20.5: Getting Data and Drawing Inferences

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We studied samples and populations in Chapter 15, and we can quickly recall the basic points here. We often infer a conclusion about a population from a description of a sample that was drawn from it. When we do:

1. Our premises are claims about the sample.

2. Our conclusion is a claim about the population.

For example, we might draw a conclusion about the percentage of people who favor sending troops to a certain region from premises describing the responses of 700 people to a poll on the subject. In such a case, our inference is not deductively valid. It involves an inductive leap.

But if we are careful in our polling, our inference can still be inductively strong. This means that if we begin with true premises (which here means a correct description of the sample), we are likely to arrive at a true conclusion (about the entire population).

A good inductive inference from a sample to a population requires:

1. A large enough sample.

2. A representative (unbiased) sample.

These same principles apply when we are sampling as a part of scientific investigation. All things considered, we want larger samples, keeping in mind that there are information costs the larger a study gets. The larger a sample we test on, the longer the study will take. So, when testing timesensitive treatments (like vaccines for Covid-19) we might decide to test a smaller sample in the interest of getting a drug to market faster. We also need to keep in mind that if a sample is restricted to a certain group (age, gender, socio-economic status, etc.) the results will only be understood as applying to that population. More diverse populations will give us more universal conclusions.