## What Is Random Factor Analysis?

Random factor analysis is a technique used to determine the quality of a firm's output using a randomly collected sample. This greatly reduces the time and cost needed for quality control, but can also increase the error rate as the inferred quality is based only on statistical techniques using the randomly drawn sample.

Random factor analysis may also refer to a random effects model, which 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. In contrast, with fixed analysis, certain variables are controlled for or held constant.

### Key Takeaways

- Random factor analysis is a way of determining the level of quality of a firm's output by randomly sampling from its production.
- It may also refer to a form of statistical inference, known as random effects, which treats inputs as random variables.
- Random factor analysis can be contrasted with fixed factor analysis, or fixed effects, which holds certain variables constant or accounts for every available unit.

## Understanding 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 (ANOVA), a popular statistical technique, and several other methodologies, there are two types of factor models: 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.

## Examples of Random Factor Analysis

For instance, say that the purpose of an experiment is to compare the effects of different dosages of a drug on the biological response observed. A random effect factor would consider a series of dosages, drawn at random, that can take on many possible levels. By drawing randomly from among all possible levels, analysis can be undertaken more efficiently since it would be far too costly and time-consuming to evaluate every possible dosage level.

As another example, assume that 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 a large number of operators at the various facilities that manufacture the widgets. The analysis will not estimate the effect of each of the operators in the sample, but will instead estimate the variability attributable to the operators.