The ANACS grading service has changed ownership several times during its history. Under some owners, the market viewed ANACS' grading to be inferior to the top services (PCGS, NGC), while at other times it has faired better.
During the early 1980s, ANACS was owned by the American Numismatic Association (
ANA) - the founders of ANACS. It had a very good reputation at the time.
Are your coins mounted on a card with a photo certificate similar to the following? (Yours would be a bit different, but generally similar.)

If they are, I would feel fairly confident that they were graded accurately.
The realities of today's market vs. the early 1980s are such that if you were to submit the coins today to PCGS or NGC for grading, they would have a good chance to come back at a higher grade. Grading criteria have changed over the last two decades.
Can you list the grades of the coins you have. It would help me (and others) make comments on whether it was worth it to submit the coins for grading.
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When you say 11 piece gold commem set---does that include the two 1915 $50 gold coins?
Generally not, the 11-piece set traditionally features only the $1.00 and $2.50 gold commemoratives. Please note, I can't say for certain that's the case here, I'm only commenting on the typical composition of the 11-piece set.
Collecting history one coin or medal at a time! (c) commems. All rights reserved.