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This is how we generally test for the presence of one or more effects. In our experiments we manipulate one or more independent variables, we control for other independent variables, and we measure one or more dependent variables. Each independent variable (or factor) has two or more levels. Each datum comes from some condition, or combination of the levels of the factors. For example, suppose our dependent variable is VOT and our independent variables are consonant (let’s say 3 levels), following vowel (let’s say 5 levels), and stress (let’s say 2 levels) – plus the subjects who produce the speech data; and we control for certain things, such as position in word by having all consonants word-initial, and voicing by having them all voiceless. Each single VOT measurement comes from some particular condition such as “p before i in a stressed syllable” (and from a particular subject). There is a set of all measurements (from all the subjects) for each condition, e.g. “p before i in a stressed syllable”; and these can be combined with other conditions to produce larger sets for all the different levels of the different factors, e.g. all the “p” data, or all the “stressed” data, or all the “stressed p” data – any subset defined by your variables.
Analysis of an experiment with one factor is called “1-way”, of an experiment with two factors “2-way”, etc. Since you test for an effect of a factor by forming an F-ratio, there is a separate F-ratio for each factor in your experiment; these test for main effects. This doesn’t depend on how many levels each factor has. So, for example:
1-way ANOVA: F-ratio for 1 factor (regardless of its number of levels)
2-way ANOVA: F-ratios for 2 factors (regardless of their numbers of levels)
(etc.)
In our example above, there would be F-ratios for consonant, vowel, and stress factors. F-ratios can also be formed for the various subsets of the data; these are called interactions. The consonant x stress interaction looks at the effect of the stress factor on each of the different consonants, and the effect of the consonant factor on each of the different stresses.