Factors

The word factor is just another word for independent variable. Usually factors are qualitative variables; the different values that a factor can have (such as sales prices of $20, $50 or $90) are called levels of the factor.

• In Example 1 there is just one factor: the cooking temperature. It has four, ordered levels.

• In Example 2 there are two factors: Education, and type of experience. Education could be a quantitative factor whose values are just the number of years of education the salesperson has had. More likely it is an ordered qualitative factor with levels like High School, College Degree, Master's Degree, and PhD. Type of past employment experience is probably an unordered qualitative factor, with levels like laborer, office work, sales, consulting, etc.

• In Example 3 again there are two qualitative factors (both unordered): which center the employee is at, and which training program the employee was assigned to.

ANOVA applied to single-factor studies is called one-way ANOVA. ANOVA applied to multi-factor studies is called multi-way ANOVA.

Many studies have a mix of ``experimental'' and ``observational'' components. In a study, the factors that were controlled and randomly assigned by the researcher are called experimental factors. Those that merely classify subjects, but are not under the control of the researcher, are called classification factors. Example 3 is an example with both an experimental factor (which of the two programs the examinee was assigned to) and a classification factor (which training center the employee was at).

If we tried to analyze Example 3 as a one-way ANOVA using only the training program, we might mask some important differences among the centers (suppose at Center A, method 2 is much better than method 1, but at centers B and C, method 1 is moderately better than method 2; if the data is ``pooled across centers'' then we might conclude that the two methods are equally effective.

If we analyze Example 3 as a two-way ANOVA, we still must be careful: if method 1 is better than method 2 at all three sites, the evidence in favor of method 1 is strong. On the other hand, if method 2 does better at some centers and worse at others, these differences are hard to interpret without getting more information: perhaps one center has better teachers for method 2, or some centers are in geographic locations where better education is provided. At least the differences among levels of the classification factor (training site) suggest what sort of information is needed to understand the results.