Final answer:
A Correlational study is used to measure to what extent two factors vary together and to identify the strength and direction of the relationship between them, although it cannot establish causation.
Step-by-step explanation:
The type of study that measures the extent to which two factors vary together is a Correlational study. This kind of study examines the relationship between variables to determine if there is a correlation, which may be positive or negative. Positive correlation means both variables change in the same direction, while a negative correlation indicates they change in opposite directions. However, it's crucial to remember that correlation does not imply causation. Unlike experimental studies, correlational studies cannot conclusively prove that changes in one variable cause changes in another because they do not control all variables.
Observational studies include cross-sectional, case-control, and cohort studies, each with their own advantages and limitations. These studies are useful when it is neither ethical nor possible to manipulate the independent variable directly, as they rely on observations of naturally occurring phenomena rather than manipulation by the researcher. An example from human biology would be examining the correlation between smoking and lung cancer prevalence.