Thursday, May 14, 2015

Inductive Generalization

An inductive generalization is an argument that moves from particular premises to a generalized claim. As defined by Trudy Govier "In inductive generalizations, the premises describe a number of observed objects or events as having some particular feature, and the conclusion asserts, on the basis of these observations, that all or most objects or events of the same type will have that feature."

P1 - Pavlovian conditioning caused dog Fido to salivate when a bell rings.
P2 - Pavlovian conditioning caused dog Rover to salivate when a bell rings. 
P3 - Pavlovian conditioning caused dog Spot to salivate when a bell rings.
P4 - (etc.)
C - Therefore, Pavlovian conditioning causes all dogs to salivate when a bell rings.

It seems intuitive that the strength of the example above largely relies upon how many particular instances Pavlovian conditioning resulted in a dog salivating. A thousand instances of a salivating dog would be a stronger argument than only ten instances. This leads us to the concept of sample.

"In inductive generalizations, features that have been observed for some cases are projected to others. Following established practice in statistics and in science, we call the observed cases the sample and the cases we are trying to generalize about the population." Statistical sampling methodologies are beyond the scope of this post but the basic idea is that the strength of an inductive generalization largely depends on sample size and how representative it is.  

In general, increased sample size is associated with a decrease in sampling error as it is more likely to represent the population (though there are diminishing returns). For more on why this is so, see the law of large numbers and central limit theorem.

A representative sample is one in which the selected segment closely parallels the whole population in terms of the characteristics that are under examination (for example, if one third of the population has relevant characteristic X, then one third of the sample should have characteristic X). We try to make samples representative by choosing them in such a way that the variety in the sample will reflect variety in the population.

Sampling methods include Random Sampling, Stratified Sampling, Systematic Sampling, Convenience Sampling, Quota Sampling and Purposive Sampling.

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