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Answer :
Final answer:
The correct answer is A, which states that a 2x2x2 factorial design has 3 factors, 2 levels per factor, and 8 conditions. This design allows for the assessment of individual and interaction effects of the factors with a precise number of experiments required for comprehensive analysis.
Explanation:
In factorial design notation, a 2x2x2 factorial design refers to a design with three factors, each with two levels, resulting in a total of eight unique conditions or experimental groups (2x2x2=8). Each number in this notation represents a factor, and the exponent indicates how many levels there are per factor. For instance, a "2x3" factorial design would indicate two factors, but the second factor would have three levels, leading to six conditions. Similarly, if a third factor was added with two levels, we would have the aforementioned "2x2x2" or eight conditions.
The correct answer to the question 'A 2x2x2 factorial design has the following:' is A, which is '3 factors, 2 levels per factor, 8 conditions'.
By understanding factorial design, we appreciate the ability to examine not just the individual effects of each factor but also their interactions, which can provide profound insights in experimental studies. This structure of experimental design significantly impacts the total number of experiments required, along with associated costs and resource allocation.
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