The astrological profile of 1867 ADB astrologers

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Observed values

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Do astrologers according to the AstroDienst database (ADB) differ from the rest of the ADB population? Here are the facts based on the adb_export_181128_2309 file of Nov. 28, 2018. There were 1867 entries in the ADB category Vocation / Occult fields / Astrologer. How were they defined? You can find the used documents in the directory astrologer of adbstats.

Many more gigabytes of statistical ADB data can be found at astrology-research.nl, a website hosted in a mini PC in my fuse box. But few astrologers seems to be interested in statistics. So the website did not run out of resources. Evident lies and subsequent quarrels on Twitter and other social media do adsorb much more bandwidth. But nobody seems to be interested in studying the facts.

But let u now present the in the AstroDienst database found facts.

The found values constitute a lot of data, so let us focus on what most astrologers would think that are the most important factors in the chart: Sun and Moon sign and ascendant.

When assuming a risk of one in twelve, 1867/12 is 155,6 would be the expected value. Sun in Leo (156) scores as expected, having an effect size of 1,00.

Sun signs range from 141 for Sun in Virgo (effect size 0,91) to 184 (effect size 1,18) for Sun in Aquarius.

Moon signs differ less having a range of 141 for Moon in Scorpio (effect size 0,91) to 172 for Moon in Aquarius (effect size 1,11) again.

The Ascendants of astrologers differ most from 94 in the fast rising sign Pisces (effect size 0,60) to 209 found in the slow rising sign Leo (effect size 1,34). But to compare the houses, effect size measurements using control groups should be done, as the to be expected scores in fast and slow rising signs differ more than a factor two.

When using the whole ADB as a control group, not that impressive effects were found for the ascendant. Most effect sizes just fall within the 70 % found values range of a random ADB sample of that size (0,92 - 1,08 or just + / - 8 % away from the expected mean). Statisticians would thus not be impressed.

The effect sizes of Sun and Moon signs did not change that much. So, the Aquarians are still the winners of this who is who in astrology contest and the earthly Taureans and Virgo's are scoring lower. The Airy Sagittarians score the best at the Ascendant, but not that impressive.

You may interpret the effect size of 1,12 that getting an Aquarius Ascendant is 12 % more likely under astrologers in this version of the ADB. And the Taurus ascendant (effect size 0,88) is 12 % less seen with astrologers in the ADB. But the standard deviations suggest that we deal with a normally distributed pattern around a certain mean.

According to statisticians we should ignore the found differences as statistically seen irrelevant. As deviations around the expected mean up to +/- 15 % could be expected in 95 % of random samples of this size (n=1867) taken from the ADB. So statistically seen nothing special happened here.

What would be seen if we combined the effect sizes? If the risks involved with Sun, Moon and Ascendant in sign were independent, we could multiply them to get the combined risk or effect size. Below we calculated the risk of becoming an astrologer when having sun, moon and ascendant in the same sign.

The product scores are more interesting. The Earth signs Taurus (0,75 and Virgo (0,77) score again low, except for Capricorn (1,01). Water signs score somehow higher in Cancer (1,14), but not in Scorpio (0,92) or Pisces (0,98). Fire signs Sagittarius (1,28) and Aries (1,24) score higher than expected, but Leo (0,87) does not.

So people having a combined Sun, Moon and Ascendant in Sagittarius or in Aquarius are more likely to become an astrologer, whilst Earthly people having these planets in Taurus and Virgo are less likely to do so. But the effect sizes are still too small to predict or explain an individual astrologer with it. You could only speak of weak tendencies.

But are the found differences at least statistically significant? Does this combined picture of three planets in sign represents real and lasting tendencies? Probably not. As our sample size (n=1867) is too small to deal with 12^3 = 1728 possible outcomes. You cannot predict the behaviour of a 1728 sided dice after only 1867 throws.

And even when our ADB sample contained 17280 astrologers , you could expect large margins of error (> 60 % in 95% of the cases). And the found values of circa 28 % more or less (with n=1867) are then statically seen irrelevant. I explained this in my course for Dutch reading astrologers in Samenvatting en conclusie:

Stel u wilt combinaties van drie planeten in teken onderzoeken. Bij een verwachtingswaarde np = 10, moet de onderzoeksgroep 10 maal 12^3 is 17280 horoscopen beslaan. Maar de foutmarge op basis van de bemonsteringsfout bedraagt +/- 63 % in 95% van de steekproeven en +/- 80% in 99 % van de steekproeven. U komt dan uit op verwachtingswaarden van 4 tot en met 17 (95 % bi) of 3 tot en met 19 (99 % bi) die nog normaal zijn te noemen.

So the found differences of the combined effects are statistically seen not at all significant, how appealing they may seem to be to most astrologers.

Imagined values

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Suppose we were only interested in the astrological properties of the greatest astrologers as they appeared to us, because the small effect sizes found with the 1867 ADB astrologers disappointed us a bit. Indeed, our just found selection of 1867 ADB astrologers resembles astrologically seen just another random ADB sample, with most values fluctuating some 10-15 % around the expected mean. Strong effect sizes of 2 or more were not found. Maybe you expected larger effects with Sagittarius, impressive Sun-Jupiter or Sun-Uranus connections or other suggestions as found in astrology books, but they were not found.

