Section 5.1

Fundamentals of Social Statistics


The Logic of Hypothesis Testing

Recall that all research begins with a research problem.  We usually want to know the answer to a “why” or “how” question.  Our proposed solution to most research problems will specify a relationship between two or more variables.  Our specification of this type of relationship is called our hypothesis.

A hypothesis is an explanation of some observable phenomenon.

Our hypotheses will not be about a sample—it will be about a larger population that we cannot measure.  Most of the time we are forced to use samples to represent populations that we want to study.  In empirical research, we will measure our sample on the variables are interested in.  From these measurements, we end up with a bunch of numbers with which we can compute sample statistics.  The problem is that people do not want to know about our sample and our sample statistics—they want to know about the population from which the sample was drawn.

Thus, the purpose of inferential statistics is generalizing from a sample to a population.  That is, making inferences about a population on the basis of a sample. Recall that the term population does not mean the entire population of a country.  It just means everyone in a group that you want to study, for example, all delinquent juveniles that drop out of school.

A generalization is a general statement made by inference from specific cases.

An inference is a conclusion that is based on evidence and reasoning.

Such inferences are usually not drawn directly from observed sample statistics.  Rather, we usually make statistical inferences by computing test statistics.  There are many different test statistics that vary depending on the nature of the data.  The common thread of all test statistics is to evaluate the probability of an observed characteristic of a sample accurately reflecting the population parameter in which we are interested.

A test statistic is a method of reducing a set of data down to a single number that can be used to test a hypothesis.

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Last Modified:  02/18/2019

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