How random is the toss of a coin?

Background

The toss of a coin has been a method used to determine random outcomes for centuries. It is still used in some research studies as a method of randomization, although it has largely been discredited as a valid randomization method. We sought to provide evidence that the toss of a coin can be manipulated.

Methods

We performed a prospective experiment involving otolaryngology residents in Vancouver, Canada. The main outcome was the proportion of “heads” coin tosses achieved (out of 300 attempts) by each participant. Each of the participants attempted to flip the coin so as to achieve a heads result.

Results

All participants achieved more heads than tails results, with 7 of the 13 participants having significantly more heads results (p ≤ 0.05). The highest proportion of heads achieved was 0.68 (95% confidence interval 0.62–0.73, p < 0.001).

Interpretation

Certain people are able to successfully manipulate the toss of a coin. This throws into doubt the validity of using a coin toss to determine a chance result.The toss or flip of a coin to randomly assign a decision traditionally involves throwing a coin into the air and seeing which side lands facing up. This method may be used to resolve a dispute, see who goes first in a game or determine which type of treatment a patient receives in a clinical trial. There are only 2 possible outcomes, “heads” or “tails,” although, in theory, landing on an edge is possible. (Research suggests that when the coin is allowed to fall onto a hard surface, the chance of this happening is in the order of 1 in 6000 tosses.¹)When a coin is flipped into the air, it is supposedly made to rotate about an axis parallel to its flat surfaces. The coin is initially placed on a bent forefinger, and the thumb is released from under the coin surface, where it has been held under tension. The thumbnail strikes the part of the coin unsupported by the index finger, sending it rotating upward. All this is done with an upward movement of the hand and forearm. The coin may be allowed to fall to the floor or other surface or it may be caught by the “tosser” and sometimes turned onto the back of the opposite hand and then revealed. The catching method should not matter, provided it is consistent for each toss. The opponent often calls the toss when the coin is airborne, although in the case of randomization for clinical trials, this is unnecessary because one is simply looking for an outcome.Open in a separate windowThe appeal of the coin toss that it is a simple, seemingly unbiased, method of deciding between 2 options. Although the outcome of a coin toss should be at even odds, the outcome may well not be. Historically, the toss of a coin before a duel reputedly decided which person had his back to the sun — an obvious advantage when taking aim! In medical trials, a simple statistical manipulation can have a dramatic effect on the treatment a patient receives. Our hypothesis is that with minimal training, the outcome of the toss can be weighted heavily to the call of the tosser, thus abolishing the 50:50 chance result that is expected and allowing for manipulation of an apparently random event.     

Familial transmission of a dysmorphic syndrome: a variant example of Kabuki syndrome?

Familial transmission of a dysmorphic syndrome: a variant example of Kabuki syndrome?: We report a Romanian family with a dysmorphic syndrome in three generations: a boy, his mother and maternal grandfather, who all presented with the typical facial appearance, characteristic skeletal and dermatoglyphic findings of Kabuki syndrome, but no mental retardation, short stature and visceral abnormalities. The phenotype observed in this family may represent the mild end of a spectrum of clinical manifestations described in this condition. This report provides a further evidence for autosomal dominant transmission of the disorder.     

The recovery of L. Vesijärvi following sewage diversion

For 60 years the sewage of the City of Lahti was discharged into L. Vesijärvi. The eutrophication of the lake was observed as early as the 1920s but in the 1960s the pollution became obvious. The sewage was completely diverted in 1976. As a result of the diversion the bacteriological defects were eliminated within one year, restoring the recreational value of the lake. The recovery of water quality was rapid during the first two years. The oxygen content increased markedly but hypolimnetic oxygen depletion persisted. The phosphorus content decreased about 60% and the nitrogen content about 30%. After that period the recovery slowed down. The biomass of phytoplankton decreased but the abundance of heterocystous blue green algae increased causing blooms in July and August. The primary production has lately been reduced despite the lack of improvement in chemical water quality. Hypolimnetic aeration was started in order to accelerate the recovery. The results during winter stagnation have been encouraging.     

F.G. syndrome: a rare and/or extremely polymorphic syndrome?

We report a case of mental retardation associated with multiple congenital anomalies suggesting an F.G. syndrome. We discuss problems concerning genetic counselling and the management of future pregnancies. Unfortunately, no concrete strategy, concerning prenatal diagnosis, can be proposed.     

Schinzel acrocallosal syndrome: a variant example of the Greig syndrome?

A 5-month-old male is reported with clinical and radiological findings identical to those present in the Schinzel acrocallosal syndrome. The similarity with the Greig syndrome is discussed and the question is raised whether both syndromes are variant examples of the same autosomal dominant condition.     

Invasion success and threat status: two sides of a different coin?

The characteristics possessed by invasive species have been suggested to be the reverse of those possessed by species threatened with extinction, such that relationships of species’ traits to invasion success should be opposite in sign to relationships of the same traits to extinction threat. A recent study (Jeschke, J. M. and Strayer, D. L. 2008. Are threat status and invasion success two sides of the same coin? – Ecography 31: 124–130) found no evidence for this “two‐sides‐of‐the‐same‐coin” hypothesis but compared characteristics of species in each taxon that were invasive to a control group consisting of all other species. A different view of the “two‐sides‐of‐the‐same‐coin” hypothesis may be obtained if the characters of invasive species are compared to those of a control group consisting of species that have not invaded despite actually being introduced. Here, we show that changing the control group for comparison with invasive species does not change the lack of support for the “two‐sides‐of‐the‐same‐coin” hypothesis but does change views about which specific traits are consistent with the hypothesis.     