Would studying the top ten of greatest astrologers give you a better impression? In the usual astrological way of thinking it does. As chance does not exists for individuals, the sampling error does not matter. So studying in the astrological way with eye for detail the charts of the ten greatest astrologer would be of great help. As our small sample would not suffer from the by astrologers dreaded regression toward the mean. They just do their best to overcome it.

If we would start our study with William Lilly, we might assume that great astrologers tend to have Sun in Taurus, Moon in Virgo and a Pisces Ascendant. As that was the first impression we had. But the next great astrologer we would study, would have a different astrological signature. We would see many differences as well as some similarities. And after adding the tenth great astrologer we would most likely have sun and moon in sign scores between zero and two, yielding large effect sizes, as getting a second Sun in Taurus (np = (10-1)/12 expected) already would have an effect size of 2,4. Wow! Indeed chance does not exist!

Of course you could not get the whole picture with this small sample size, as you would logically seen at least miss two (12-10=2) of them. You would miss practically (statically) seen four of them (Expect 4,19), when you only studied ten astrologers. So four of the twelve possible signs would not pop up in your personal to ten sample. But the results could nevertheless impress you. You might even perceive it as a qualitatively seen a better kind of research than that of the 1867 astrologers as explained above, as you only selected and studied your personal top ten of best astrologers. And you got pretty large effect sizes as a bonus for your wise decision to leave out the many mediocre astrologers of our ADB sample of 1867 astrologers.

You might have some problems with Vedic astrologers and other fields of astrology. As they would present you another top 10 of greatest astrologers. And researchers might complain that the “From him” birth time of William Lilly does not have the more reliable AA status. So it should not be your wise cornerstone to built your small scale research on. But if you ignored those critics, you could still be convinced that you had relevant personal experience with the subject. And indeed you had. But relevant is not the same as statistically significant or scientifically seen reliable. It is just your personal experience with it.

According to statisticians, the found results of any query would not differ that much from throwing 10 times a 12 sided dice. Values of 2 and larger (Px>1) were expected 20,03 % of cases with this sample size. Values of 3 or more (Px>2) would have a likelihood of less than 5 % (4,45 %) in a one-sided statistical test. Only values of 4 and more (Px>3) would be significant in a two-sided test with a p-value of 0,67 %. So, only effect sizes of 4*12/10 = 4,8 and higher would be called statistical significant by statisticians.

And at the lower range of expected values the value of 0 against 10/12 expected would not have any predictive value, as that value would be expected in at least four cases (41,89 %), when throwing 10 times a 12 sided dice. Could you predict another sample of top 10 astrologers with it? Probably not.

But you could share your by chance found findings on an astrology forum and could get many likes from an astrology minded audience. When? Why? Because you argued in their way, unaware of sampling issues. But of course you should not come with data that refuted their expectations. Then they would ignore you. An example of this can be found here: Venus Aspects: Statistical proof of astrological effect.

The problem here lies in your control group. What is the best expectation of the average mean. Normally it would be the combined found values in the case and control groups.

But in our study of 1867 astrologers we did not get an impressive picture, as most values fluctuated some 10 % around the expected mean of 1/12, having no predictive value at the individual level. The final result does not even resemble William Lilly's astro-signature, as his Sun in Taurus has a risk of 94 %, his Moon in Virgo a risk of 92 % and his fast rising Pisces Ascendant had a seemingly low risk of 60 % of becoming an astrologer. So if we had to ask what are the odds of William Lilly becoming an astrologer, bookmakers basing their decisions on large numbers would not bet on Lilly.

So, the astrological problem found here is that astrologers have to deal with ADB statistics that do not fit their theories. And if they correct for this by only selecting the top ten best astrologers, statisticians would tell them, that they could as well throw dices. Do we deal with lies, damned lies, and statistics? And who is the liar?

And in between Falls the Shadow

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And in between Falls the Shadow, wrote the poet T.S. Eliot in the Hollow Men:

Between the idea / And the reality / Between the motion / And the act / Falls the Shadow

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? Should they provide 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 (like svi) were also 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 argue: “The economy flourishes. My merit!” Did under Donald Trump the US economy flourish? Yes, at least for a while. Did he cause it? For his small part, 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 a matter of one particular claim against so many other factors.

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. The transit was just an unrelated coincidence a scientist would soundly argue. 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 anecdotal evidence of your astrology teachers? Just like religious people might say that God or the Devil did it, because those kinds of things also happened to occur in their sacred books. For them it would thus not be a coincidence, but an act of providence.

All those statements claim causative relations or at least meaningful coincidences. They can simply be postulated, but the predictive or explicative value of the claims involved are often impossible to prove. What about the many other factors that the proponents did not take into account? What makes the difference between a random coincidence and a meaningful coincidence? What effect size a Mars transit should have on the risk of an accident to be predictive? How could you ever determine the validity of their remarks?

