13.1.3: Sample Diversity

In addition to selecting a random, large sample, you can also improve your chances of selecting a representative sample by sampling a wide variety of members of the population. That is, aim for diversity─so that diversity in the sample is just like the diversity in the population. If you are interested in how Ohio citizens will vote in the next election, will you trust a pollster who took a random sample and ended up talking only to white, female voters? No. Even though those 50 white women were picked at random, you know you want to throw them out and pick 50 more. You want to force the sample to be diverse. The greater the diversity of relevant characteristics in your sample, the better the inductive generalization, all other things being equal.

Because one purpose of getting a large, random sample is to get one that is sufficiently diverse, if you already know that the population is homogeneous—that is, not especially diverse—then you don't need a big sample, or a particularly random one. For example, in 1906 the Chicago physicist R. A. Millikan measured the electric charge on electrons in his newly invented oil-drop device. His measurements clustered around a precise value for the electron's charge. Referring to this experiment, science teachers tell students that all electrons have this same charge. Yet Millikan did not test all electrons; he tested only a few and then generalized from that sample. His sample was very small and was not selected randomly. Is this grounds for worry about whether untested electrons might have a different charge? Did he commit the fallacy of hasty generalization? No, because physical theory at the time said that all electrons should have the same charge. There was absolutely no reason to worry that Tuesday's electrons would be different from Wednesday's, or that English elections would be different from American ones. However, if this theoretical backup weren't there, Millikan's work with such a small, nonrandom sample would have committed the fallacy of hasty generalization. The moral: Relying on background knowledge about a population's lack of diversity can reduce the sample size needed for the generalization, and it can reduce the need for a random sampling procedure.

When you are sampling electrons or protons, if you’ve seen one you’ve seen them all, so to speak. The diversity just isn't there, unlike with, say, Republican voters, who vary greatly from each other. If you want to sample Republican voters' opinions, you can't talk to one and assume that his or her opinions are those of all the other Republicans. Republicans are heterogeneous─the fancy term for being diverse.

A group having considerable diversity in the relevant factors affecting the outcome of interest is said to be a heterogeneous group. A group with a relatively insignificant amount of diversity is said to be a homogeneous group. For example, in predicting the outcome of measuring the average height of two groups, Americans and Japanese, the diversity of American ethnicity makes Americans a heterogeneous group compared to the more homogeneous Japanese group. It is easier to make predictions for homogeneous groups than for heterogeneous groups.

Being homogeneous is relative, however. The Japanese might be more homogeneous than Americans relative to measurements about height, but the Japanese might be more heterogeneous than Americans when it comes to attitudes about socialism and about how to care for infants.

Exercise \(\PageIndex{1}\)

The most important goal in sampling is

a. randomness
b. representativeness
c. diversity
d. large sample size

Answer

Answer (b).

Exercise \(\PageIndex{1}\)

Suppose you know the average height of Japanese men and of American men. If you randomly pick a hundred Japanese businessmen, you can be more sure of their average height than you can be if you pick American businessmen. Explain why.

Answer

The variety of the Japanese data is less than that of the American data because Japan is a more homogeneous society. The American people are more ethnically diverse and so are more genetically diverse, and genes affect human growth. Suppose the average Japanese man is 5' 5", and the average American man is 5' 8". Then the point the message is making is that the average of the 100 Japanese men you pick will be closer to 5'5" than will the average of the 100 American men be to 5'8"