One-Way Analysis of Variance

One-way analysis of variance (ANOVA) is a data analytic tool that allows examining differences in a dependent variable based on one independent variable containing two or more levels. For example, say a researcher wants to study the effect of videogames on learning. In this experiment, all participants were randomly assigned to three experimental conditions: one group of participants learned the material by playing an instructional videogame, another group of participants learned the material through traditional instructional method by receiving a lecture, and the third group, a control group, did not receive either manipulation and just completed the dependent variable measure. The researcher wants to know whether there are differences based on these instructional methods. To examine these differences, one-way ANOVA would be appropriate.

ANOVA is appropriate for both independent groups and repeated-measures design. One-way ANOVA, independent group design is the simplest of these designs. This design is also sometimes referred to as the simple randomized-group design or single factor experiment, independent group design. This design has two key characteristics: random selection and random assignment. Random selection means that study participants are drawn randomly from the population, and random assignment means that participants are randomly assigned to experimental conditions. For example, in the videogame study example, each participant had an equal chance to end up in either experimental group, and their assignment to an experimental group was determined completely randomly.

The null hypothesis in this experiment asserts that the effects of both methods and the effects of the no treatment control group have the same effect on learning, but the alternative hypothesis asserts that at least one or maybe more levels of the independent variable (here, training) have different effects on the dependent variable, which in this case is learning. Because significant one-way ANOVA results suggest that at least one difference across condition exists, instead of stating that the videogame condition is significantly different from lecture, and lecture is different from the control condition, as a t-test would, one-way ANOVA is called an omnibus, or overall, test. These differences in the dependent variable are inferred on the basis of a test, called an F test, comparing systematic variance to unsystematic variance.