A man lives in the desert. He hears a story about some substance called water. He is told every living thing needs it.
"Well," says he. "I see no water here, but I do see cactus. And cactus is a living thing, clearly getting by without water so water must not be real."
A man from New Orleans, Louisiana claims he as seen water. Furthermore, he knows from personal experience that water boils when it reaches a temperature of 212 degrees F (100 C). Another man from Alma, Colorado claims he has seen water and furthermore knows that water boils at 193 F (89 C).
Each accuses the other of having "false water", contaminated water or "not the real water". Our desert dweller hears of this and declares it further proof that water isn't real, and that these two gentleman are just a couple of crazies, making things up.
The above is more parable than anecdote, so don't try to analyze it too deeply. It is meant to be as absurd as it sounds.
Given the relative improbability of proving or disproving the existence of God through hard evidence, we fall back to anecdote. But as you can see, this is very problematic, and the conclusions are likely wrong due limited information, personal bias, or any number of other factors.
The debate between New Orleans and Alma, for instance isn't about one being right and the other wrong. They have simply failed to understand one characteristic of water, namely the boiling point varies with altitude. At sea level water boils at 212 Farenheit in New Orleans. Alma Colorado is not at Sea level, it is 10,000 feet above sea level. And at that altitude, water boils at 193 degrees Farenheit.
And this is the problem with claiming God does or does not exist based on anecdote.
"Bad things happen to good people therefore there is no God"
"I witnessed a miracle therefore this is a God"
"One person is miraculously saved from death by God, and a child is killed senselessly, therefore either God is the biggest jerk ever, or he doesn't exist."
"Religious people have done violent things, and caused terrible wars, therefore there is no God."
"I prayed and felt something special therefore there is a God." or more specifically, "I prayed and felt something special about a specific religion, or leader, therefore there is a God, and this is his one and only truth."
"People of lots of different faiths claim to have had spiritual experiences letting them know their respective faith is the one and true faith. Clearly they can't all be the one true faith, therefore there is no God."
These conclusions are all various forms of logical fallacy. None of these anecdotes individually or together definitively, conclusively, scientifically justify a logical conclusion that deity does or does not exist.
They may be sufficient to disprove certain claims regarding the nature, character or motive of deity. But that is all. So, from a perspective of logic, rather than attempting to discredit deity or claim absolutely the existing of deity, it seems a rational person seeking to apply scientific principles would do better to consider the alternatives, rule out the impossibilities, identify the improbabilities, accept the uncertainties and consider the possibilities.