Why would astrologers expect a meaningful coincidence? Because accident proneness was supposed to increase during a Mars transit according their astrology books. That could be a valid reason why astrologers would see this particular case not as random coincidence, but as case of synchronicity. The accident was expected. But then questions about the effect sizes and risks involved have to be taken into account. As even a hypothetical risk of a factor 2 or 4 more accidents during a Mars transit would not be that predictive if the normal risk of getting an accident is say one accident per hundred days. Most people (96-98 %) would then have that transit without getting into trouble. It could be a good reason to postpone a dangerous job or a tour with sixty innocent children in your touringcar. But the relative risks and their confidence intervals you need to base your decisions on (“informed guess”) are not mentioned in your astrology books. And if you could not decisively predict that event beforehand, your explanation afterwards will also have a very limited value. Actually, it would just be biased speculation, that was framed as an educated guess.

If you have a hazardous job or sport, having two to three times more risk on having an accident might increase an already high risk to an unacceptably high risk. Like bad weather could be a good reason to postpone a dangerous task. But if your risk of having an accident was low, say once in a year, having it temporarily increased to two to three times a year would probably not affect your health. Many times you had this transit before and nothing happened.

But if this text about How to Predict Accidents & Injuries were true, then even the position of the injury could be predicted!

When we have an accident or injury, we often feel blind-sided. We never saw it coming! Well, sometimes you can astrologically. First, you want to see harsh aspects (square, quincunx, opposition; conjunction by Saturn, Uranus, Neptune, Pluto) to the body part that is affected in the chart. Say someone breaks their foot - in that case, you'd want to see harsh aspects to their Neptune, 12th house cusp, or 12th house ruler, as these all rule your feet. If someone sprains their wrist, you'd want to see harsh aspects to their Mercury, 3rd house cusp, or 3rd house ruler, as these all rule your wrists. You don't need a bunch of harsh aspects, especially if it shows in their chart that they're prone to accidents/injuries in general, or difficulties with that part of their body.

So up to four outer planets should have a harsh aspect with a planet, house cusp or ruler symbolising that body part. If we use an orb of 1 degree for all four aspects, up to 2 (degrees)*4 (transiting outer planets )*6 (harsh aspects) *3 (sensitive points) / 360 = 144/360 is 40% of the chart would be at risk. If that part of the circle contained the planet, house cusp or house ruler associated with the body part, you would be in trouble. In practice that area would be smaller because of overlap, so that some small area's could have a bunch of harsh aspects and most areas of your natal chart would be spared. But astrologers could play a little with the orbs or houses systems to make the above prediction come true. And with the normally used wide orbs you could explain any accident using this method. But what would be the p-value of that prediction?

The typical defence of astrologers when being confronted with discrepancies like above, is that they deal with qualities of a higher order than could be grasped by statistically oriented people. And of course most astrologers like this kind of framing of the world of astrology. But is this a good reason to keep believing in the we know it better and ever rules of astrology? How would you explain your astrological rules to your students? Or to your children? How would you define them? What should they have to learn?

See: Qualitative versus quantitative approaches in astrology

The qualitative approach, especially that of astrological symbolism, is easy to learn, flexible to use, amusing and exciting, but has little predictive value. Explanations done with it can look very powerful, but what astrologers call the synthesis of the complex chart to come to the essence of it, too often resembles the process of framing: Those who use a frame try to influence the way others look at reality through words and the images and feelings they evoke. The frame becomes a pair of glasses through which we see certain information and not others.

The quantitative approach is a not that easy to learn, amusing and exciting as the qualitative method. But it suffers less from selective attention and can be really predictive if large control groups are used. Using statistical analytical methods, you can even predict that under certain circumstances you could not predict anything! And that great feature could spare you a lot of time. No need to speculate, no need to procrastinate at night.

When astrology books use vague terms as could or might to hint to expected correlations between the above and below, they could and should be replaced with more predictive effect sizes and confidence intervals. Then the actual found data and effect seizes could be rather comforting when confronted with your supposed to be difficult Pluto transit.

An expected mean is just an expected mean, but quite often in astrology as well in other branches of irrational thinking that expected mean is a by tradition coloured opinion. But if you wanted to predict with it statements like Aries people tend to be more aggressive, you should find your suppositions back in the Aggressive ADB category. Empirically inclined ADB editors added typical cases to show you the way.

The sampling error

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What we encountered with our top ten of greatest astrologers was the sampling error, which always happens when you only study a part of the population instead of the whole population. But most astrologers and other believers in supernatural things have difficulties with statistical rules. They believe that chance does not exist when they encounter things that fit their expectations. They imagine that they then see things more clearly that others.

But their initial thrill when only having studied some small samples, or doing “my own low-key empirical research” as Sue Tompkins named it in Aspects in astrology, is likely to disappear when they would study larger samples. Because then they would see the by statisticians expected regression towards the mean. Only with the moral help of a lot of other astrologers (Yes Sue, you can do it!), probably also doing some poorly designed small scale research, Sue Tompkins could finish her book.

