Answer to Question 1
aIn an experiment, you would create different levels of stress in at least two groups and see how they differed. People would be placed in different groups randomly. You specify the groups associated with the IV and measure the DV.
bIn a case study, you study a single individual (or a few) in great depth. To study stress, you would keep detailed notes about the conditions in which the person experienced stress and how he or she coped, along with other reactions.
cIn archival research, you could identify some naturally occurring event and see how it affected people in terms of stress, such as increases in admissions to psychiatric facilities, death or suicide rates, divorces, or other records that could be associated with stress
Answer to Question 2
Survey, archival, and observational research rely on data obtained without manipulation of any variables. In fact, for archival and observational research, the people or animals that provide the data may not even be aware that they are being observed and measured. Because there is no manipulation of variables, we don't know why different people or animals act differently; we can only spot patterns of behaviors, which is the hallmark of correlational research.
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