| This is a seemingly witty phrase generally used to discount the value of anecdotal evidence. It means that a single report or story is irrelevant in the face of scientifically-collected data. Usually, in fact, people who say, "the plural of 'anecdote' is not 'data'," would mistakenly believe the term 'anecdotal evidence' to be oxymoronic. But it's not.
The word anecdote comes to English from the Greek anekdota, meaning "unpublished items".1 Evidence which is anecdotal, therefore, is distinguished from scientific evidence by the fact that anecdotal evidence has not been vetted, is not variable-controlled, and does not undergo peer review.
There are two implications of, "The plural of anecdote is not data," that need addressing: - The first is that personal, remembered, and other unpublished accounts are useless in refuting published data, and entirely irrelevant to a contested assertion. That's simply wrong; data is usually collected in the first place because anecdotal evidence flagged something as worthy of investigation. Anecdotes are not data, but they play an important role in contributing to knowledge. An anecdote is a form of information. It is a form of evidence, to be given its due weight.
- The second implication of the phrase is that data alone can prove something as true, while anecdotes cannot. Absurd! (But specious, I admit.) The truth is that neither data nor anecdotes prove anything. Scientific theories are never, ever, ever proven. They can only be disproven. A good scientific theory is merely one which best fits, interprets and explains available scientific data. "Scientific proof" is a misnomer, as this writeup by pimephalis explains well. Uninterpreted data, all by itself, is actually worth less than anecdotal evidence; anecdotes at least offer an explanation for a given case, while uninterpreted data, alone, is meaningless.
With that said, I must concede that information derived from scientific data may rightly be given more weight than anecdotal information. And refuting data-backed information with anecdote-backed information is usually pointless. A theory for which data is not available is not as convincing as one that is backed by data. The strongest theories are convincing because they are backed by a lot of data; but they can never be considered 'proven'.
The best retort to the statement, "The plural of anecdote is not data," is, "And the plural of 'datum' is not 'proof'!"
Or if you're feeling silly, you might just say, "Oh yeah? Well the plural of data is!"
1. by way of French. Source: "anecdote". Merriam-Webster Online. | 
