This program will not tell you explicitly what sample size to use. Instead, you must give it information on the sizes of the differences that you want to be able to detect, on the variability of the response (e.g., modulus of rupture (MOR)), on the correlation between the predictor (e.g., modulus of elasticity (MOE)) and the response, on the significance level that you want to achieve, on the number of factors and levels, and on the number of replicates.
Given this information, the program will calculate the probabilities that you will be able to detect the differences in which you are interested (power). If these probabilities are too low (say below .90), then you will have to find a predictor that is more correlated with the response, accept a larger significance level (say .10 rather than .05), accept a higher risk of not statistically detecting the differences in which you are interested, or be willing to consider larger sample sizes.
Note: If the number of replicates is small, then these power calculations may overestimate the power (and thus underestimate the required sample size) unless the data is analyzed via an analysis of covariance. For .05 significance level tests, the program allows the user to check the theoretical calculations via simulations.
Which kind of test do you want to consider?
The PRE-SPECIFIED requirement is associated with a statistical subtlety that a user might want to discuss with a statistician. It involves the issue of ``multiple comparisons.''