"We examine ourselves to see if any of the Spirit’s fruit is being manifested in us."
I haven't found this in the Bible, what I found is:
2Co 13:5 Test yourselves to see if you are in the faith; examine yourselves! Or do you not recognize this about yourselves, that Jesus Christ is in you--unless indeed you fail the test?
Even in this verse the emphasis is on Christ and not on self which is what The Holy Spirit was sent for.
Joh 15:26 But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me: