If not, we should avoid using statistical syllogism to arrive at a conclusion about whether Fritz smokes. Otherwise we will be committing the fallacy of ignoring relevant evidence . Note that it doesn't take actual statistics on an alternative reference class to make a given reference class inappropriate. If a study showed that most cocker spaniels are docile, it would not be safe to conclude that Laddie, an abused cocker spaniel, is docile. If we ignore this information and make the inference anyway, we will be ignoring relevant evidence .
Generalization is the subject of oddly conflicting attitudes.
Many people are quite willing to generalize on the basis of a few cases or even a single case, thereby committing the fallacy of small sample or hasty generalization . The foundation of the reasoning lies in mathematics, which is deductive. The relevant mathematical result, qualitatively stated, is that most of the large samples that could possibly be drawn from a population have compositions close to that of the population . More specific results can be given for particular sample sizes. Moreover, the margin of error can be reduced by increasing the sample size.