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Love signs
Fail world's largest tests (N=27m)

Geoffrey Dean

Abstract -- Three recent studies (Sachs 1998, Castille 2004, Voas 2007) with a combined sample size of 27 million couples have failed to find the slightest evidence for sun sign effects, thus confirming the results of earlier studies (which are briefly reviewed). Studies of sun sign compatibility largely avoid the problems that plague the testing of individual signs, namely those due to demography (depending on place and country some months have more births than others) and astronomy (due to the Earth's elliptical orbit some signs have more days than others), which here generally cancel out. We follow the tests in some detail to see how huge samples can tease out apparent astrological effects only to find them explained by recording bias and other glitches in the data. Despite the giant magnifying glass of huge samples, no sun sign effects could be detected. Interestingly, many studies have shown that sun sign self-attribution has a tiny effect size typically around 0.08, showing that some people have sufficient belief in sun signs to shift their self-image in the believed direction, albeit only slightly. But the same belief seems to have no effect when picking a partner (effect size <0.000,001), showing that such beliefs may shift their own self-image but not the actual behaviour of others. That is, even for them, the real world always prevails over astrology world. In short, lonely hearts (and anybody else including astrologers) who worry about sun signs (and by extension astrology itself) are absolutely wasting their time.

Married couples tend to be similar in many ways including age, height, education, social class, and attractiveness. The effect sizes can be substantial, for example bright men prefer bright women (r = 0.5) and tall men prefer tall women (r = 0.3). In addition, sun sign books, websites, and women's magazines insist that sun signs are just as important for successful romance. For example Judy Hall (Sun Signs for Lovers: The Astrological Guide to Love, Sex and Relationships, Octopus 2005) says "Sun signs can reveal whether people are passionate or romantic, faithful or flirtatious; and whether they are looking for passion or friendship, fidelity or freedom" (page 7). Hall is a professional astrologer, counsellor, and tutor at the London School of Astrology.

Traditionally the harmonious aspects between sun signs (conjunctions, sextiles, trines) are favourable while inharmonious aspects (squares, oppositions) are unfavourable. For example Linda Goodman (Love Signs, Pan-Macmillan 1980) says "when you find a trined, sextiled or conjuncted relationship between two SunSigns ... love then takes on a deeper dimension" (page 3). Sometimes astrological authors rate pairings on scales of 1-5 or 1-10, which can then be summarised in numerical form as in the plots below, where the predominance of conjunctions (0), sextiles (60) and trines (120) is clearly visible.

Sun sign compatibility according to six authors. The vertical scale is the compatibility rating as a percentage of the maximum possible. The preferred aspects are conjunctions (0), shown in red, and sextiles (60) and trines (120) shown in black. Aspects on the right are to signs later in the zodiac, aspects on the left are to earlier signs. Where an author gives ratings for subgroups, for example Odle gives separate ratings for love and friendship, and King gives separate ratings for males and females vs love, sex, and marriage, the ratings have been combined.

As shown by the above plots, astrologers can disagree on particular sun sign pairings, for example King and McKinley (like Ptolemy, see below) rate the opposition (180) as largely unfavourable, Hall and Mitz rate it as average, and the other two rate it as largely favourable. Similarly Hall rates the inconjunct (150) as moderately favourable, contrary to the others including Ptolemy ("if the luminaries be in trine or sextile to each other, the cohabitation will most usually be lasting; but if ... in signs inconjunct, or in opposition, or in quartile [90], the cohabitation will be speedily dissolved upon slight causes, and the total separation of the parties will ensue", Tetrabiblos, Book 4, Chapter 5, Ashmand translation).

Similarly, as shown in the appendix to History on this website under Sun Signs, Russell Grant and Mystic Meg disagree completely on the compatibility of Gemini-Virgo (90, "sexual incompatibility" vs "sex style matches perfectly"), and similarly on Virgo-Aries (150), Virgo-Pisces (180), Libra-Libra (0) and Aquarius-Libra (120).

Astrologers can also disagree with themselves when their rating of X-Y differs from their rating of Y-X. Thus in the above plots only King, Petulengro and Mitz show no internal disagreement, whereas the ratings by McKinley, Odle, and Hall disagree with themselves on respectively 15%, 22% and 47% of the possible 144 pairings, as when Hall rates Aquarius-Aries (60), Gemini-Virgo (90) and Cancer-Libra (90) as favourable, but not favourable the other way round.

