out of 15 could be expected in 2,53 % of cases and the risk of getting > 3 cases of Mercury in Scorpio would become 3,12 %. That result would not have enough statistical significance.

But astrologers could believe that chance could not exist in this particular case. As they really experienced it on their sacred astrology forum. This fitting their theory occurence actually happened and was not self-censured in their here and now kicking and alive active Forum!

What is happening here? It is called regression toward the mean. But found means do differ between particular groups. Without doubt publication of this small scale plumber study in a scientific paper is unlikely to happen, because the results could so easily be refuted by doing some more observations. Only when suspected astrological effects could be confirmed by many more unbiased observations, we could speak of trend. But readers only studying their favorite Astrological Telegraph stories could be mistaken. Just like the Christian Bible is only a fairy tail.

Regrettably, writers of astrology books seldom mention probabilities. Instead, they typically use suggestive terms like could and might in tautological statements that are always true and thus cannot be predictive. Nevertheless, doing some fact checking should not hurt. Did we see more often find Mercury in Scorpio under ADB plumbers than expected?

The ADB has a category Vocation / Building_Trades / Plumber. Here are the results of the adb_export_181128_2309 export file, which has 10 entries.

With an expected frequency np is 10/12 = 0,83, Mercury in Scorpio showed up twice against 0,8 expected (mean effect size 2,4). Moreover, personal planets in Scorpio were found twice as often than expected. But as this plumber sample is very small, it is not yet possible to statistically associate Scorpio with plumbers. Even if some astrological symbolism seems to apply. Because higher and lower values than expected happen all the time when taking small samples of a larger population. And this ADB category of 10 plumbers from ten thousands of plumbers is unlikely to be representative.

The binomial calculator

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But let us start with calculating the probabilities. You can download the binomial calculator spreadsheet used here as: Binomial_distribution_for_astrology.xlsx or Binomial_distribution_for_astrology.ods.

It has two entry fields: n = for number, denoting the number of throws with a dice or the sample size and p = for probability is, which is the probability of the event you are interested in. Here we have a sample of 10 plumbers (n = 10) with a risk that planet X is found in one of the 12 signs of 1/12. If you fill in +1/12 for p, the calculator calculates it as 0,08333 for you. But don't forget to enter the + sign, otherwise you see an error.

If you would fill in n is 1, you would get that in 91,67 % (1 - 11/12) of cases the score would be 0 and in 8,33% (1/12) of cases the score would be 1. That is obvious. But when the sample size grows, the binomial calculations become increasingly more complex and the binomial calculator will be of great help.

The binomial calculator on the right shows that the value zero for planet in sign is expected in 4,189% (Px=0) of cases. Although the frequency zero scores are lower than the expected mean of 0,83, zero is also the most likely value (mode), so you cannot simply equate individual zero outcomes with less often than expected.

We found them 34 times of the 70 counts (48%), thus only 6% more than the expected 29 or 30 of a random ADB sample of 10 (np=70*0,4189 = 29,3). Some zero values could be special, but we cannot infer which ones they are are. A much larger sample size would be required to study this. How large? You could estimate the needed sample size by filling in higher values for n: with n = 50, P(x -0) = 1,29 %, so getting a 0 would be significant at the 5% level, with n =70 the risk of getting a zero would be 0,35 %.

We might observe that 6 of the 34 found zero values were found in the water sign cancer. How special is that? We might expect the 34 zero values to be evenly distributed between all 12 signs. The binomial risk involved with this event is 3,94 % (Px=6, n=34 and p = 1/12) and P (x>5, n=34 and p = 1/12) is 5,96% .

The risk of getting a frequency of one is 38,08%. Frequencies of 1 were found 35 times (50% of 70), against 26 or 27 times expected (np is 70*0,3808 = 26,66). But because this second most likely value is so near the mean of of the group (0,83), we could ignore the found cases because of their small effect size (12/10 = 1,2) .

The risk of getting a frequency of two for a particular planet in sign with 10 throws is 15,58%. Now 13 out of 70 (18,6%) values of 2 were found against 15,58% (10,9) expected, so nothing special happened. But their concentration in the water sign scorpio is remarkable. We come back on it later.

The risk of getting a frequency of three is 3,78%. There were three cases (6%) against 3,8% (2,6) expected. They were Jupiter in Aries and Sun and Mercury in Pisces. Again water signs predominate. Frequencies of 3 or more were expected to be found in 4,45% of cases (The 1-Cum value for k = 2 or P(x>2)). That is more often than the 2,5 % statisticians would consider unusual. But getting two frequencies of 3 in one sign (pisces) is unusual, as the second case could be expected to be in another sign 11 of the 12 times.

