The Dream (1910) by Henry Rousseau.[/caption]What do you do when the fire alarm in your office building goes off and everyone heads for the exit? You know for a fact that this is a well-rehearsed ritual, triggered, as long as anyone cares to remember, not by a ticking bomb planted by a terrorist but by the charred remains of a toast left unattended by a careless co-worker somewhere in the building.
Of course, you join the exodus and head for the exit. This is because the cost of what statisticians call Type I error in situations like this one is “asymmetrical”. In case the fire alarm was triggered by a ticking bomb and you ignore it, you risk losing life and limb.
A Type I error is committed when a true null hypothesis is rejected. When an office fire alarm goes off, the null hypothesis is that the alarm is caused by a grave security threat, perhaps a bomb planted by a terrorist. The alternative hypothesis is that a burnt toast occasioned the fire alarm. You would rather drop everything and head for the designated assembly area than risk the consequences of a security breach even if the probability of such an event is tiny.
When our ancestors were still living in the wild at the mercy of the beasts of prey, they had to make similar calculations. Was the rustle in the bush caused by a gust of wind or a crouching tiger? A Type I error, which in this case meant ascribing the rustle to a gust of wind when, in reality, a hungry tiger was prowling nearby, could be quite unpleasant.
Conversely, false null hypothesises can be accepted, giving rise to Type II errors. If a superstitious person is boarding in an old house, then he may take fright at nocturnal sounds, accepting his own null hypothesis that nocturnal sounds in an old house are made by ghosts. The alternative hypothesis is that aging manmade structures can creak and groan, producing sounds which get amplified at night.
The costs of Type II errors can be prohibitive, too. For example, if airport security checkpoints fail to catch armed terrorists, the consequences can be catastrophic.
Type I errors cannot be decreased without increasing Type II errors and vice versa. If, to minimize Type II errors, security screenings at airports are made too stringent, many innocent passengers would be caught up in the dragnet, increasing Type I errors. However, minimising Type I errors means relaxing security measures, risking the possibility of waving along armed hijackers and bombers through security checkpoints, raising Type II errors and security breaches.
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