Unfortunately there is insufficient evidence to draw a conclusion. Again - without knowing the app I can't make comments on it. I do know the Foobar program and extensions - a lot of people have used it. It matches to within 0.1 dB, is true double blind (abx), and allows you to have a decent number of tests. I usually use 15.
From your original thread ..... you had results of 3/5, 5/5, 3/5 and 1/1. Although quoting 60%, 100%, 60%, 100% looks significant - in reality for the small number of tests performed, it actually points more toward the probability of 'guessing' rather than statistically proving the difference.
For me personally - I can't tell the difference, and have yet to meet anyone that can (as long as they come from the same master, and were transcoded without introducing artifacts/errors) for normal listening. There are some samples over on hydrogenaudio - where specific tracks have been abx'd - but these specific tracks are very few and takes trained listeners to ehar them. Over there - they do realise (for the main part) that for general listening, properly transcoded 320 kbps mp3 or 256aac are essentially transparent.
However - I'm always open to new discovery. I'm just naturally skeptical without the evidence
You have anyone else close to you (say within the Sydney audio community) that you could have a group conduct a series of blind abx's - preferably using Foobar? That would be fascinating!