Statistical Generalization

Overview and Discussion

Scientific generalizability within case study research has often been challenged. Some scholars argue that statistical generalization is often not as relevant for case studies because the sample sizes are typically quite small and are often not representative of the population. For this reason, theoretical generalization is often used in case studies in which a previously developed theory is used as a template against which one can compare the empirical results of the case study. With this in mind, caution should be used when applying statistical generalization to case studies.

In order to statistically generalize the findings of a research study the sample must be randomly selected and representative of the wider population. It is important that the proportion of participants in the sample reflects the proportion of some phenomenon occurring in the population. The wider population must be properly defined prior to selecting a sample. Even when a sample is selected using random sampling methods, the ability to produce a representative sample depends on the adequacy of the sampling frame and any bias in from the selected sample units. Such biases can limit statistical generalization.

Application

Consider the following example of statistical generalization. If less than 2% of 5,000 randomly selected Canadian adults with chronic health problems report lacking access to healthcare, then one could generalize to say that only a small percent (or about 2% $pL the standard error) of Canadian adults with chronic health problems report lacking access to healthcare. This conclusion is justified given the sample size and the randomness of the selection. It would be incorrect to say that exactly 2% of Canadian adults with chronic illness lack access to healthcare, because the margin of error needs to be taken into account. Researchers also need to be sure that they refer the appropriate group. For example, it would be incorrect to say “About 2% of Canadian adults lack access to healthcare,” because the results refer only to adults with chronic illness and not adults in general (i.e., with or without illness).

John Nolt, Dennis Rohatyn, and Achille Varzi suggest that the general form of statistical generalization includes: n percent of s randomly selected A are B; therefore, about n percent of all A are B. Here s indicates the sample size, A is a property that defines the population about which you are generalizing (i.e., Canadian adults with chronic health problems), and B is the property studied by the survey (access to healthcare).

Random selection refers to a selection procedure in which all members of a population have an equal chance of being sampled. This implies that each sample member had an equal chance of being chosen. If the sample is sufficiently large, most sample members of a given population are approximately representative of that population.

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