Short answer: a study is usually called “statistically significant” when its result would be unlikely under a specified statistical model, often using a p-value below a chosen threshold such as 0.05.
Statistical significance is one of the most misunderstood phrases in research. It does not mean the result is important, large, true, or free from bias. It means the observed data are difficult to explain as random variation under the assumptions of a particular test.
What a p-value does and does not say
A p-value is often used to judge statistical significance. If a study reports p = 0.03, it is saying that, under the null model used in the test, data at least this extreme would be relatively uncommon. It is not saying there is a 97 percent chance the hypothesis is true. It is not saying there is only a 3 percent chance the result was due to chance. Those are common but incorrect interpretations.
The 0.05 threshold is a convention, not a law of nature. A result just below 0.05 should not be treated as a discovery while a result just above 0.05 is treated as worthless. Context matters. Study design, sample size, prior evidence, effect size, and measurement quality all affect how much weight the result deserves.
Why significance is not enough
A tiny effect can be statistically significant in a huge sample. A large-looking effect can fail to reach significance in a small study. A badly designed study can produce a significant result that is still misleading. This is why careful readers ask whether the result is practically meaningful, reproducible, and consistent with other evidence.
Statistical significance is a useful tool when used carefully. The danger comes when it is treated as a stamp of truth. A good scientific conclusion should rest on more than a single p-value.