The study found no significant difference between the two groups. ___, the researchers concluded that the treatment had no measurable effect. Which transition best fits the blank?

The second sentence is a logical consequence of the first (no difference → no measurable effect), so 'Therefore' fits best.

The volcano had been dormant for over two centuries. ___, geologists continued to monitor it closely, aware that dormancy is not the same as extinction. Which transition best fits the blank?

The second sentence contrasts with an expectation set up by the first (a long-dormant volcano might seem safe to ignore), so 'Nevertheless' fits best.

The bridge had passed every scheduled inspection for a decade. ___, engineers recommended an unplanned structural review after nearby construction altered water flow beneath its supports. Which transition best fits the blank?

The recommendation runs counter to what the good inspection record might lead readers to expect, so a contrast transition like 'Nonetheless' fits best; it isn't an example, a similarity, or a direct result of the inspection history itself.

The novel received mixed reviews upon release. ___, it went on to sell over a million copies within its first year. Which transition best fits the blank?

Mixed reviews would typically predict modest sales, so the strong sales figure is a contrast to that expectation, best signaled by 'Yet.'

The vaccine trial's initial results appeared promising, with early participants showing strong immune responses. ___, researchers cautioned against drawing firm conclusions, noting that the trial's first phase included too few participants to rule out chance results. Which transition best fits the blank?

The second sentence tempers the optimistic first sentence with a caution, which is a contrast relationship best signaled by 'However.'