The purpose of archive research is to conduct a comparative analysis. The researcher looks at the existing records to conduct a qualitative analysis of research material and determine new developments on the subject of the research. You can use, for instance, data from the U.S. Census Bureau or the Bureau of Labor Statistics to answer a research question. For example if you want to understand the current divorce rate in America compared to 50 years ago, you can use data from the U.S. Census Bureau.
Observational research is usually used by ethnographers. The researcher observes and records data to understand the natural behavior of an individual being studied. The researcher must not interfere with the subject's natural behavior. A marketing researcher, for instance, might use observation research to understand consumer behavior in a certain location. This is done by observing how consumers interact with products.
The goal of a case study is to explore further knowledge in the public domain. It is based on existing research data to further understand present time situations. Research starts with defining research questions before choosing case studies to explore. You must then determine the techniques to gather and analyze information. After examining and assessing data you make a report based on your findings.
Surveys are used to define and analyze a demographic group through sampling. You have to define exactly what you would like to know before beginning survey research. Pollsters use this kind of research method in opinion polls to understand which candidate, product, or issue is more popular and why. Surveys are most often administered face-to-face, through email, questionnaire, or by telephone.