Planets in the water sign pisces are special, as they had the largest variance, even if their 9 out of 70 score is close to the expected mean. Groups having more or less variance than expected are worth attention. So we should look at both the column totals and their variance.

The totals are the sum of 7 planets that could be in the signs above or not. In theory any sign could hold 0 to all of the 70 measured planet positions, but in practice you may expect variations around the mean value of 70/12 (5,83) for planets per sign. So we can use again the binomial distribution with n =70 and a risk of 1/12 per event. See the table below.

The risk with any of the possible 71 outcomes of k is shown after Expect (value) under P(X=k). Under Cum. you see the risk of getting a value P(x < k or x = k). The values under 1-Cum are 1 - P(x < k or x= k) or P(X > k), so to get P(x=k or x > k), you have to look one cell above in the 1-Cum table.

The lowest total value of 1 is found for the cardinal water sign Cancer. P(X=1) is 1,44% and P(X=0 or 1) is 1,67%, so this finding is statistical significant. Plumbers have according to this small ADB sample less likely planets in cancer with an effect size of 1 found against 70/12 expected is 12/70 is 0,17. This is a strong and significant effect. Do we have a case for astrology here?

The second lowest value of 2 was found in Virgo. P(X=2) is 4,52% and P(X = 2 or < 2) is 6,18%, so this finding is not statistical significant. But planets in Virgo are found 70/24 times less often than expected under this sample of plumbers, having a not significant effect size of 24/70 is 0,34. This implies that you cannot be sure that plumbers always have less planets in Virgo. There could also be a small positive effect.

For statistical reasons found totals from 2 to 11 are not that relevant. They are according to the binomial distribution just too close to the expected mean to be statistical significant. And the more closer to the expected mean, the smaller their potential effect size will be.

But a found value of 11 would still be an interesting borderline case. As having a P(X=11) has a low risk of 1,72%, but P(X>10) is with 2,97% not any more below the 2,5 %. In practice it would show a high Cohen's d value, awaiting more studies to be done.

For Libra and Pisces we saw the value 9. Nine has the not that impressive effect size of 9*12/70, or being 1,54 times more often found than expected. The risk involved with is 6,24% and values of 9 or more could be found in 12,67% of random ADB samples, so statisticians would not be impressed. But the counts of the balanced Libra had much less variance (0,20) than that of the unpredictable water sign Pisces (1,35). And that could again be a case for astrology, though astrologers might formulate it different.

The water sign Scorpio had 12 times planets in it, against 70/12 = 5,83 expected (effect size is 144/70 = 2,06, p > 11 = 1, 25% using p is 1/12 and n = 70 in the binomial). The risk involved with getting a frequency of 12 or more hits with 70 throws is only 1,25%, so one can positively associate planets in scorpio with plumbers, having an effect size of 12*12/70 is 2,1. Do we have a case for astrology here?

Statisticians would admit that getting 1 or 12 planets in sign against 6 (5,83) expected would be an unlikely finding, when a single test was done. It would be significant at the 5% alpha level and the NULL hypothesis that plumbers do not more or less often have planets in Scorpio or Pisces than just by chance could be expected, would thus be rejected.

But we did not test one hypothesis, but we looked at twelve counts for Planets in sign and found that two values were out of range. Notice that astrologers scanning a chart for peculiarities, actually do the same.

We found the lower than expected value for Planets in Pisces (1 found, effect size 0,17, risk 1,67%) and the higher than expected value for Planets in Scorpio (12 found, effect size 2,06, risk 1,25%).

We did some low scale data-mining and then significant results with an alpha of 0,05 are not that impressive any more. When doing 12 observations some 12/20 = 60% false positives could be expected against 5 % false positives in a single test. And getting two or more of them instead of the expected value 0 (54%) or 1 (34 %) would have a risk of 11,84%. See the picture on the right. So, we cannot simply state that we found AND the LOW value of one planet in Pisces and the HIGH twelve planets in Scorpio under plumbers, both being statistically significant with an alpha of 5%, so we have a great case for astrology. Using an alpha of 1% or lower would be more appropriate under those circumstances.

Another problem is that we did not deal with independents risks, see A sampling experiment without replacement in 79 art critics. It just implies that if we get a high value for Planets in Scorpio, the risk for other signs will be lower than 1/12. But this is not a big problem compared to that of data-mining.

Events with a low risk of 1,25 % are unlikely to be repeated again in small scale studies, unless plumbers really do have much more often planets in Scorpio. Again, you could use the binomial distribution to see how large a study must be to find at least one case (k > 0). Fill in p = 0,0125 and experiment with the value n to estimate the size of the study needed. P(x = 1 or x > 1) is the 1-Cum value for P(x =0), so with n is 10 it is 12% , with n is 100 it is 72% and with n is 200 it is 92 %. So when studying 200 plumbers we still had not 95% certainty to repeat one case!

