Arend Lijphart, Comparative politics and the comparative method”, APSR (1971), pp. 682-693.

Summary: In two articles–this one and another written in 1975–Lijphart advocated greater use of case comparisons as a political research method. In his view, political scientists had embraced large-sample statistical methods. While statistical methods are not necessarily bad, they have advantages and disadvantages, and some of their disadvantages could be overcome through greater use of small-sample comparative methods.
The summary below is based primarily on the 1975 article, which conveyed the same arguments as this 1971 article did, but with greater clarity. The 1971 article faced many criticisms; the 1975 article clarifies and tones down some of the original arguments.
Main Argument:
In the original (1971) article, Lijphart outlined four scientific methods; the first was the experimental method and the three others were nonexperimental methods (statistical, comparative, case study). He notes that political scientists shied away from comparative studies (that is, case comparisons) because of the well-documented methodological problems arising from “many variables, small N.” Lijphart then outlines four sub-types of the comparative method with the potential to minimize the effects of this methodological complication.
In the 1975 article, Lijphart revises his argument to suggest that there in fact only two different solutions to the problem: One can either increase N (and then switch to the statistical method) or decrease the number of variables (and stick with the comparative method). One decreases the number of variables by carefully selecting a small number of highly comparable cases
Lijphart concedes that this definition draws, at best, a thin line between statistical (SM) and comparative (CM) methods. Researchers should be aware of the advantages and disadvantages of each method rather than deciding which method to use based solely on possible Ns.
SM has three main weaknesses. First, particularly in international relations, it tends to focus on comparing whole nations. The reason is partly pragmatic: there is more data available on nations than on city councils, corporate governance, and other intrasocietal units. On the other hand, CM involves selecting data at the most appropriate level. Second, SM relies heavily on “global” data with questionable reliability and validity. For example, GNP depends partly on exchange rates, so it may not be reliable, but we use it anyway because it is available globally. Third, statistical correlations among societies may not be independent. Lijphart mentions “Galton’s problem”: correlations may be only the result of historical learning.
CM also has weaknesses, of course. First, researchers may have difficulty finding sufficiently similar cases to control for other possible factors. Second, comparative studies lead to less generalizable conclusions. Third, when possible cases are limited, data selection may pre-determine the hypothesis.
Nonetheless, Lijphart advocates greater use of comparative methods to complement the statistical methods dominating the literature at the time.