Action research is a model that allows practitioners to identify, study, and address problems and issues that directly concern them: research which leads to action (Wadsworth). This type of research is found most often in educational settings and is often performed collaboratively.
Participatory research action (PAR) is a subset of action research which actively involves the researchers and the participants in a cycle of research and action.
Wadsworth, Y. (1998). What is participatory action research?. Action Research International Paper 2.
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In single-subject research, also called single-case research design, the researcher studies an individual or small group over a period of time to determine the effectiveness of a specific treatment or intervention. The research and analysis is quantitative and the subject serves as the control group.
A case study is a detailed observational study of an individual or a specific group.
Single-Case Research Methods for the Behavioral and Health Sciences by 
