chapter 26: generalizations and surveys

Chapter 26:Generalizations

and Surveys

Inductive Generalizations (pp. 280-284)

• Arguments to a general conclusion are fairly common.

• Some people claim that all inductive arguments are arguments to general conclusion, but such an approach does not divide arguments into two exclusive and exhaustive classes: valid deductive arguments and inductive arguments.


• Criteria for evaluating an inductive generalization – 1. As the number of objects taken into account

increases, the generalization is strengthened.– 2. Care must be taken to show that the cases upon

which you make your generalization are typical.– 3. The more diverse the sample is, the better the

basis for the generalization is.• A sample is the group on which the conclusions of a survey

are based. It’s a subset of a population.

– 4. The stronger the conclusion, the weaker the argument is.


• Inductive Counterexample– An inductive counterexample is an instance

that shows the conclusion is false. If you reach a universal conclusion, it only takes one exception to show that the conclusion is false. If you claim that your conclusion holds for the majority of cases, it takes something over fifty percent of all cases to provide an inductive counterexample.


• Sample size and the strength of the inference – So long as your sample is typical and diverse, the

larger the sample, the stronger the argument is.

• Principle of the uniformity of nature– The principle of the uniformity of nature holds that

causal relations that will hold in the future are of the same kind as those that have held in the past.

– The principle of the uniformity of nature is assumed by inductive arguments; it cannot be proven on the basis of either an inductive or a deductive argument.

Inductive Generalizations: Example (pp. 280-284)

• Assume you’re writing a history paper on General Motors. At some point, you want to make a remark on the general reliability of Chevrolets. If you’re going to do so, the larger the number of individual automobiles in your sample, the stronger your argument will be (1). The objects in your sample should be typical Chevrolets (2), which means that while you might have a couple that were racecars, most of them would be family cars. The sample would need to be diverse (3). You could not deal only with the cars made in the past ten or fifteen years. You’d need to concern yourself with Chevrolets made in the 1920s and 1930s as well as those made in the 1990s and later. You’d want to talk with me about by 1974 Vega, as well as talking with folks who drove far better cars. And the more tentative your conclusion is, the better the evidence would support it (4).

Sampling and Surveys (pp. 285-291)

• A sample is random if every member of a population has an equal chance of being chosen to be included in the sample.– Randomness is an ideal: no actual surveys

are perfectly random.– Most surveys that are reported in the media

are assumed to be random or approaching randomness within specifiable limits.


• Purposive sampling models (nonrandom surveys) – 1. Haphazard samples

• These are based on whatever happens to be at hand.

• Many historical surveys are haphazard simply because many historical artifacts have been lost. This is one reason why there are relatively few accounts of “everyday life” during a given historical period and why you might be a bit skeptical about such accounts.


– 2. Homogeneous samples• These are drawn from a fairly narrow range of

theoretical variables, often rare case studies.

– 3. Quota sampling • This divides a population into relevant groups and

samples the groups in proportion to their prevalence in the population.

– 4. Structural samples• These samples are made relative to relationships

in a given, often socio-cultural, structure.• This might concern relationships among groups in

an educational or corporate community.


– 5. Snowball sampling• In this sampling technique you receive references

from those in the original sample to increase the size of your sample.

– 6. Expert choice sampling• This assumes that experts in a certain area have

some special understanding of what it typical.


• Probability (random) sampling models– 1. Randomness and its absence (bias)– Bias is anything short of randomness: for one reason

or another, not all members of a relevant group have an equal chance of being chosen for the sample.

• a. Randomness as an ideal• b. Approaches to random choice• c. On tables of random numbers

– Statisticians consider surveys in which individuals are chosen on the basis of a table of random numbers the more random than those based on any other method of attempting to establish a random sample.


• 2. Simple random samples with replacement– Any object that is chosen for the survey is returned to

the pool from which the sample is drawn after it has been “counted.”

– This is commonly used for infinite or indefinitely large populations.

• 3. Simple random samples without replacement– Any object that is chosen for the survey is not

returned to the pool from which the sample was drawn after it has been “counted.”

– Sampling without replacement is usually used for finitely large populations.


• 4. To evaluate a survey you need some knowledge of how the survey was undertaken.– a. Confidence level

• The confidence level reflects the degree of accuracy which experience indicates can be assumed on the basis of a sample of a certain size for a population of a certain size.

• The confidence level for most reported surveys is 95 percent.

– b. Margin of error• The margin of error is the percentage by which past

experience suggests actual behavior might deviate from the results of a survey within a certain confidence level.


– 5. Stratified random surveys• In a stratified random survey, the population is

divided into categories (strata), and each stratum is surveyed randomly.

• The number of objects surveyed in each stratum should be the same.

– 6. Systematic sampling• Systematic sampling consists of choosing every

so-manyeth object after a random choice of the first object.

• This is common in quality-control studies.


• It is very easy to introduce bias into a survey. The method of surveying can introduce bias. In 1936, a Literary Digest telephone survey indicated that Alf Landon would win the presidency. At the time, telephones were most prevalent among “the rich.” A similar bias might be introduced by an Internet survey today. The way the questions are phrased can influence what people will deem “the correct” answer. How those surveyed are chosen can bias the survey. Using a table of random numbers is considered the least biased. So, next time you hear the results of a Time-ABC poll, you might ask questions about how the survey was conducted.

chapter 26: generalizations and surveys

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