Signal detection theory

Signal detection theory is a statistical technique designed to locate a signal against a background of noise. In addition it describes one of the more important cognitive tasks that brains perform. Every sensory organ in an animal is inundated with a variety of stimuli. Most of this will be noise or meaningless information, but some of it will be highly valuable and informative. The background stimuli are noise, while the information is a signal. The nervous system and primarily the brain use various algorithms to attempt to detect these signals. Like all such adaptations the signal detection algorithms in animals have been under intense pressure from natural selection and is strongly shaped by evolution. The actual algorithms used and the evolutionary pressures that shaped them may help us understand one aspect of why people believe crazy things.

Basic theory
In basic signal detection theory there are two possible states for a signal: present or absent. Individuals attempting to detect the signal will either say it is present or absent. Combined, that leads to four possible combinations, labeled as follows:

In understanding how signal detection works in the animal (and hence human) brain we must look at the costs and benefits from an evolutionary standpoint. Obviously accuracy is highly valued, so algorithms that perform correct rejections and get hits will be selected for. In an ideal world we would move towards maximum accuracy in both categories. In reality this doesn't happen because identifying hits and correctly rejecting false alarms become contradictory goals. At a certain point, in order to increase our identification of hits we have to increase sensitivity to the signal, though this increases false alarms. To reduce these we must lower sensitivity. So the real nitty gritty is the evolutionary trade-off between increasing correct identifications of a signal and decreasing false alarms by setting the optimal threshold.

The optimal threshold for most signal detection is not going to be to "split the difference." The cost of false alarms are usually significantly less than the cost of a miss. The classic example is a rabbit in a field looking out for predators. A false alarm, while costly to a degree (leaving a food patch, exerting energy running away), it is nothing compared to the cost of missing a predator. The evolutionary pressure may be so strong towards avoiding a miss that false alarms become very frequent. This will lead to the detection of subjectively meaningful signals and patterns in an environment even when none exist. Even completely random stimuli will falsely appear to be detectable meaningful information.

Data fit
This fits the data very well. Humans are masters at finding patterns where none exist. The famous Rorschach Inkblot Test is a perfect example. This detection of a meaningful pattern may also explain a great deal of the attachment to woo, quackery, and pseudoscience. People may come to believe that the Universe will give them what they want (à la the Law of Attraction) because they detect a pattern in what they think about and what they observe. People may come to believe that homeopathy will cure disease because when they get a cold they swallow some water and seven days later they are fine. Perhaps the concept of God and religion are also by-products of hyperactive pattern recognition observing nature.

Since we are naturally inclined to detect patterns where there are none we must develop tools that can help us avoid such bias. The best tools we have at our disposal are science and the scientific method combined with rigorous statistical analysis. These tools help us move past our bias and see what really is a signal and what is really just meaningless noise. Unfortunately, people get attached to their perceived patterns in the noise.