Final answer:
The study design where researchers compare a group with a trait (cases) to a group without the trait (controls) is known as a Case-control study, which is an observational study.
Step-by-step explanation:
If a researcher was interested in whether the use of estrogen replacement therapy (ERT) caused colon cancer in postmenopausal women and they recruited a group of women with colon cancer (cases) and another group of women without colon cancer (controls) as subjects, this type of study design is known as a Case-control study. A case-control study is an observational study where subjects with a trait of interest are compared retrospectively with subjects without the trait. This method was exemplified by Doll and Hill's early research on smoking and lung cancer. Case-control studies are valuable for establishing associations between risk factors and diseases, often used in situations where randomized controlled trials are not feasible.