Inductive Generalizations

1.    An inductive generalization generalizes from a sample to an entire class. We use the sample to reach a conclusion about a target class.

·       Sample: the part of a class referred to in the premises of an inductive generalization.

·       Target population: in the conclusion of an inductive generalization, the members of an entire class of things.

·       Property in question: in inductive generalizations, the members of the sample and target population share a property or feature in common.

2.    The premises of an inductive argument are not offered as definitive evidence for the truth of their conclusion. Inductive generalizations are either strong or weak. How do we determine if an inductive generalization is strong or weak?

3.    Kinds of Inductive Generalizations:

 

Enumerative Inductive Generalization (Universal)

1. All observed X's are f.

Therefore, probably,

2. All X's are f.

Restricted Enumerative Inductive Generalization

1. All (or most) observed X's are f.

Therefore, probably,

2. Most X's are f.

Inductive Argument to a Singular Conclusion

1. All, or most, observed X's are f.

2. Case A is an X.

Therefore, probably,

3. Case A is f.

Statistical Inductive Argument

1. N percent of observed X's are f.

Therefore, probably,

2. Approximately N percent of unobserved and observed X's are f.

 

 

4.    Representativeness. In a strong inductive generalization, the sample must represent the target class.

·       A representative sample is a sample that possesses all relevant features of a target population and possesses them in proportion that are similar to those of the target population.

·       A feature or property P is relevant to another feature or property Q if it is reasonable to suppose the presence or absence of P could affect the presence or absence of Q.

·       The less confidence we have that the sample of a class or population accurately represents the entire class or population, the less confidence we should have in the inductive generalization based on that sample.

·       A biased sample is a sample that is not representative

·       If the population is heterogeneous, then the sample should be random or otherwise constituted so as to represent the target population. A random sample of a population is one in which every individual has an equal chance of being selected.

5.    Random variation and margins of error.

·       When we generalize from the percentage of a random sample that has a certain feature to the percentage of the target class that has that feature, the larger the sample size, the higher the confidence level or the smaller the margin of error.

6.    Sample size. Typically, the larger the sample the better. Are the size and representativeness of the sample appropriate for how guarded the conclusion is?

·       Except in populations known to be homogeneous, the smaller the sample in an inductive generalization, the more guarded the conclusion should be.

7.    Fallacies of inductive generalizations

a.     Hasty generalization: a generalization based on a sample too small to be representative.

b.     Appeal to anecdotal evidence: a form of hasty generalization presented in the form of an anecdote or story.

c.     Refutation via hasty generalization: when we ask someone to reject a claim on the basis of an example or two that run counter to the claim.

d.     Biased generalization (biased sample): a generalization about an entire class based on a biased sample.

 

Procedure for Evaluating the Strength of Inductive Generalizations

1. Determine that indeed you have an argument and that it is an inductive generalization.

2. Identify the conclusion, which usually contains the target population. If no explicit target population is mentioned, extrapolate to the most reasonable population. Note the degree of confidence with which the conclusion is stated.

3. Be able to identify the premises,  which usually contains the sample on which the generalization is based.

4. Note any basic mathematical information (the size of the sample, percentages, etc.). Do the numbers add up? Are they overly precise (the problem of pseudo-precision)?

5. How variable is the population with regard to the trait or property that the argument is about.

6. Consider any information given regarding how the sample was selected.

7. Try to evaluate the representativeness of the sample, drawing on common sense, background knowledge, etc.