Learn English – ‘Sorry, have you got the time, please?’

If it were my managers, I'd probably break tchrist's rule, but you could use

When I worked it out, I got a different answer. I had... [and then state the correct version].

That gives the manager the opportunity to see that you may indeed be right; or to state that they don't care about your version and you should use theirs anyway. In either case, you have pointed out the correct version and your honour is satisfied. In putting it this way, you are calling into question your own ability compared to your manager's. There's a similar but not identical scenario in another question.

I would avoid, where possible, words like 'rather' and 'quite', in the sense of 'quite good'. They are imprecise and overworked. In any case, if you say you got 'very good' comments, using 'rather' and 'quite' may mean you are tending to be too modest.

So for starters you could say:

1. We received very positive reviews.

The word 'appraise' is used more in the sense of 'evaluate'. In your case I would use its root 'praise'.

1. Our results were praised by the reviewers.

   'Affirmative' hints at something being positive but doesn't really say it directly. I think you need to say they were affirmative of something. How about:

2. The reviewers comments affirmed the strength of our results.