(Michigan Corpus of Spoken Academic English) is a online search engine where you can enter words or phrases and see them as they are used in authentic academic speech. I highly recommend this site for those of you struggling with academic phrases in English and when and how to use them.
Below I have pasted 3 of the 66 results in MICASE for the phrase "on the other hand" to give you a sense of how this works.
"...formed by western by notions of form, sound quality and harmony. Jarrett the improvising solo pianist, on the other hand, applies principles of formal construction, remarkably similar to North Indian raga performance..."
"... it's a picture of weeds it's a painting of weeds, she set her easel up and painted some weeds uh, on the other hand you can just ignore that title and and, think of it, as pure design this is, uh this is the, that kind..."
"...is a very strong strand of voluntarism in the scriptural tradition, that they're coming out of. Um, on the other hand, there are also things in that scriptural tradition which seem to be pointing in a somewhat differe
I also recommend the MICASE English Self Study page which features sound files and interactive quizzes and such for the advanced English learner.