Which Analysis Should I do?

2005-12-07

First, determine which variable in the problem is the Response Variable. This is often called the Y Variable.

• Is Y continuous or a count?
  • If Y is continuous, the methods of this course are valid if it follows, at least approximately, a normal distribution. The normal distribution has a separate parameter for variance which must be estimated by a mean square.
  • If Y is a count, we have methods for the Poisson and binomial distributions. For these distributions, the variance is computed from the mean so we don't need to estimate it.

Next, determine which variable or variables are the Explanatory Variables. They are often called the X Variables.

• How many X variables are there?
• For each X variable, determine if it is continuous or categorical or if it can be either.

Next, determine the design points, that is, all the distinct combinations of levels or values of the X-variables.

• If Y follows a normal distribution, is the variance is the same at each design point (that is, can we assume homoscedasticity)? If so, we can use a pooled variance estimator. In an ANOVA, this will be called the Residual Mean Square, Error Mean Square or Pure Error Mean Square.
• Are there replicated observations on at least one design point? If so, we can estimate Pure Error.
• If the number of replicate observations is the same at each design point, the design is balanced. The analysis of some unbalanced designs is too complicated to be done without a computer.

Finally, choose the analysis from the following chart.