Critical Thinking: A User’s Manual Chapter 10 Evaluating Inductive Generalizations

Inductive Generalizations  An inductive generalization is an inductive argument that concludes that some, most, or all of a particular group has some feature based on evidence that a portion of that group has the feature.  The conclusion of every inductive generalization is a general claim.  A general claim is a claim that makes a statement about all, most, or many members of a group or set.

General Claims  All swans are white.  One-third of college students smoke cigarettes.  Junk food is high in calories.

Every cat I’ve ever owned was a good pet. I bet that all cats make good pets. P:  Issue:

 Every cat I’ve ever owned was a good pet. I bet that  all cats make good pets.

Anatomy of Inductive Generalizations P: A sample S of the members of T have F  All (or many or most) members of T have F S = sample T = target F = feature

Every cat I’ve ever owned was a good pet. I bet that all cats make good pets. P:  S: T: F:

P: 80% of the 1,126 respondents nationwide randomly polled by telephone opposed the military policy toward gays of “Don’t Ask—Don’t Tell.”_______________________________  A large majority of Americans oppose the “Don’t Ask—Don’t Tell” policy regarding gays serving in the military. S: T: F:

Evaluating Inductive Generalizations  Inductive Generalizations may be strong or weak.  Consider how well the sample represents the target.

Evaluating Sample Randomness  A random sample is one in which all members of the target have an equal opportunity to be in the sample.  Randomness aims to ensure that the diversity of the target is represented in the sample.  When an inductive generalization’s sample misrepresents the target, the argument is a biased generalization.

Which argument is stronger? A poll taken of students in the dormitories at OSU showed that most of the respondents thought that availability of campus parking was not a serious concern. Thus, it’s likely that most students at OSU don’t think that parking on campus is a problem. A poll taken of students at the campus bookstore at OSU showed that most of the respondents thought that availability of campus parking was not a serious concern. Thus, it’s likely that most students at OSU don’t think that parking on campus is a problem.

Your turn!

Evaluating Sample Size  The larger the sample, the stronger the argument.  When the sample is too small to offer even minimal support for the conclusion, the argument is a hasty generalization.

Which argument is stronger? A poll taken of 95 students at the campus bookstore at OSU showed that most of the respondents thought that availability of campus parking was not a serious concern. Thus, it’s likely that most students at OSU don’t think that parking on campus is a problem. A poll taken of 250 students at the campus bookstore at OSU showed that most of the respondents thought that availability of campus parking was not a serious concern. Thus, it’s likely that most students at OSU don’t think that parking on campus is a problem.

Complete Analysis plus Evaluation Step 1: Write a Basic Analysis of the passage.  Identify the passage.  Analyze the passage. Step 2: If it is an argument, determine whether it commits a fallacy.  Identify the fallacy, and explain how it is committed. Step 3: If it is a nonfallacious argument, diagram it.  Verify that your diagram is consistent with your Basic Analysis.

Complete Analysis plus Evaluation Step 4: Identify the kind of argument.  If the argument is deductive, identify it as a categorical argument or a truth-functional argument.  If the argument is inductive, identify it as an analogical argument, an inductive generalization, or a causal argument.

Complete Analysis plus Evaluation Step 5: Evaluate the argument.  If the argument is categorical, state the syllogism in standard form, and demonstrate whether the argument is valid or invalid using either a Venn diagram or the rules for valid syllogisms.  If the argument is truth-functional, translate the argument, and demonstrate whether the argument is valid or invalid by identifying the argument form, using the truth table method, or using the shortcut method.  If the argument is analogical, evaluate its strength by considering the evidence provided for the analogy and the relevance of the analogy to the feature.  If the argument is an inductive generalization, then evaluate its strength by considering sample randomness and sample size.

ShopperTrak provides shopper-traffic counting technology and data analysis for retail businesses. According to ShopperTrak’s Retail Traffic Index (SRTI), shopping traffic rose by 1.1% in Manhattan last month. It’s likely that shopping traffic across the United States rose by approximately 1% last month.

This passage contains an argument. The issue is whether shopping traffic across the United States rose by approximately 1% last month. The conclusion is that shopping traffic across the United States rose by approximately 1% last month. The premise is that shopping traffic in Manhattan rose by 1.1% last month.

 ShopperTrak provides shopper-traffic counting technology and data analysis for retail businesses. According to ShopperTrak’s Retail Traffic Index (SRTI),  shopping traffic rose by 1.1% in Manhattan last month. It’s likely that  shopping traffic across the United States rose by approximately 1% last month.   

This passage contains an argument. The issue is whether shopping traffic across the United States rose by approximately 1% last month. The conclusion is that shopping traffic across the United States rose by approximately 1% last month. The premise is that shopping traffic in Manhattan rose by 1.1% last month. This argument is an inductive generalization. The argument is weak because it is biased and hasty. The sample is not random, and there is only one instance in the sample.