In "small-scale study," the hyphen clarifies that the study was small in scale, not a study on scales designed for mice. If one of your modifiers is an "ly" adverb, a hyphen isn't needed. In "extensively researched paper" for example, a hyphen isn't necessary because the meaning is clear.

Should large scale be hyphenated?

Predictions from large-scale global climate models can be a valuable resource for city planners. Note: When the adjective follows the noun, the words are NOT hyphenated. Examples: ... [In these cases, "well known," “up to date,” and "large scale" follow the nouns they're modifying, so they are not hyphenated.]

Is small to medium hyphenated?

Do I need more hyphens somewhere? Thank you. It's correct without further hyphens. You're saying it's somewhere between a small city and a medium-sized one.