Based on modifies the subject of the main clause of the sentence.
Based on the test scores, Scott selected the top candidates.
This is incorrect because it makes it sound as if Scott (the subject) is based on the test scores.
This could be rewritten as:
On the basis of the test scores, Scott selected the top candidates.
or
Scott selected the top candidates on the basis of their test scores.
On the basis of modifies the main verb of the sentence.
On the basis of the test scores, Scott selected the top candidates.
This is correct because the test scores were used to make the selection.