## DEFINITION of Random Factor Analysis

Random factor analysis is a statistical analysis technique used to determine the origin of random data in a data collection. Random factor analysis is used to decipher whether the outlying data is caused by an underlying trend or just simply random occurring events and attempts to explain the apparently random data. It uses multiple variables to more accurately interpret the data.

## BREAKING DOWN Random Factor Analysis

Random factor analysis is commonly used to help companies better focus their plans on potential or actual problems. If the random data is caused by an underlying trend or random recurring event, that trend will need to be addressed and remedied accordingly. For example, consider a random event such as a volcano eruption. Sales of breathing masks may skyrocket, and if someone were to just look at the sales data over a multi-year period this would look like an outlier, but the analysis would attribute this data to this random event.

In Analysis of Variance, a popular statistical technique, and several other methodologies, there are two types of factors: fixed effects and random effects. Which type is appropriate depends on the context of the problem, the questions of interest and how the data is gathered.

With a fixed effect factor, data has been gathered from all the levels of the factor that is of interest.

For instance, the purpose of an experiment is to compare the effects of three specific dosages of a drug on the response. "Dosage" is the factor; the three specific dosages in the experiment are the levels; there is no intent to say anything about other dosages.

A random effect factor then includes a factor with many possible levels. Interest is at all possible levels, but only a random sample of levels is included in the data.

For example, a large manufacturer of widgets is interested in studying the effect of a machine operator on the quality of a final product. The researcher selects a random sample of operators from the large number of operators at the various facilities that manufacture the widgets. The factor is "operator." The analysis will not estimate the effect of each of the operators in the sample, but will instead estimate the variability attributable to the factor "operator."