Statistical Arguments and Logic

Deductive Argument

Aim for conclusion to be 100 percent certain

Valid

All premises true then conclusion must be true

Sound

Argument is valid and all premises are true

Non-Deductive Argument

Aim for conclusion to be probable

Strong

Premises make conclusion likely

Cogent

Argument is strong and all premises are true

Statistical Generalization

Moving from a sample to a whole group

Statistical Application

Moving from a whole group to one individual

Hasty Generalization

Fallacy caused by small sample size

Sample Size

Evaluation question is the sample large enough

Biased Sample

Evaluation question is the sample representative

Reference Class

The group being used to make a projection

Statistical Generalization Form

X percent of observed Fs are G

Statistical Generalization Conclusion

X percent of all Fs are G

Statistical Application Form

X percent of Fs have feature G

Statistical Application Premise 2

Individual A is an F

Statistical Application Conclusion

Individual A has feature G

High Percentage

Evaluation question for strength of application

Reference Class Choice

Evaluation question for most appropriate group

Weak Generalization Example

One person did X so most people do X

Biased Generalization Example

Only asking people in one specific place

Strong Generalization Example

Large national survey of all customers

Weak Application Example

Using a tiny percentage to predict behavior

Reference Class Example

People in the world vs people who voted