Error usually refers to how much functions, formulas, and statistics fail to fully explain or model a true or theoretical value. In other words, error is the difference between an actual and predicted value. While some degree of error or uncertainty can exist in statistical analyses, identifying and quantifying error can help us explain the presence of error.

Consider a contractor hired to replace the roof on a house. The contractor can calculate an estimated price for the job with a number of variables. Some variables could include the dimensions of the roof, the pitch, and the type of roof. However, variability in these and other factors can result in a different final cost. Both contractor and homeowner will be interested in not only the estimated cost, but the error of the formula used to estimate the cost.

The following are examples of types of error in ANOVA:
Residual error
The variability that remains after all the main effects and interactions are identified.
Family error rate
The maximum probability of obtaining one or more confidence intervals that do not contain the true difference between level means.
Type I and Type II error
The probability of rejecting a true hypothesis or accepting a false one.