Question

In: Statistics and Probability

Two independent factors, X1 and X2, are deemed to have significant 2-way interaction when? A) the...

Two independent factors, X1 and X2, are deemed to have significant 2-way interaction when?

A) the effect of X1 depends on the level of X2

B) the effect of X1 is independent of the level of X2

C) X1 and X2 are highly correlated

How many experimental runs will be conducted in a 2^5 experiment with 2 replicates per each run combination?

A) 5

B) 32

C) 64

Expert Solution

Two independent factors, X1 and X2, are deemed to have significant 2-way interaction when?

A) the effect of X1 depends on the level of X2

We illustrate this through an example:

Suppose we are conducting a taste test to determine which food condiment produces the highest enjoyment. Our two independent variables are both categorical variables: Food and Condiment.

The interaction term is: Satisfaction = Food Condiment FoodxCondiment

We shall include only two foods (ice cream and hot dogs) i.e. two levels of factor Food and two condiments (chocolate sauce and mustard) i.e. two levels of factor condiment in our analysis.

If someone asks , “Do you prefer ketchup or chocolate sauce on your food?” Undoubtedly, we will respond, “It depends on the type of food!” That’s the “it depends” nature of an interaction effect.

Hence iteraction is significant when the effect of X1 depends on the level of X2.

In 2^5 experiment, we have 32 level combinations and if we use 2 replicates, then under each replicate we use 32 level combinations, hence we need 64 run combinations.

orchestra answered 2 years ago

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