Atheists typically attack Christian appeal to "anecdotal evidence". They brand it to summarily discount miracles, answered prayer, special providence, and the like. These are chalked up to coincidence and bias. I've discussed this in the past, but I'd like to make some additional observations.
One of the ironies of their objection is that atheists are only too happy to resort to anecdotal evidence when they think it serves their purpose. Take Hume's notorious claim that "A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined…But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country."
What is that if not an appeal to anecdotal evidence? Hume never witnessed a resurrection. No one in his social circle did.
Nor can it be said that his objection isn't confined to person experience because he is basing that conclusion on his reading of history, for reported miracles crop up in ancient history and church history.
Or take his illustration: "The raising of a house or ship into the air is a visible miracle."
That may have been impressive to Hume and his 18C readers, but it's unwittingly quaint to a modern reader, raised on aerospace technology. We have a different sample than Hume.
Which brings me to the next point: it seems to me that the distinction between experimental evidence and anecdotal evidence is generally a difference of degree rather than kind. What makes the appeal to anecdotal evidence unreliable in some instances is when the sample is unrepresentative. In that event, it's fallacious to extrapolate from anecdotal evidence.
But the same challenge confronts experimental evidence. I daresay experimental evidence is invariably incomplete . So it becomes a question of whether the experimental sample is representative. In that respect, experimental evidence is anecdotal as well. Both experimental and anecdotal evidence rely on samples. But it's hard to avoid circular justification. How can you know in advance that your sample is representative? After all, isn't the point of testing a sample group to discover something about the sample group that you didn't already know?
Take a horse doctor. Suppose he's been in the business for forty years. He's treated many horses. Yet isn't that anecdotal?
It really depends on whether horses have stable traits. If one horse is much like another, then anecdotal evidence is representative.
But the same thing would be said for miracles, answered prayer, special providence.
The experimental method works best for inanimate processes with invariant reactions. Even in that case, you can have systems that are too complex, with too many unknown variables, as well as known, but uncontrollable variables, to extrapolate from the sample at hand. Take meteorology.
And it's even more uncertain when you introduce personal agents into the mix. That's what makes the stock market so unpredictable. Real life is volatile and unforeseeable in a way that ideal experimentation is not. Anecdotal evidence for religion is not a class apart from the same kind of evidence we rely on for almost everything we believe in.
There is, of course, the danger of bias and coincidence when we interpret reported miracles, answered prayer, and special providence. But, once again, that's scarcely unique to religion.