Nevertheless, the agreement among astrologers is still good enough to ensure that sun sign compatibility (if it exists) should be detectable in groups of married couples. For example the mean correlation between the above plots is r = 0.61 (df=10, p=0.04) the individual correlations being as follows:

            King   Odle  Petul   Hall  McKin   Mitz   Mean
King               0.60   0.72   0.45   0.57   0.68   0.60
Odle        0.60          0.80   0.63   0.60   0.70   0.67    
Petulengro  0.72   0.80          0.69   0.65   0.66   0.70   
Hall        0.45   0.63   0.69          0.32   0.42   0.50
McKinley    0.57   0.60   0.65   0.32          0.61   0.55            
Mitz        0.68   0.70   0.66   0.42   0.61          0.61   Mean 0.61

Here the most agreeing astrologers are Odle and Petulengro (r=0.80) and the least agreeing are Hall and McKinley (r=0.32).

Compatibility is good for testing
Tests of sun sign compatibility largely avoid the problems that plague the testing of individual signs, namely those due to demography (depending on place and country some months have more births than others) and astronomy (due to the Earth's elliptical orbit some signs have more days than others). For example demographic information is rarely detailed enough to allow the calculation of accurate expectancies. But in tests of sun sign compatibility the variations due to demography will generally apply to both partners and will therefore cancel out, while the variations due to astronomy are automatically covered in the calculations, so an accurate expectancy for any given sign combination is easily obtained. Thus if the proportion of a given sign among husbands is X and the proportion of a given sign among wives is Y, the expected frequency of that combination is XYN where N = sample size. If the observed frequency is Z, the ratio observed frequency / expected frequency (which is the Obs/Exp ratio plotted in the figures) is Z/XYN.

Early research
Marriage and divorce records are a good source of compatible and incompatible births. But studies of sun sign pairings in such records have generally produced only negative results. For example Daneel (1970, 1972) found no significant deviations from chance for 884 and 1608 German divorces, Silverman (1971) found the same for 478 American divorces and 1586 marriages, although a second sample of 1382 marriages found a small but significant surplus of sextiles and trines equivalent to an effect size of 0.06, and Boning et al (1978) found no effect for 736 Dutch marriages. Studies involving other planets and precise aspects have generally been just as negative, for example Shanks (1983) found nothing significant for 960 marriages.

A recent Swiss study
An apparent exception is a study of sun sign compatibility by Gunter Sachs (The Astrology File, Orion 1998) who analysed birth data from the Swiss Federal Office of Statistics for couples who married or divorced between 1987 and 1994. It was the largest sample yet (358,763 married couples and 109,030 divorced couples). Of the 144 sign pairings, 25 were individually significant for marriage and 13 for divorce, so Sachs concluded that "star signs clearly are of particular importance when it comes to choosing a partner" (page 70) although they "play a far less significant role in divorce than in marriage" (page 95). This conclusion was supported by a follow-up study in which each spouse was given a false birth date picked at random. The results were "statistically entirely unremarkable" (page 203).

However, a check of his original results shows that his cutoff level for significance is about p = 0.13, contrary to his claim of p = 0.05 (page 44), which means that in each case 144 x 0.13 = 18.7 pairings are expected to be individually significant by chance alone. Overall there are 25 + 13 = 38 individually significant pairings vs 2 x 18.7 = 37.4 expected by chance alone, which means that Sachs's results actually provide no support whatever for sun sign effects.

Furthermore, as noted by Suitbert Ertel in Sach's Astrology File on this website under Sun Signs, the sign preferences of husbands should tend to agree with the sign preferences of wives, but the mean rank correlation between preferences over the 66 unduplicated pairings AR-AR, AR-TA, ... SG-PI, AQ-PI was a negligible 0.075 (p=0.53) for marriages and -0.12 (p=0.31) for divorces, the last being in the wrong direction. (Ertel's rankings used preferences based on Sach's published expectancies, which are rounded and occasionally lead to ties. When Ertel's test is repeated with unrounded expectancies to avoid ties, the mean rank correlations are 0.136 (p=0.28) and 0.073 (p=0.56), respectively. The differences are small and do not affect the outcome.) Ertel concluded there was "no hint of the correspondences we would expect if Sach's results were genuinely due to astrology". More obviously, as shown in the figure below, the deviations from expectancy do not match the predictions of astrology.

Sachs's sun sign results for marriage and divorce show little similarity with the previous figure. Other than the apparent excess of conjunctions (shown in red), which is probably due to recording bias (see later), the ups and downs are all over the place. Also, contrary to astrological expectation, those for marriage tend to agree with those for divorce (r = 0.50).

