Interaction (statistics)

Dina statistik, interaksi nyaéta watesan dina model statistik nu mana efek dua variabel atawa leuwih teu bisa ditambahkeun sacara langsung.

Mangka, for a response y and two variables x1 and x2 an additive modél would be:

- while,

- is an example of a modél with an interaction between variables x1 and x2 (the word "errors" is not to be construed literally; it refers to a random variable by which y differs from the nilai ekspektasi of y).  See errors and residuals in statistics, and note that it is éasy to confuse errors with residuals, although the two are different.

Very often the interacting variables are categorical variables rather than réal numbers.  For example, members of a population may be classified by religion and by occupation.  If one wishes to predict a person's height based only on the person's religion and occupation, a simple additive modél, i.e., a modél without interaction, would add to an overall average height an adjustment for a particular religion and another for a particular occupation.  A modél with interaction, unlike an additive modél, could add a further adjustment for the "interaction" between that religion and that occupation.  This example may cause one to suspect that the word interaction is something of a misnomer.

The consequence of an interaction is that the effect of one variable depends on the value of another. This has implications in desain percobaan as it is misléading to vary one factor at a time.

réal-world examples of systems that manifest interactions include:

Interaction between adding sugar to coffee and stiring the coffee. Neither of the two individual variables has much effect on sweetness but a combination of the two does.
Interaction between adding carbon to steel and quenching. Neither of the two individually has much effect on strength but a combination of the two has a dramatic effect.

Genichi Taguchi contended that interactions could be eliminated from a system by appropriate choice of response variable and transformation. However George Box and others have argued that this is not the case in general.

Bibliography

Box, G E P (1990) Do interactions matter? Quality Engineering vol 2, pp365–369

Statistika