References about this question: Basic Logic of the Analysis of Variance; Carrying Out an Analysis of Variance; Hypothesis Testing with the Analysis of Variance; Assumptions in the Analysis of Variance; Effect Size and Power for the Analysis of Variance; Factorial Analysis of Variance; Recognizing and Interpreting Interaction Effects; Analysis of Variance in Research Articles

Question: For the following problems, a hypothetical survey was taken among couples and their average degree of contentment in the relationship assessed as a function of 1) how much passion was experienced and 2) how much they communicated.Passion and communication are key to a successful relationship, but it is also possible that too much passion may create jealousy and trouble in the relationship.Also, too much communication could involve too much self-revelation and be potentially detrimental to the relationship.Therefore, many different types of scenarios can be imagined, including different main effects and interactions.

Determine whether there is a main effect of passion, a main effect of communication, and an interaction between the two.Do not worry about whether they are statistically significant.

Use the following digits to represent each effect:

1 = Main effect of Communication

1 = Main effect of Passion

1 = Interaction

0 = No main effect of Communication

0 = No main effect of Passion

0 = No Interaction

Keeping the order above, brings the digits together into a single number.

For example, if there is a main effect of communication, no main effect of passion, and an interaction, write 101

If there is no main effect of communication, a main effect of passion, and no interaction, write 010

If there are the two main effects including an interaction, write 111

If there are no effects at all, write 000

And so forth...

For the following experiments, do whatever is necessary (use the margin means, draw the line graphs or bar graphs if necessary) and tell use which effects seem to exist:

#1.

Passion Low High Never 5 5 Communication Often 5 5Passion Low High Never 1 1 Communication OftenPassion Low High Never 1 Communication Often 1Passion Low High Never Communication Often 5\f\f\f\f