But what is the value of an astrology book where all possible aspects almost by magic do fit astrological symbolism, but no account of the research methods, found effect sizes and their confidence intervals is given ? Where is the actual research? Did Sue Tomkins report on found facts or only on her expectations? I am afraid she studied foremost the last. As it is rather difficult if not impossible to empirically study the effect of one aspect in the light of the whole chart. To do so, the complexity of the whole chart should be analysed in terms of known probabilities. But astrology books do not provide that kind of information. Astrologers only give vague symbolic clues. But with this associative garbage in, garbage out technique, astrologers can only repeat their belief in established aphorisms, which they joyfully present to you (I saw it again!) as groundbreaking qualitative research. But only from their small and biased point of view.

In what most people regard as reality there are two major exceptions, where we would not expect to see a regression to the population mean with larger sample sizes. First, when there would be some real categorical astrological correlation, like having Sun in Aquarius seemingly predisposing to astrology. Aquarius deals with groups, so current astrologers might be more inclined to group thinking, though they classically see themselves as independent philosophers. And to find out if there has been a shift in time from one dominating sun type, subgroups of the 1867 astrologers could be studied. But when using smaller study groups the sampling error will increase dramatically.

The second instance in which we do not expect a regression to the mean with a larger sample size is some form of bias. The negative effect size of having a Pisces ascendant (0,60) is an obvious example of a systemic bias, because when we corrected for the fast rising signs in the Northern hemisphere its effect size turned into 1,08, having a small positive effect of + 8 %. It is still rather small, so it could be the result of the sampling error. Another form of bias which is more difficult to correct for is the uneven distribution of slow planets in the signs in the ADB.

But how large must a found effect size be, so that it could NOT that easy be explained away by statisticians as just being a result of the sampling error? That depends on the amount of cases in that study. It is thus equivalent to what ordinary people call being experienced. The more cases that were studied, the better would be the research. Here quantity of research definitely coincidences with quality of research.

But the difference with what astrologers conceive as being experienced, is that all the cases and controls must be studied in the same way, preferably as part of one objective study. Only then one can provide exact comparative numbers: We studied 1867 ADB astrologers and compared them to the ADB as a whole. We found the following differences: .... This kind of quantitative research differs qualitatively enormously from the in my opinion talk of astrologers, where exact information about what was exactly done and encountered is not provided. Here reliance is solely given to the expert opinion of the so-called experienced astrologer, who also studied “uncountable” charts without using proper control groups.

An experienced astrologer could indeed have studied thousands of charts over the years, but it is unlikely that he or she did this in a systemic and objective way. Most of the poorly documented impressions of experienced astrologers could thus be based on shared prejudices, selective attention, sampling errors and other well known fallacies of thought and perception. This is the reason why most scientists consider astrology to be a pseudoscience.

Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claims; reliance on confirmation bias rather than rigorous attempts at refutation; lack of openness to evaluation by other experts; absence of systematic practices when developing hypotheses; and continued adherence long after the pseudoscientific hypotheses have been experimentally discredited.

For the top 10 astrologers only effect sizes of 3,6 and larger would be statistically seen significant, but with larger sample sizes more precise estimations could be done. As the sampling error depends on the sample size (n) and the risks (p) involved with the event. The larger the sample size n, the smaller the sampling error will be. For this reason academic researchers prefer to study large samples resulting in better predictions of mean value. But the smaller the risk p involved with the event, the harder it will be to get enough cases (np being the expected value) to do your statistical calculations with. This makes unbiased astrology research dealing with unlikely events like specific transits and aspects hard to achieve.

And you certainly would get a lot of problems when you had to interpret their effects in the light of the complexity of the whole chart and its manifold interactions. You might want to focus on one particular transit, but concurrent transits, progressions and so many other not astrologically determined factors could spoil your first impression. For this the reason scientists prefer to use very large case and control groups when they study the effects of some single factor, as with large samples those other disturbing factors tend to level out in case and control groups, because of the law of the large numbers.

But when interpreting one natal chart, there is no control group. The astrological evaluation will fully depend on your correct evaluation of what are the essential astrological events and circumstances at stake and your prior knowledge of similar situations. A medical doctor can rely on plenty of scientific information and scientifically tested investigation methods to discern what is normal or abnormal in his patient. Based on the correct diagnosis he can propose several treatments for the disease that could favourably change the prognosis for the patient. But trustworthy evidence-based background information is lacking in astrology. So the astrologers statement that the coincidence of transit A with event B was a meaningful coincidence is just a subjective speculation, as long as other factors relating to event B were not considered and no serious studies were found that confirmed that relationship before. When you said the transit did it, as this was suggested by some astrology books you read, no judge would be impressed. As astrology books typically are funny mixtures of astrological fact, believes and fiction, that do no adhere to most scientific methods.

Lack of trustworthy background information also plays a role when astrologers try to discover (actually speculate on) the effects of a newly found asteroid on natives in small scale “qualitative” I know it studies, but at the same time also have to take into account the influence of many more supposed to be effective other astrological factors like planets in sign and house and their aspects, without having any empirical knowledge or even clue of their probably very wide confidence intervals. This bad habit results in pseudo-deductive methods like Armchair theorizing:

Armchair theorizing, armchair philosophizing, or armchair scholarship is an approach to providing new developments in a field that does not involve primary research and the collection of new information -- but instead analysis or synthesis of existent scholarship, and the term is typically pejorative, implying such scholarship is weak or frivolous.

