using the sample information to determine the factor–level combination that will
give the maximum yield. From the table, we see that crop yield increases when the
nitrogen application is increased from 40 to 60 (holding phosphorus at 10). Yield
also increases when the phosphorus setting is changed from 10 to 20 (at a fixed
nitrogen setting of 40). Thus, it might seem logical to predict that increasing both
the nitrogen and phosphorus applications to the soil will result in a larger crop
yield. The fallacy in this argument is that our prediction is based on the assumption
that the effect of one factor is the same for both levels of the other factor.