My AncestryByDNA testing results are: 72% European, 16% Sub-Saharan Africa, and 12% Indigenous American. This suggests Iberian origins. However, all my known ancestors are Irish and most still live here. Can any more information be gained from this result? I'm new to this subject.
AncestrybyDNA has a detailed help page that describes how to interpret their results. In particular, low percentages of an ethnicity that you don't expect could "be the result of statistical noise". In other words, they don't have enough data to give an accurate figure, and some of their results are essentially meaningless.
Unless I'm misreading their help page, they seem to be basing these predictions on a very small number of different ethnic groups: the "test provides your ancestral proportions based on years of collaborative research of populations representing 4 ancestral groups.".
Do AncestrybyDNA offer any sort of raw download of your data? I wasn't able to see it mentioned. If you have the raw data (list of markers), you could use other services to get another opinion. In my answer to the question about east Asian ancestry I mentioned their are other ways to test the "admixture" of ethnic origins from the raw data, using services like gedmatch.com. This will give other estimates, based on different sample populations and ways of processing it.
It's important to realise all these reports are just estimates, none are perfect.
Having said that, if the AncestrybyDNA test does not provide the raw data you can use elsewhere, and tests with such a small number of ethnic groups, it seems much less useful than most other tests. The reviews on Yelp are mostly fairly negative.
Testing with another company (such as 23andme or FamilytreeDNA) would give you more usable data, but really for your background the admixture (ethnic origins) tests are not yet at the point where the results are of interest. They're mainly useful for confirming or otherwise some existing suspected ancestry from another country, which it sounds like you don't have.
So, to answer your question directly, no, I don't think any more information can be gleaned from that result, unless they have a way to download the raw data, and, more importantly, you should should not take too seriously the "result" they do give.
You did AncestryBYDNA? Not Ancestry.com 's AncestryDNA, but the old AncestryBY DNA from DNA Diagnostics Center? AncestryBYDNA has a high noise threshold, I believe 10% (whereas the 23andme, AncestryDNA, and FTDNA population finder have about 2% I believe). But anything over 10% may be considered true ancestry. Still, I would get Ancestry.com's Ancestry DNA and or the other two companies when I have the money. I don't know why DDC still has AncestryBYDNA,its outdated and while no admixture test is perfect, AncestryBYDNA is the most inaccurate.