The on mathematical logic and the empirical found sampling error based statistical testing methods tried to put an end to these popular, just on individual bias based speculating malpractice's.

But doing multivariate analysis on all the possible factors in the individual chart, is impossible with so many uncertain factors even when doing very large scale research. But astrology book writers typically solved that empirical problem by simply applying the once established traditional rules of astrological symbolism to the newly discovered planets signs and houses. As this seemed right according to their believed in astrological constitution. And this on bias and prejudice based constitution became their natural rule of law.

And if some astrological factors were found to statistically significant as in the study of the Gauquelins, the found effect sizes were too small to predict anything with it. So you cannot base your well-framed astrological (or political) stories on it.

Scientists would evaluate this not evidence-based habit as foggy prejudice or bias, but astrologers and politicians would say that this kind of associative thinking always worked for them.

They argued: If we cannot objectively measure their effects in the light of the whole chart and so many other unknown not astrologically determined factors, we could at least speculate on them again applying our initial believed in basic assumptions.

The Constitution of the United Kingdom or British constitution comprises the written and unwritten arrangements that establish the United Kingdom of Great Britain and Northern Ireland as a political body. Unlike in most countries, no attempt has been made to codify such arrangements into a single document. Thus, it is known as an uncodified constitution. This enables the constitution to be easily changed as no provisions are formally entrenched.

And this malpractice indeed makes astrology (and the usual political strategies) clearly a special art of self-deception.

The used method is discussed on the Wikipedia page: Circular reasoning:

Circular reasoning (Latin: circulus in probando, "circle in proving"; also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. The components of a circular argument are often logically valid because if the premises are true, the conclusion must be true. Circular reasoning is not a formal logical fallacy but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade.

But the major empirical problem with astrological symbolism is that none of its premises have ever been found to be true in any serious statistical tests. So you can believe in the heroic tales of them who died for the ideals of Great Britain in a Great War, but many soldiers could tell you another story. If we once listened to them.

Using the binomial distribution to predict confidence intervals

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The risks involved with dices of all kinds, including a dice with 12 faces as used in astrology, have been calculated by Renaissance astrologers and mathematicians. The mathematics is rather simple, as we deal with a hit or a miss. But it becomes more complex, when we throw more dices. The risk of a hit is p and that of a miss is 1-p. When doubling p is 1/2, when throwing dices it is 1/6 and in astrology probabilities around 1/12 are usually encountered.

See: Geronimo Cardano and the Book on Games of Chance which is an article in which we explain how we used the normal and binomial distributions to evaluate found frequencies.

Between fun with dices and the law of the large numbers, there is a lot of room for speculation, the polymath Gerolamo Cardano found out.

According to the binomial distribution (expected p = 1/12, n=1867) on the right, values from 133 to 179 could be expected in 95 % of cases when just taking a random sample of the ADB with 1876 members. They were selected in the picture on the right.

Only values of 132 or lower (CumPx =132 is 2,46 %, effect size is 132*12/1867 = 0,85) and 180 or higher (Px>178 is 2,44 %, effect size is 180*12/1867 = 1,16) would have a large enough deviation from the mean, to be considered statistically significant in one counting the found sample experiment using an alpha of 5%.

The statistical concepts involved with it are really simple. If astrologers really would have twice as often Sun in 9 (we actually found an effect size of 1,05, thus only 5 % more often), we would not deal with the variation around the expected sample mean of 1867/12 = 155,6 (np) of random ADB charts, but with a variation around np is 1867/6 is 311,2 which would be typical for the subcategory astrologers.

And then we would have a really convincing case for astrology. As we would not see the expected values between 133 to 179 in 95 % of cases dealing with p = 1 /12, but actual found values ranging from 300 to 343 dealing with p = 1/6 having a strong effect size of 2 with a clear 1,80 - 2,20 confidence interval.

When measured values do differ that clearly from the expected values, the so-called Null hypothesis stating that the differences between found and expected values were just the result of chance had to be firmly rejected.

See the values in the green calculator on the left where the normal approximation of the binomial distribution is used. The Z score of expressing differences between found and expected values in terms of standard deviations from the mean would be 13, predicting with almost 100,0 % certainty that we deal with different population means and not just the kind of false impressions based on the standard error one would get when doing small scale research.

You can see the values in the picture on the left showing under Expected values and corresponding effect sizes. With an effect size of 2 the values predicting with 95 % certainty the expected (mean 155,6, range 132,2 - 179,0) and found means (311 found, range 300 - 343) do not overlap. Nor did their 99 % confidence intervals overlap (186 < 270). And the last is very important, because we did not test or scan for a single astrological hypothesis like Do astrologers have more often have a Sagittarian sun?, but tested many astrological assumptions at the same time.

