Final answer:
Analytical observational study designs involve measuring and observing variables without manipulation. There are several types, including cross-sectional, case-control, and cohort studies, each with its advantages and limitations in research.
Step-by-step explanation:
Analytical observational study designs like cross-sectional, case-control, and cohort studies are used in situations where we do not manipulate or control variables but instead measure and observe them in a sample over time or at a single point in time. A cross-sectional study collects data just once at a certain point in time, providing a snapshot that can suggest potential associations, as in the initial investigations linking smoking to lung cancer. With case-control studies, researchers retrospectively compare groups with and without a trait to find correlations with past behaviors, but these have limitations due to reliance on subjects' memory or honesty. Cohort studies, on the other hand, follow groups over time, observing the development of outcomes among subjects exposed and not exposed to certain factors.