Is Sedum acre L. a CAM plant?

Summary Sedum acre L. collected from its natural stands south of Darmstadt (Germany) showed ¹³C values typical for C₃ plants. This suggests that in situ at the natural stand CO₂ was fixed mainly via the C₃ mode of photosynthesis rather than via the CAM mode. However, experimental water stress shifts the CO₂ exchange pattern from the C₃ type to CAM type. Simultaneously, a diurnal rhythm of malic acid oscillation, typical for CAM, and increase of PEP-carboxylase and malic enzyme activities developed. Hence, Sedum acre is obviously to be classified as a facultative CAM plant. Because of the temperature characteristics of CO₂ exchange in Sedum acre, in situ CO₂ should be harvested from the atmosphere mainly during the seasons where water stress situations capable of inducing CAM are unlikely to occur.     

Prevalence of Edwards' syndrome. Clustering and seasonal variation?

Summary The incidence of Edwards' syndrome was found to be 1 per 4857 newborn children of 34000 consecutively newborn children in two Danish counties. Six of the 7 cases were born during the months of February through April.The incidence was high compared with the expected incidence of Edwards' syndrome of approximately 1 per 10000. This might be due to clustering in the area studied during the period 1967 to 1973.The finding of variations in incidence of children with Edwards' syndrome in different parts of the world, as well as the finding of seasonal variation in birth of such children, indicates that some of the etiological factors of nondisjunction of chromosome 18 are of an environmental nature.     

Haematemesis: a new syndrome?

Three patients presented with symptoms suggesting a Mallory-Weiss tear. Endoscopy showed a localized, clearly demarcated area of bright red mucosa near the gastro-oesophageal junction; this was thought to have arisen by retrograde intussusception of the stomach during vomiting or retching and may have caused the haemorrhage.     

UFD1L and CDC45L: a role in DiGeorge syndrome and related phenotypes?

Molecular genetics is contributing to the understanding of normal and abnormal cardiovascular development and morphogenesis. Deletions of chromosome 22q11.2 have been associated with distinct phenotypes that result from a failure to form derivatives of third and fourth branchial arches, including DiGeorge syndrome (DGS) and velo-cardio-facial syndrome (VCFS). The biochemical mechanisms underlying these phenotypes remain undetermined. A recent study provides new insight into the mechanism by which gene deletions produce the DGS and VCFS phenotypes.     

Atypical presentation of the Prader-Willi syndrome. Mosaic trisomy 15?

We report a female with Prader-Willi syndrome and hemihypertrophy. We discuss the possibility of an undetected mosaicism for trisomy 15 explaining this unusual feature.     

Biosynthesis of S-associated proteins following self- and cross-pollinations in Brassica campestris L. var. ‘T. 15’

Summary Homozygote plants for the (S) self-incompatibility gene have been produced in Brassica campestris L. var. T 15. Stigmas from plants designated S ₁ S ₁, S ₂ S ₂ and S ₄ S ₄ were extracted and their protein separated on an isoelectric focusing mini-gel. Differences were observed between proteins from stigmas of the three S-homozygous groups: S-genotype specific proteins were determined for S ₁ S ₁ and S ₂ S ₂ stigmas that were absent in the self-compatible S ₄ S ₄ stigmas. Carbon dioxide (CO₂), which is known to block the self-incompatibility reaction in Brassica, was applied to [³⁵S]-methionine unpollinated, self- and cross-pollinated stigmas to observe the effect of external CO₂ on the synthesis of these S-associated proteins. The results indicate that pollination triggers a dramatic reduction in protein synthesis in general and in the synthesis of S₂-associated protein after self-pollination in particular.     

Viruses and autoimmune disease--two sides of the same coin?

Some viruses have the ability to modulate the development of autoimmune diseases. Virus infections have long been associated with the exacerbation of autoimmune disease, however, there is also evidence that viruses can actually protect against autoimmune disease. Several experimental models have been developed to investigate how some virus infections can prime for and trigger autoimmunity whereas others ameliorate the pathway leading to clinical disease. It is possible that the type I interferons, via interleukin 12, provide the link between viruses and autoimmunity.     

Hypoalbuminaemic hyponatraemia: a new syndrome?

Six patients with severe hyponatraemia had neurological features of hyponatraemia and pronounced hypoalbuminaemia. All had biochemical features typical of the syndrome of inappropriate secretion of antidiuretic hormone with low serum osmolality and an inappropriately high urinary osmolality. All were given infusions of whole plasma or albumin solution, or both, to restore their plasma albumin concentrations to normal, which led to a dramatic increase in plasma sodium concentrations and serum osmolality, with a concomitant fall in urinary osmolality in all patients. Neurological features were reversed in four patients. It is suggested that severe hypoalbuminaemia is an important cause of appreciable hyponatraemia; infusions of plasma and albumin in such patients may reverse the biochemical and clinical features and should form the basis of management.