But if planets in Scorpio really could be found twice as often under plumbers as our small ADB sample suggested, encountering them again would not have risk of 1/12 but of 1/6 (0,16667). The risk involved with getting P (X >11, n =70, p =1/6) is not 1,25%, but 50,7% as seen on the picture on the right. Getting twelve planets in scorpio would be a quite common under plumbers and only a relatively small study was needed to confirm it.

In all cases, it is always easier to do a single study with a large sample size than many small scale studies to proof any significant effect. If you increased the sample size to 120, the risk of getting a false negative value of 10 or lower would only be 0,37%.

But astrologers like ADB editor Richard Vetter have serious problems with the empirical rules involved with Statistics: Most of them see the sampling error involved with any astrological study as a particularity that brings in meaning, as chance does not exist in their view of the world.

Because of its quantitative view of numbers statistics are most inadequate to test the truth of astrology. The primary supposition of statistics - that accidental distributions are present everywhere - is fundamentally opposed to the astrological conception. ... In statistics particularities are systematically excluded and eliminated. In statistical testing all the things that are unique and special will fall outside of the table - though, in astrology´s view, individuality is the world´s central building-stone.

Anyway, after reading our findings an astrologer might say: As I said, I associated plumbers with Scorpio and water signs in general. So these observations could not happen just by chance. And yes indeed, astrologers who clearly predicted and published this before had a case for astrology even with this small sample size. But we are not aware of them. Of course, astrology book authors that vaguely (might, could be) associated Scorpio with plumbers could not be credited for doing the initial research, as they predicted the opposite as well.

Sadly, this is still the state of current astrology, that forgot to do the plumbers work with the plumbing tools of the 16th and 17th century again.

The problem according to most statisticians is that you cannot base a rule on incidental observations. Even if your findings were quite remarkable. You could only base a specific working hypothesis on them. And after that much more cases should be studied to make an astrological rule of it. If the found effects were large and not just by chance findings, doing some more research to confirm them is not that difficult as we saw above. Just as doing some more research, to refute false positives is not that difficult too.

If any astrologer had observed and published that plumbers had much more planets in Scorpio than expected before, then the above ADB findings could be a confirmation of that theory. But of course astrologers cannot first study the ADB, then formulate their hypothesis and after that present the same ADB findings as a proof it it. That trick might impress other astrologers, but not statisticians.

The world if full of phenomena. Some are usual for you, but most of them are not. If you would better look at the individual level, no grain of sand would be the same. You will always encounter more unusual events, if you look for them long enough. Most of the times, they just happen to exist by chance, like getting three times a six with three dices (p = 0,463 % with one attempt).

That would be an unlikely event. You could win a game with it, making the outcome even more exciting. But looking at the position of Jupiter to explain statistical rules is of no help. The empirical rules are just there. You can calculate the risks involved with it using the binomial distribution (p = + (1/6)^3) and experiment with n. Look for value 1-Cum for k =0, meaning P(k > 0). If you did 10 attempts, (n =10), the risk becomes 4,53 %. If you did 100 throws, you would encounter it at least in 37,1 % of the cases. With 1000 throws, you will see some cases in 99,0 % of cases.

But the position of Jupiter, might still explain why some people do gamble more on some days than others, like the writer Geronimo Cardano of the Book on Games of Chance did. But we cannot check the historical facts, unless Cardano kept a diary.

We Googled a bit to get astrological opinions on the astrology of plumbers. What did astrologers expect? Planets in water? Planets in Scorpio?

Discover Your Life’s Calling | Vocational Astrology| Career Astrology

Sun in the 6th house suggests having the identity of a worker, being identified with one's workplace role or trade. A man with Scorpio Sun in the 6th house was known to everyone as Todd the Plumber. Sun in the 6th house may represent a strong concern with health, an urge to purify, detoxify, and achieve maximum health. A woman with Sun-Pluto conjunct in Virgo in the 6th house is a disciplined practitioner of yoga, and is very health- and diet-conscious. Her day job is as an auditor and investigator (Pluto) for a large health insurance company (Virgo).

It is tempting to believe these by astrologers expected co-incidental observations, because they are presented in such an obvious way. The astrological symbolic associations are presented by the anecdotal story teller as a matter of fact. Referring to Todd the Plumber sounds like a real-time mythical fact. But would statisticians agree with his speculations on Todd the Plumber?

