### Random Zeros

What is the difference between a random zero and a fixed zero? This dataset includes a random zero. Does this impact the analysis of this data? How so? What can you do about this?

### The Experimental Design

Does it make a difference how the data is collected? How does the experimental design impact the analysis of the data in this study? Is this something that you should report? How? Why?

In the context of the design of the study, both *Age* and *Gender* should be viewed as explanatory variables. The intent of the study was to obtain 50 males and 50 females in each of three age groups, for a total sample size of 300. For whatever reasons, this was not quite accomplished. There were 48 males and from each of the 3 age groups, and 51, 51 and 47 females in the three age groups, so that there were 144 males and 149 females, and 99, 99, and 95 people in the three age groups.

### What kinds of questions can be asked?

Given this set of data, what questions could be asked by researchers? Who decides which questions are going to be the focus of the analysis? What if something else comes up that the researcher has not considered? What role should the statistician play? What responsibilities does the statistician have?

In this case study, with both *Stress* and *Smoking* treated as responses

- Is there an interaction between the responses
*Stress*and*Smoking*? - Does the explanatory variable (factor)
*Age*affect the joint responses or does it affect one response but not the other, or does it affect neither response? - Does the explanatory variable (factor)
*Gender*affect the joint responses or does it affect one response but not the other, or does it affect neither response? - Do the two factors interact to affect the responses?

When one of the two variables is a response (say *Stress*) and the other (say *Smoking*) is a ‘factor’

- Are there interaction effects—two-way or three-way--among
*Age*,*Gender*, and*Smoking*on the response variable? - Which factors among the three possible affect the response variable?