User:Lintu Ramachandran/sandbox

= Origin =

Automatic Encoding
In 1979 Hasher and Zacks conduct experiments and discover that frequency of occurrence is one of the aspects that are continually registered in the memory, regardless of age, ability or motivation. . Automatic processing of fundamental information: the case of frequency of occurrence. The American Psychologist, 39(12), 1372-1388. In 1984, they call this process the automatic encoding. The same paper describes evidence that shows that frequency information is stored for a wide variety of events and this encoding is not affected by practice or instructions or any differential variables. The differential variables included age, sex, intelligence etc.

Infant study
To test whether infants could recognize numerical correspondences, Starkey et al designed a series of experiments in which 6 to 8 month old infants were shown pairs of either a display if two objects or a display of two objects. While the displays were still visible, infants heard either two or three drumbeats. Measurement of looking time revealed that the infants looked significantly longer toward the display that matched the number of sounds. In these studies, it was found that infants looking time decreased after being shown several arrays with the same small number of items but that looking time recovered when a novel number of items was shown

The Contigency Rule
Later on, Barbara A. Spellmen from University of Texas describes the performance of humans in determining cause and effects as the contingency rule ΔP, defined as

ΔP = P(E|C) - P(E|~C)

where P(E|C) is the probability of the effect given the presence of the proposed cause and P(E|~C) is the probability of the effect given the absence of the proposed cause. The ΔP value as a result is always bound between -1 and 1. Even though the contingency rule is good in predicting decisions of people in case of events resulting from a single case, when it comes to predicting outcomes of events multiple causes, there exists a large deviation from the contingency rule called the cue-interaction-effect. Cue-Interaction-Effect In1993 Baker Mercer and his team used video games to demonstrate this effect. Each test subject was supposed to help a tank travel across a mine field using a button that sometimes worked correctly in camouflaging and sometimes did not. As a second cause a spotter plane, a friend or an enemy would sometimes fly over the tank. After 40 trials, the test subjects were asked to evaluate the effectiveness of the camouflage and the plane in helping the tank through the minefield.

Mathematically, there are two contigency values possible for the plane as shown in table below: From the experimental results, it was found that the subjects rated the effectiveness of the camouflage as higher in the .5/0 condition, in which the contingency for the plane was small, than in the .5/1 condition, in which the contingency for the plane was large, even though Pcamouflage was the same in both conditions.

Gigenzer Contributions
Gigerenzer claims that the results are consistent with the ecological rationality -context-bound inferential and mathematical abilities| that human beings have acquired in the course of human evolution. Gigerenzer and his research group attribute the supposed 'errors' in question to condition of the experiments which make it difficult for human beings to exert their intellectual abilities properly | conditions very different from the sort of environmental context in which those abilities were acquired. Thus, it is no wonder that the subjects give wrong answers in these experiments; therefore, if an experimenter provides such settings that the subjects can exercise their intellectual abilities specific to the informational structure ofa particular environment and a particular way of informational representation, then they can give an answer complying with the laws of logic and probability. Gigenzer publishes a paper titled “The psychology of good judgment: frequency formats and simple algorithms”, coining the term frequency format hypothesis term for the first time. =Supporting Arguments=

Evoltuionary Perspective
Gigenzer argued that from an evolutionary point of view, a frequency method was easier and more communicable compared to conveying information in probabilities. He argues that probability and percentages are rather recent forms of representation as opposed to frequency. The first known existence of a representative form of percentages is in the seventeenth century. He also argues that more information is given in the case of frequency representation. For instance, instead of conveying data as 50 out of 100, using the frequency form, as opposed to saying 50%, using the probability format, gives the users more information about the sample size. This can in turn make the data and results more reliable and more appealing.

Elaborate Encoding
An explanation given as to why people choose encounter frequency, that in the case of frequencies, the subjects are given vivid descriptions, while with probabilities only a dry number is given to the subject. This could in turn mean that the frequency encounters are remembered by the brain more often than in the case of probability numbers. Thus this might be a reason why people in general intuitively choose frequency encountered choices rather than probability based choices.

Sequential Input
Yet another explanation offered by the authors is the fact that in the case of frequency, people often come across them multiple times and have a sequential input, compared to a probability value, which is given in one time. From Joyce Medina’s Brain Rules, sequential input can lead to a stronger memory than a onetime input. This can be a primary reason why humans choose frequency encounters over probability.

Easier Storage
Another rationale provided in justifying the frequency format hypothesis is that using frequencies makes it easier to keep track and update a database of events. For example, if an event happened 3 out of 6 times, the probability format would store this as 50%, whereas in frequency format it is stored as 3 out of 6. Now imagine that the event does not happen this time. The frequency format can be updated to 3 out of 7. However for the probability format updating is extremely harder.

Classifying information
Frequency representation can also be helpful in keeping track of classes and statistical information. Picture a scenario where every 500 out of 1000 people die due to lung cancer. However, 40 of those 1000 were smokers and 20 out of the 40 had a genetic condition predisposed to possible lung cancer. Such class division and information storage can only be done using frequency format, since a number .05% probability of having lung cancer does not give any information or allow to calculate such information. =Refuting Arguments=

Ease of Comparison
Critics of the frequency format hypothesis argue that probability formats allow for much easier comparison than frequency format representation of data. In some cases, using frequency formats actually does allow for easy comparison. If team A wins 19 of its 29 games, and another team B wins 10 of its 29 games, one can clearly see that team A is much better than team B. However comparison in frequency format is not always this clear and easy.If team A won 19 out of its 29 games, comparing this team with team B that won 6 out of its 11 games becomes much harder in frequency format. But, in the probability format, one could say since 65.6%(19/29) is greater than 54.5%, one could much easily compare the two.

Memory Burden
Tooby and Cosmides had argued that frequency representation helps update data easier each time one gets new data. However this involves updating both numbers. Referring back to the example of teams, if team A won its 31st game, note that both the number of games won(20->21) and the number of games played(30->31) has to be updated. In the case of probability the only number to be updated is the single percentage number. Also, this number could be updated over the course of 10 games instead of updating each game, which cannot be done in the case of frequency format.