Actually, most astrologers also exhibit datamining when they scan individual charts for special features like aspects, predominant signs or houses. They do their “discoveries” without control groups, but rely on rather vague ideas of how a normal chart should look like. So when studying the earlier mentioned top 10 astrologers, they would not only look for Sun, Moon and Ascendant in a systematic way, but would selectively pick out anything special more often.

What we did and most astrologers habitually do when scanning a chart for prominent features is datamining, doing many measurements at the same time. But when using this technique some 5 % (or 1 in 20) false positive higher or lower than expected values would be found just by chance, when using the 95 % confidence interval (having an alpha of 0,05). When looking for exceptions to the rule in the three tables presented above of 12 planets in 12 signs, 12 house cusps in 12 signs, 12 planets in 12 houses, 3 times 144 is 432 values were measured, having an expected false positive rate of 432/20 is 21,6 (95% ci 13-31) using the 95 % confidence interval (type I error).

Those false positives could initiate a lot of unneeded speculation on astrology boards. For this reason the more strict one against hundred random samples criterion would be more reasonable. When using the 99 % confidence interval, we would on average have 4,32 (1-9) false positives in the first three tables needing some special exploration. Of course, when we dealt with real and strong effect sizes like factor 2 or more in our sample of astrologers, we would not have to deal so much with those kind of questions. We would only have to deal with questions about the impact of the found effect size. But when dealing with a small effect size of 1,2 instead of 2.0, the question arises: is their is any likely positive effect size at all?

Some astrologers might criticise our approach as not being exact, but it is still more conclusive than the results of the usual low-key empirical research implicitly done by astrology book writers. They can only speak of might and could be effects, without mentioning any confidence interval of their expectations. So they are always right, but without predicting anything at all.

Expected values and effect sizes

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From the found values we could estimate effect sizes, by dividing the found values by the in the ADB expected population means. But effect sizes also have a confidence interval.

If you throw a dice once and you got the value of six, would that imply that the value six had a risk of six times more often found than expected? Yes, as that was the only found value in your at first glance experiment, but more tests should be done to give the other five sides of the dice a chance to pop up. As they had a natural chance of n-p = 1-1/6 = 5/6 (83,3%) to be missed.

In our ADB studies expected values and effect sizes were calculated using the whole ADB as a control group. For Sun and Moon the expected mean values based on 1/12 risks could be used, but for many other measured values, the found values in the ADB served as a better control group. See: Using a control group to evaluate frequencies.

But it they are not available one could assume a 1/12 probability to get an impression of the range of expected values. This is done in the long table of the binomial distribution on the left above. What could we according to the polymath Cardano expect?

According to the binomial distribution above, the lowest Sun in sign value of 141 for Sun in Virgo could be found in 1,62 % of cases when just taking a random sample of the ADB. But getting a value of 141 or lower with p is 1/12, would just by chance have a risk of 11,82 %. Statisticians would not be impressed by it. More studies with other cases should be done.

When using the Sun in virgo values of the ADB control group in the green calculator (picture on the right under Expected), we see a 95 % confidence interval of 130 (129,8) up to 176 (176,2) corresponding to effect sizes of 0,78 - 1,07.

The found value of 141 (effect size 0,92) would thus not be statistical significant. The risk of getting getting a value of 141 or lower had a cumulative risk of 15,57 % assuming a normally distributed distribution. As the found value deviated only 1 standard deviation from the expected mean (Z-score of -1,01).

The highest found value for Sun in Aquarius (184) falls outside the range of in 95 % of cases expected values when taking a random sample from the ADB. As P(X >183) is 1,35 % and thus smaller than 2,5 %. We found 184 (9,9 %) of them against 1867/12 = 155,6 (8,33 %) predicted, having an effect size of 1,18.

Because our sample was retrieved from the ADB, using the in the ADB found frequency of Sun in Aquarius being 4601/55047 or 8,36 % would be more appropriate.

This yields the same effect size 1,18 (95 % range 1,02 - 1,34), which is statistically significant at the 95 % level (having a range of 133- 180), but not yet at the 99 % level (having a range of 125 - 187).

See the values under Expected in the picture on the left.

The Z score of 2,3 and Cohen's d effect value of 3,03 indicate that there is little overlap between the estimated population means of the case and control group, as they differ more than two standard deviations (Z score of 2,3).

The binomial risk of getting P(x>183) is 1,22% .

Practical relevance of found values and confidence intervals

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When it comes to practical relevance, the small effect size of 1,18 and its confidence interval (95 % range 1,02 - 1,34) must be leading. As the mean of a group is just the mean of a group, but not all members of a group behave like their mean. Within groups found variation (intra-group variation) is as important as between groups (inter-group) found variance. This has been discussed in Predicting at the individual level in 79 art critics.

Suppose that we would not have found that small, but significant group difference of 18 %, but a huge effect size of having 100 % more risk of becoming an astrologer as a Sagittarian. What then? Few Sagittarians would choose for that exceptional profession and only one sixth of the astrologers would be a Sagittarian. So, could you predict with it? Maybe, but not that well. And would thus a reading afterwards like: John is an astrologer. John has Sun in Aquarius. Sun in Aquarius is found twice as often with astrologers. No wonder that John became an astrologer! have any explanatory value? No.

