Recently someone commented that he felt that I was making a generalization. I assume that he meant a hasty generalization. But, it does bring up the subject of what is a generalization? You see, we must first ask whether making generalizations is itself bad. So, what is a generalization? Well, there are two meanings, one from scientific studies and one from social studies and philosophy. In science a typical definition of a generalization is:

Generalization (or generalisation) is an essential component of the wider scientific process. In an ideal world, to test a hypothesis, you would sample an entire population. You would use every possible variation of an independent variable. In the vast majority of cases, this is not feasible, so a representative group is chosen to reflect the whole population.

For any experiment, you may be criticized for your generalizations about sample, time and size.

You must ensure that the sample group is as truly representative of the whole population as possible.

For many experiments, time is critical as the behaviors can change yearly, monthly or even by the hour.

The size of the group must allow the statistics to be safely extrapolated to an entire population.

In social studies, there is a variation on the definition, since in social studies and philosophy it is not really possible to exactly repeat everything in a scientific way:

A generalization (or generalisation) of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning.[citation needed] Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it is the essential basis of all valid deductive inferences. The process of verification is necessary to determine whether a generalization holds true for any given situation.

The concept of generalization has broad application in many related disciplines, sometimes having a specialized context-meaning.

Of any two related concepts, such as A and B, A is considered a “generalization” of concept B if and only if:

every instance of concept B is also an instance of concept A; and

there are instances of concept A which are not instances of concept B.

Wow! Now there is a complex definition of a generalization. But, I want you to catch the drift. A generalization is part and parcel of both logic (philosophy) and science. As part of logic it participates in social studies, historical studies, etc. Is is a vital part of analysis. Without generalizations it becomes impossible to posit theorems, to see patterns in history or archeology or social studies, etc. Generalizations are a vital part of our human existence, for we are not omnipotent. We cannot know everything thus the best we can do is to generalize.

This creates the problem of knowing when you have made an accurate generalization and when you have not. We have a saying about hasty generalizations. What is a hasty generalization?

Hasty generalization is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence — essentially making a hasty conclusion without considering all of the variables. In statistics, it may involve basing broad conclusions regarding the statistics of a survey from a small sample group that fails to sufficiently represent an entire population. Its opposite fallacy is called slothful induction, or denying the logical conclusion of an inductive argument (e.g. “it was just a coincidence”).

Context is also relevant; in mathematics, the Pólya conjecture is true for numbers less than 906,150,257, but fails for this number. Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.

Hasty generalization can also be a basis for racist beliefs and prejudices, in which inferences regarding a large group is based upon knowledge of only a small sample size of that group.

So, here is the problem that we have as humans. On the one hand, we must reach our generalizations often from a sample that is less than 50% of the existing population. On the other hand, any sample that is too small and not representative leaves us with the danger that any conclusions that we reach will not be accurate. That is the human condition. We are not omnipotent.

Having said that, I have taken graduate level statistics. There are many statistical ways to try to ensure that a sample is representative and accurate. But, when all is said and done, our generalizations are proofs that we are not omnipotent. They are proofs that we are not omnipotent because of the various examples of generalizations that have been inaccurate despite the use of the best statistical methods.

But, here is a final thought. Can we simply accuse everyone of hasty generalization based on the fact that we are not like the generalization and we have friends that are not like the generalization? The answer is no. You see, we also commit the hasty generalization error when we cite ourselves and a couple of friends and claim that this disproves someone else’s generalization.

Let me give you one example. In the 2008 election, 9 out of 10 African-Americans voted for President Obama. It is utterly useless to claim that you know several African-Americans who are Republicans and that this–therefore–disproves the “myth” that African-Americans vote mostly Democrat (at least in prior elections). The data set of African-Americans who regularly vote Democrat is a data set that includes all African-Americans who vote. In this case the generalization is not really a generalization because the sample set is equal to the population set.

The question becomes more difficult as the sample set decreases in size to less than 50% of the sample population. But, the bottom line is that we cannot claim that someone else’s generalization is false simply by saying that I (you) and a couple of friends are not like that. The question is not whether I (you) can find a couple of friends who do not fit the generalization. The question is whether the majority of the target population fits the generalization.

I know that this has been a philosophical / mathematical posting. But, I hope it helps you think through what a generalization is, and–more important–when to decide that someone else is engaging in a hasty generalization.

## Leave a Reply -- who knows what might happen?