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I have a method which I need to test its performance for real data set.

Is it correct to say:

This part of the chapter aims to test the performance of the method A *when applying on* the real datasets*.

Or This part of the chapter aims to test the performance of the method A *when applying to* the real data sets*.

Which of my sentence is correct grammarly? and why?

Thanks in advance.

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You should probably say:

This part of the chapter aims to test the performance of method A when applied to the real data sets.

Since the method is not itself performing the application, you should use "applied" rather than "applying". Also, "to" is the better preposition in this case. "Applied on" is more appropriate when one tangible object is physically applied to another. For example, "She applied the ointment on the wound."

Also note that I removed the definite article "the" before "method A". No definite article is needed since "method A" is already identified by name, and presumably there is only one "method A".

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