For astrologers, who are not accustomed to use control groups, this argument seems to work. So it could be seen as valid argument on astrology forums. But statisticians would say: If you only knew that John had Sun in Aquarius, having a two times more often risk of becoming an astrologer and you also could know that some 3 % of the ADB population were astrologers, what would be the risk according to the ADB of John becoming an astrologer? Only six percent. So, this is not a good explanatory reason to assume that John became an astrologer.

But in practice the risk of becoming an astrologer is much lower, because astrologers are obviously over-represented in the ADB. And the major problem is that we only found an effect size of 1,18. In this case when you only knew that John had Sun in Aquarius, having 18 % more risk of becoming an astrologer and you also knew that some 3 % of the ADB population were astrologers, the ADB risk of John becoming an astrologer would be 3,54 % instead of 3 % .

In that case you had to look to other chart factors, as the combination of many fitting astrological indicators could increase the risk. But to do so, you have to know the risks. Astrology books do not provide them. And then you have to make them up. But astrology books provide you a lot of room for story telling. So you can play with it, like Cardano once played with binomial risks and lost a lot of money.

The values for the Moon in sign differ from 141 for Moon in Scorpio (P < 142 = 11,82 %) to 172 for Moon in Aquarius again (P > 171 = 9,27 %). Both values fall outside the 70 % range of most likely values when just taking a random ADB sample (143-168), but are still within the in 95 % to be expected found values of random ADB samples assuming a probability of 1/12. Could you predict with it? Probably not. When we calculated their confidence intervals, they could have a positive and negative effect as well.

The values for the ascendant differ most, but that pattern is strongly influenced by the effect of ascension length at different latitudes. Many statistical significant effect sizes were found for the sign of the ascendant, but using p = 1/12 would be bad idea because of the fast and slow rising signs, so we used the ADB as a control group to calculate the effect sizes. See: The ADB as a control group.

When correcting for this systemic bias, the found effect sizes are not that impressive any more. See the for the houses expected found and expected values below.

The expected effect size range was 0,85 - 1,15 or + / - 15 % for the 95 % confidence interval. It is 0,80 - 1,20 or + / - 20 % when using an alpha of 0,01. But all Ascendant values were within the in 95 % of cases predicted values around the expected mean. Could you predict with it? Probably not.

Effect sizes in the Placidus houses

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What were the found and expected values in the Placidus houses? The expected standard deviation can be calculated as the square root of variance np(1-p), which is 11,95 with n is 1867 and p = 1/12. This would result in an expected effect size range of 0,85 - 1,15 or + / - 15 % using the 95 % confidence interval of a normal distribution. It is 0,80 - 1,20 or + / - 20 % when using an alpha of 0,01. The actual found standard deviation of the effect sizes of planet in house are placed at the end of the rows. The are given as a percentage.

In this case the effect sizes in the Placidus houses were calculated based on the expected values of the ADB control group they were part of.

Do we see effect sizes for planets in house that lie outside the expected values? Thus effect size values larger than +/- 15 % or more appropriate +/- 20 % because we are doing data mining in a table with 144 values. Only two values met the 99 % confidence interval criterion: Neptune in 10 (1,21) and Mercury in 6 (0,79). But they could be expected in a table of 144 items.

The highest score is for Neptune in 10 (1,21). Neptune in 7, Uranus in 10, Mercury in 9 and Sun in 12 all score 1,17. The lowest score is for Mercury in 6 (0,79). Then come Venus in 5 (0,81), Neptune in 1 and Venus in 8 with 0,82 and Sun in 7 and Mercury in 7 with 0,84. But they all have their confidence intervals.

Twelve values fall outside the the 95 % confidence range against 144/20 is 7,2 false positives expected (type 1 error). When using the more reasonable 99 % confidence interval, some 1 % or 144/100 or on average 1,4 false positives could be expected. So the effect size values for Neptune in 10 (1,21) and Mercury in 6 (0,79) are likely due to chance. They certainly do not present outliers.

When calculating Cohen's d values, we see other values. Here effect size is expressed as the found difference (observed values minus expected values) divided by the some averaged standard deviation of the two groups. See: Cohen's D value. They tell us how the two found values in case and control groups (our best estimate of their means) differ in terms of found variation in the two groups. Because this sounds rather abstract, let us provide you an example that is more easy to comprehend.

Suppose we studied gender differences and found out that girls performed some 20 % better than boys on a particular test after doing thousands of experiments. Because of the sampling error we have to take both group sizes into account as well as the variation in test performance within the two groups. It is clear that when we only studied 10 boys and 10 girls, huge differences and effect sizes would be found just by chance without having any statistical significance (See: Imagined values). They would result in large confidence intervals with regard to effect size. There could be a lot of speculation, but never a clear winner.

The variation within both groups is also of importance, as we cannot expect that all boys scored 90 and all girls scored 110 accounting for the 20 % found difference of their mean scores. Maybe only 10 % of the brightest girls (remember our top ten astrologers) or only 10 % of the stupidest boys were responsible for the effect. Selective attention to the last could be a wrong reason for scapegoating a whole group (boys are stupid).