A more recent French study
However, a more recent French study by Didier Castille (Birth day effect on natality rhythms, Correlation 22.2, 20-32, 2004) produced intriguing results. From the Institut National de la Statistique et des Etudes Economiques (National Institute for Statistics and Economic Studies) he had obtained the dates of birth for all married couples to whom live children were born between 1977 and 2000. Couples were excluded if either spouse was born on 1 January, since this date was about 40% more frequent than any other probably due to immigrants who did not know their exact birth date, or if either date was obviously in error such as 31 June. The result was a total of nearly 17 million couples. Castille was studying the number of days 0-364 between the birthdays of husband and wife rather than their sun signs, but since each sign averages 365/12 = 30.4 days, his counts can be converted to a roughly equivalent sun sign separation. Spouses born just a few days apart could of course have different sun signs whereas this approach gives them the same sun sign, so the conversion is far from exact. Nevertheless it should be good enough to pick up any sun sign effect in such a huge sample. As shown in the figure below, the results show no clear conformity to what astrology predicts.

Days between 16 million French couples' birthdays from Castille (2004) converted to approximate sun signs between spouses. Once again the ups and downs are all over the place. The number of same-birthday couples (hidden in the red result) was 26% more than the 46,000 expected.

The above results show a small consistent deficit of squares (90) but no consistent excess of sextiles (60) or trines (120). The apparently large excess of same-sign couples (shown in red) appears large only because the scale is small; thus the corresponding effect size is a tiny 0.0039. So this enormous sample offers no useful support whatever for sun sign effects. The excess of same-birthday and same-sign couples is highly significant, but according to Castille an explanation "is yet to be found" (page 30).

A definitive British study
However, an explanation arises from a recent study by David Voas (Ten million marriages: A test of astrological love signs, Cathie Marsh Centre for Census and Survey Research, University of Manchester UK, available at http://www.ccsr.ac.uk/research/lovesigns.html) using 2001 census data gathered in England and Wales by the Office for National Statistics. Voas notes that although the quality of the data is very good, three factors can upset any study: (1) Variations due to chance. (2) Recording errors. Some people may not know their birthday or the birthday of the person they are completing the form for. Others may make mistakes, or write illegibly, or decline to respond, or lie. (3) Self-attribution. Some sign pairings may occur more frequently than expected if people seek these matches and avoid others. (The Thomas theorem in sociology holds that if people perceive something as real, even if it isn't, it will have real consequences, as when the 17th century belief in witches led to many thousands of innocent people being burned at the stake.) Fortunately it is possible to allow for the above factors. For example post-census surveys and quality checks provide information about response and non-response, while self-attribution and genuine sun sign effects can be disentangled by testing only people without knowledge of sun sign compatibilities.

Voas also notes that more than a hundred standard tables summarising the census results have been published. If they do not cover a particular interest, special tables can be commissioned including any of the data collected, subject to the usual considerations of data protection. Once a table has been created it becomes publicly available. In this case a table showing the pairings by sun sign of 10,317,649 married couples in England and Wales 2001 had already been commissioned by someone describing himself as "a philosopher with a degree in statistics" who was "investigating the truth behind astrology".

The table was in general agreement with the results of Castille. It appeared to show a small but significant tendency for people to marry partners of the same sign (about 22,100 more than the 861,800 expected), and a smaller tendency to marry adjacent signs, but no clear conformity to what astrology predicts. Nevertheless the significant excess of same-sign couples seemed large enough to justify investigation. So Voas commissioned a full breakdown of husbands and wives by day and month of birth (366 days x 366 days x four subgroups by husband's age, or nearly 670,000 combinations). As shown in the figure below, this new data showed an apparent month effect that was slightly larger than the apparent sign effect. So both effects were largely due to couples with matching birthdays.

Results from Voas (2007). The excess of same-month couples (2.7% more than the 861,540 expected) is slightly larger than the excess of same-sign couples (2,6%). The number of same-birthday couples is about 40% higher than the expected 28,300.

Voas notes that, while some people may be drawn to each other because they have the same birthday, the excess of same-birthday couples is probably largely due to response error. Census forms are typically completed by one member of the household, who through carelessness or forgetfulness may enter their own birthday for that of their spouse. Such errors are supported by a census validation study that found 10,900 couples where one spouse had assigned their own sex to the other. If people can make mistakes about their spouse's sex they can also make mistakes about birthdays.

Indeed, the most common birthday was 1 January (2560 vs 77 expected) with 1 July (563) in second place, indicating that some people entered 1 January (or 1 July) if an exact birthday was not known, a practice known to occur in old people's homes and for people born overseas. Recall that Castille observed the same in French data, and the same is visible in the previous plot of Sachs's data. (There were even more opportunities for the adjustment of birth dates in the 18th and 19th centuries, see Social Artifacts on this website under Gauquelin.)

