Processual Archaeology
Processual archaeology was an intellectual movement of the 1960s, known then as the "new archaeology", which advocated logical positivism as a guiding research philosophy, modeled on the scientific method—something that had never been applied to archaeology before. The processualists rejected the cultural-historical notion that culture was a set of norms held by a group and communicated to other groups by diffusion and instead argued that the archaeological remains of culture were the behavioral outcome of a population's adaptation to specific environmental conditions. It was time for a New Archaeology that would leverage the scientific method to find and make clear the (theoretical) general laws of cultural growth in the way that societies responded to their environment.
New Archaeology
The New Archaeology stressed theory formation, model building, and hypothesis testing in the search for general laws of human behavior. Cultural history, the processualists argued, wasn't repeatable: it is fruitless to tell a story about a culture's change unless you are going to test its inferences. How do you know a culture history you've built is correct? In fact, you can be gravely mistaken but there were no scientific grounds to rebut that. The processualists explicitly wanted to go beyond the cultural-historical methods of the past (simply building a record of changes) to focus on the processes of culture (what kinds of things happened to make that culture).
There's also an implied redefinition of what culture is. Culture in processual archaeology is conceived primarily as the adaptive mechanism that enables people to cope with their environments. Processual culture was seen as a system composed of subsystems, and the explanatory framework of all of those systems was cultural ecology, which in turn provided the basis for hypotheticodeductive models that the processualists could test.
New Tools
To strike out in this new archaeology, the processualists had two tools: ethnoarchaeology and the rapidly burgeoning varieties of statistical techniques, part of the "quantitative revolution" experienced by all sciences of the day, and one impetus for today's "big data". Both of these tools still operate in archaeology: both were embraced first during the 1960s.
Ethnoarchaeology is the use of archaeological techniques on abandoned villages, settlements, and sites of living people. The classic processual ethnoarchaeological study was Lewis Binford's examination of the archaeological remains left by mobile Inuit hunters and gatherers (1980). Binford was explicitly looking for evidence of patterned repeatable processes, a "regular variability" that might be looked for and found represented on archaeological sites left by Upper Paleolithic hunter-gatherers.
With the scientific approach aspired to by processualists came a need for lots of data to examine. Processual archaeology came about during the quantitative revolution, which included an explosion of sophisticated statistical techniques fueled by growing computing powers and growing access to them. Data collected by processualists (and still today) included both material culture characteristics (like artifact sizes and shapes and locations), and data from ethnographic studies about historically known population makeups and movements. Those data were used to build and eventually test a living group's adaptations under specific environmental conditions and thereby to explain prehistoric cultural systems.
Subdisciplinary Specialization
Processualists were interested in the dynamic relationships (causes and effects) that operate among the components of a system or between systematic components and the environment. The process was by definition repeated and repeatable: first, the archaeologist observed phenomena in the archaeological or ethnoarchaeological record, then they used those observations to form explicit hypotheses about the connection of that data to the events or conditions in the past that might have caused those observations. Next, the archaeologist would figure out what kind of data might support or reject that hypothesis, and finally, the archaeologist would go out, collect more data, and find out if the hypothesis was a valid one. If it was valid for one site or circumstance, the hypothesis could be tested in another one.
The search for general laws quickly became complicated, because there were so much data and so much variability depending on what the archaeologist studied. Rapidly, archaeologists found themselves in subdisciplinary specializations to be able to cope: spatial archaeology dealt with spatial relationships at every level from artifacts to settlement patterns; regional archaeology sought to understand trade and exchange within a region; intersite archaeology sought to identify and report on sociopolitical organization and subsistence; and intrasite archaeology intended to understand human activity patterning.
Benefits and Costs of Processual Archaeology
Prior to processual archaeology, archaeology was not typically seen as a science, because the conditions on one site or feature are never identical and so by definition not repeatable. What the New Archaeologists did was make the scientific method practical within its limitations. However, what processual practitioners found was that the sites and cultures and circumstances varied too much to be simply a reaction to environmental conditions. It was a formal, unitarian principle that archaeologist Alison Wylie called the "paralyzing demand for certainty". There had to be other things going on, including human social behaviors that had nothing to do with environmental adaptations.