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Would it be incorrect to refer to an experimental design as "crossed" if one of the treatments is a continuous variable rather than a categorical variable? The continuous variable covers roughly the same range for each factor level as part of the design. But due to the nature of the data it isn't really possible to have matching values across factor levels, just a similar range for each group.

To me this seems similar in spirit to a crossed experimental design but is it correct to refer to it as this in a publication?

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The distinction between a crossed and nested is related the arrangement of the factors and the factors' levels and not whether the levels are continuous or categorical.

From paraphased from Wikipedia: "A fully crossed experiment whose design consists of two or more factors, each with possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors.

As long as all of the combinations of all factors' levels are possible it is considered a fully crossed designed.

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Whether an experiment is crossed or nested really depends on the structuring of the factor levels. Factors could either be crossed with other factors or nested within other factors.

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