The structure of equivalence classes.
Count four simple things—size, nodes, singles, direction—to predict and fix equivalence class learning before you start.
01Research in Context
What this study did
Green et al. (1987) built a four-number recipe that describes every equivalence class.
The recipe is: how many items, how many nodes, how many singles, and which way the arrows run.
They showed how old data fit the recipe and how to plan new tests with it.
What they found
Any set of equivalent stimuli can be drawn with four simple counts.
Change one count and you predict how hard the class will be to learn.
The recipe lets you compare different labs and procedures apples-to-apples.
How this fits with other research
Arntzen et al. (2018) used the recipe to explain why pictures plus a six-second delay triple class formation.
Lantaya et al. (2018) showed the recipe still works when you swap three-array matching for a simpler go/no-go setup.
Perez et al. (2020) looks like bad news—blocking the correct choice hurts class formation—but the recipe predicts this: fewer observed arrows raise the node count and make learning harder.
Why it matters
Before you run your next equivalence program, write down the four numbers. If the node count is high or you have many singles, add extra trials or prompts. The recipe turns "it didn’t work" into a clear plan you can fix on Monday.
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Join Free →Map your next stimulus set with the four counts; if nodes > 2, insert extra training blocks on those items first.
02At a glance
03Original abstract
THE STRUCTURE OF EQUIVALENCE CLASSES CAN BE COMPLETELY DESCRIBED BY FOUR PARAMETERS: class size, number of nodes, the distribution of "singles" among nodes, and directionality of training. Class size refers to the number of stimuli in a class. Nodes are stimuli linked by training to at least two other stimuli. Singles are stimuli linked by training to only one other stimulus. The distribution of singles refers to the number of singles linked by training to each node. Directionality of training refers to the use of stimuli as samples and as comparison stimuli in training. These four parameters define the different ways in which the stimuli in a class can be organized, and thus provide a basis for systematically characterizing the properties of stimuli in a given equivalence class. The four parameters can also be used to account for the development of individual differences that are commonly characterized in terms of "understanding" and connotative meaning.Methods are described for generating all possible combinations of parameter values, and a formula is introduced which specifies all of the parameter values for an equivalence class. Its utility for interrelating experimental procedures is demonstrated by analyzing a number of representative experiments that have addressed equivalence-class formation.
Journal of the experimental analysis of behavior, 1987 · doi:10.1901/jeab.1987.48-317