Furthermore, more spouses than expected were listed as sharing the same day of birth (but a different month) or the same month of birth (but a different day) as the other spouse. This is not necessarily relevant to the analysis of sun signs, although it would be relevant to Castille's day counting, but it does illustrate the way in which recording errors can occur.

A crucial disentangling test
Back at the excess of same-month couples, Voas wondered if (despite the positive effect of recording errors) there might still be some kind of seasonal affinity and if it could be astrological. Here the partial overlap between sun signs and months allowed a crucial test. The first third of each sign occurs in one month and the rest in the next month. If signs have an effect then couples with both spouses born under the same sign in different months should be more common than those born under different signs in the same month.

The results were conclusive. Same-sign-different-month couples were not significantly more numerous than expected by chance, whereas different-sign-same-month couples were significantly in excess. Voas concluded that sun signs played no role in the observed excess of same-month couples.

But what about the slightly-higher-than-expected counts for adjacent signs or months? Here Voas explains a census procedure called "imputation". When the census office encounters illegible or missing dates of birth (which account for about 0.5% of all responses), the day is entered as the 1st of the month, and the months are assigned in rotation. Thus if the dates for both spouses were missing, one would be entered as 1st of month M and the other (usually the wife because they are typically listed on the form after husbands) as 1st of month M+1. Such cases will therefore usually assign wives to the month or sign following their husbands, which is precisely what is observed in the previous plots including Castille's. Because of the tendency to give 1 January as a birthday (which date Castille had therefore removed from his data prior to analysis), both the same-sign/month effect and the following-sign/month effect (ie the value of observed/expected frequency) should be highest for Capricorn/January. And the results confirm it:

Capricorn same-sign = 1.061, following-sign = 1.008
January same-month = 1.054, following-month = 1.007

Results for cleaned data
Voas then removed these response errors by excluding from the data all couples where one or both spouses are born on the 1st of a month, and by excluding from same-sign couples those with the same birthday or month of birth. The effect of these exclusions reduced the sample size from 10,317,649 marriages to 9,500,773 and gave the results shown below:

Results for cleaned data based on Voas (2007)

The excess of same-sign marriages is now less than 0.2% (p=0.08), no more than would be expected by chance, and much less than the previous 2.7% (p<10^-100), confirming the bias due to recording errors and the processing of missing data. Overall there are no variations more than expected by chance, as shown below for the 144 sign pairings.

Results using cleaned data for 144 sign pairings. Left: the distribution of 144 effect sizes ranges from -0.000,07 to +0.000,07, mean <0.000,001 equivalent to a success rate in predicting compatibility by sun sign of no more than 50.00005% vs 50% expected by chance. Right: the distribution of 144 significance levels is close to uniform, showing that no sun sign pairing is even marginally significant more than expected by chance.

Interestingly, sun sign self-attribution has a tiny effect size typically around 0.08, showing that some people have sufficient belief in sun signs to shift their self-image in the believed direction, albeit only slightly. So we might expect the same belief to lead such people to consider sun signs when picking a partner. That no effect can be detected even with enormous samples shows that their beliefs may shift their own self-image but not the actual behaviour of others. That is, even for them, the real world always prevails over astrology world.

Conclusion
These three studies (by respectively Sachs, Castille and Voas) are the largest tests of sun sign astrology ever undertaken. After allowing for response and procedural biasses, the distribution of spousal birthdays is as close to random as one is likely to find in a real-world situation. Voas concludes as follows:

"Astrologers are likely to complain that full birth charts are needed to predict personality accurately. There are two responses. First, to the extent that astrology has influenced everyday belief, it is almost entirely through the use of sun signs; if those were seen as useless when it comes to assessing personality and romantic compatibility, then astrology would lose its hold on the public imagination. Secondly, the basic signs are important even in professional charts. If they had any direct influence, however small, the giant magnifying glass of this huge sample would reveal it. No effects can be detected.

"The only remaining defence is that sun signs mean nothing on their own. [However] such a claim would mean that no generalizations about sun signs could be true. Virtually all astrologers, however, make statements about the supposed influence of different elements of a chart, including the sun sign."

In short, lonely hearts (and anybody else including astrologers) who worry about sun signs (and by extension astrology itself) are absolutely wasting their time. Nevertheless sun sign astrology is unlikely to go away, simply because there is a huge commercial profit to be made from its continued existence, along with wide ignorance of how to judge its claims.

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