With a small Cohen's d value the estimates of the group means overlap and this will result in an minimal effect size with a large confidence interval having no statistical significance at all. Even insurance companies would pay little attention to them.

With larger Cohen's d values the risk that the groups on average differ increases. With huge Cohen's d values, the differences between found values (expected mean values) is that large (2 averaged standard deviations), that the difference between the expected group means is likely to be statistical significant. But could you predict with it?

Girls (as a group) would for sure on average perform 10 % (=/- 1 % ) better than boys (as a group).

The Cohen's d value takes into account both the expected (found) variance as the actual found effect size. So it gives us probably the best hint to the right direction.

But when it comes to predicting effect sizes and their confidence intervals do matter, as small effects sizes can be very statistical significant, but not be that predictive in practice at all. But large effect size's found when doing “my own low-key empirical research” as Sue Tomkins named it in Aspects in astrology, are likely to disappear when you study larger samples.

Under the header Mars and other effects in 79 art critics, we showed that planets in house are not that evenly distributed as most astrologers might assume. Maybe for that reason Mercury in 6 (effect size 0,79), having a Cohen's d of -1,23 scores not that impressive as Saturn in 5 (effect size 0,84), having a Cohen's d of -2,97.

Chiron in 2 (2,40), Uranus in 10 (2,21), Neptune in 10 (2,18), North Node in 1 (2,03), Moon in 4 (2,01) and Saturn in 9 (2,00) have the largest Cohen's d value.

Moon (-2,78) and Saturn (-2,96) in 5 scored lowest, pointing to strong negative correlations that did not fit the astrologers profile.

Another way to look at the values, is to compare the variance of the absolute found values in rows. This is done using the Chi Square test. In this case the distribution of house positions of Neptune is very significant: 0,4 % expected in random ADB samples. As you can see above, Neptune in 7, 9 and 10 house scores high and Neptune in 1, 6, 8 and 11 scores low. So having the great deceiver in the houses of relations, belief and work seems to predispose for becoming an astrologer. Believe it or not.

The other house positions that seem to matter are that of Venus (2,3 %) and Mercury (4,7 %). But the house position of Mars (97,1 %), Jupiter (99,5 % ) and to a lesser extent Pluto (85,3 %) do not differ from random ADB samples.

Aspects between planets

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Aspects between planets are considered to be very important by astrologers. They have thus been measured and compared to the aspects found in the ADB. Of course the same orbs were used. But if you look at all aspects of 1867 ADB astrologers, and thus are dealing with the law of the large numbers, the found effect sizes are not that impressive.

The highest value for Sun - Mercury aspects (1,07) score only 7 % higher than expected according to the ADB. Jupiter aspects being often associated with astrology, do not impress with effect sizes between 0,96 and 1,03.

The lowest scores are for Mercury-Venus (0,95), Uranus - Chiron (0,90), Uranus - North Node (0,94) and North Node -Chiron (0,95).

Below you see the counts of found aspects divided by the expected aspects based on a large ADB control group. So we speak of effect sizes. More explanation is given under The actual risks involved with aspects in 79 art critics.

The good news for astrology students is that you can skip the interpretation of the many not that large effect sizes in the by us presented tables of aspects between 12 planets. As most, except the extreme values, would just fall in the not being that statistically significant range. To help you decide which one's are not to skipped requires some calculations. We will provide a table for this later.

The statistical problem with aspects is that they are manifold, but tend to have low probabilities. So their individual effects are in practice impossible to analyse given the many other factors supposed to be active in the whole chart. An astrology researcher could try using multivariate analysis to disentangle all the chart factors like epidemiologists study factors involved with morbidity, but few astrologers would follow him or sell his books. Why? Because the results would disappoint them. So, most astrologers prefer to speculate using astrological symbolism, which is the by their branch accepted malpractice astrologers can adhere to, when they do not know anything at all about the subject. And they imagine themselves that their holistic intuition will tell them the truth. Astrological symbolism could be a universal language that somehow might be magically true, but is impossible to check in the empirical way. And as long as the typically vague astrological speculations cannot be proven to be wrong, they are still seen as valid by the astrological community. It could be called their alternative Null hypothesis. Of course no astrologer could ever empirically proof the astrological claim that Neptune deals with illusion, but astrologers still believe in it.

But what did we see in the table above? Effect sizes deviating only some 5 percent around some expected mean do not have any predictive value for statisticians. But if you still believed in astrological symbolism you would not look at the numbers but to the quality assigned to them. But then you dealt with another kind of statistics, having more or less risk involved with it. But how would you define that risks?

The highest effect size was found for Neptune conjunct Pluto (1,97). With 154 cases found against 78,1 expected, this is a statistical significant effect having a confidence interval of 1,67 - 2,27. Uranus conjunct Neptune scored lowest with 0,11 (0 - 0,23). Here 4 cases were found against 34,90 expected, which is a remarkable difference. The conjunction existed from 1821-3 and more recently from end 1988 to 1998.