After rigorous statistical analyses have shown a very low likelihood (usually 5% or less) of a result having occurred by chance alone, the result is said to be

Statistically significant.

Explanation:

The common example is tossing a coin.

The probability of tossing a head is .

The probability of tossing five heads in a row is .

p < 5 %, so this is a statistically significant result.

if someone tossed five successive heads, I would start thinking that the coin was loaded.

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