No, as single case study on Todd the Plumber would not impress them. It would be just be a case of better framing some history, without doing some serious research with control groups. In our ADB sample of 10 we did not encounter any Sun in scorpio plumber, but there is a 42% risk we missed it. So what?

Do workers actually more often have the Sun in the sixth house? No astrology book we saw ever presented any research on it. But at the same time most in astrology believers would take the above presented expectation just for granted. But are they correct?

We did not yet research this question, but we do have some ADB data on plumbers. Indeed, the scores on Sun in 4th (2 found, effect size 2,57), 6th (2 found, effect size 2,78) and the 7th (2 found, effect size 2,70) houses were at least higher than expected. The above effect size calculations were based on Using a control group to evaluate frequencies, thus not on the binomial 1/12. As they can differ a factor 2 because of fast and slow rising signs.

But do we have a case for astrology here? Probably not, as much more astrological research should be done on plumbers.

Astrologers could speculate a lot with the found variance in any sample. But when we submit the Sun in House row to a Chi square test, the value of 10,78 was found. See: chi-square.xlsx. And that tells us that in 46 % of the cases such a distribution could just pop up by chance, thus by taking some random sample from the ADB. But we admit, a little more often (54%) the found values were not as expected.

The ten plumbers of the ADB had the highest Chi square score (variation) on Jupiter in sign (14,9), then on Sun sign (11,2) and then on Mercury (10,9). Here differences mattered most. But no value was statistically significant.

That is the advantage of doing quantitative statistical research. It gives you a hint to what is more likely a rule and what is certainly not.

More interesting are the tables in binomial_limit.xlsx which shows the binomial risks in percents involved with each event. It gives minus P(x< or = k) for a smaller than expected value and P(x> or = k) for a larger than expected value.

Only a value between 0 and +/- 2,5 % would be statistically significant with an alpha of 0,05. Uranus in cancer (4 found) and Neptune in Libra (5 found) met this criterion. Getting a value of 3 or more for Jupiter in aries was expected in 3,41% of random ADB samples.

But could you predict with it? With items that have a large but not that not significant effect size? Certainly not. Even with very significant effect sizes in the order of two times as likely one cannot that easily predict as was shown in The calculation of the effectiveness of medication:

All outcomes are statistically seen huge effects: There will be no discussion about the direction of the effect, as there is minimal overlap with regards to the estimated mean cure rate. So there is knowledge as actionable information you can base your decisions on. But when doing individual predictions, there still will be a lot of uncertainty. Will the treatment work for me?

In both groups some people are cured (80 + 40 =120) and some are not (20 + 60 = 80). Most often it works with a cure rate of 80% against 40% found for placebo. That can be said. But at the individual level, predictions can only be given as possibilities. And explanations of established facts also have to take them into account.

So one cannot say to an individual person: Oh, you are cured, so you must have had the medicine (this only applies to 80/120 of them), or conclude that the not cured patients must have had placebo (this only applies to 60/80 of them). The same uncertainty exists when you interpret facts afterwards as it does when you had to predict them before. But the last is typically ignored by people who see something that fits their expectations.

And in between Falls the Shadow or Between the idea / And the reality / Between the motion / And the act / Falls the Shadow (T.S. Eliot)

Without doubt statistical techniques have become troublesome for astrologers. Just like the fact checking of journalists can be annoying for politicians. Should astrologers get rid of the ADB? Or at least exclude the more sceptical ADB editors like the annoying user ganglion? Should they try to provide more convincing alternative facts? Of course not. Astrologers initiated, maintained and are still the major contributors of Lois Rodden's groundbreaking project. But contributions from other parties - hated or not- should always be welcome. As all facts do matter.

Are then the statistical techniques used by scientists the problem? Of course not. Statistical techniques have always been used and propagated by predictive astrologers. Statisticians do not lie, they just present empirical facts where others can base their decisions on. The problem lies more in the different interpretations that scientists and astrologers give to statistical phenomena like the sampling error.

A sitting president like Donald Trump could reason: The economy flourishes. My merit! Did under Donald Trump the US economy flourish? Yes! Did he cause it? Partly, but at the expense of other things like the sustainability of our environment. So a cost-benefit calculation should also be done. As it is not simply this particular claim against so many other possibilities.

An astrologer could say: You had an accident. No wonder, when looking at your Mars transit! Was Mars responsible for your accident? That seems unlikely. As it is not simply this particular claim against so many other possibilities. The transit was just an unrelated coincidence a scientist would say. Did you study it genuinely as proposed in The relative risk of having an accident during a Mars conjunct Ascendant transit? Or did you just rely on the unproved In my opinion magic story telling of your astrology teachers?

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Replication crisis