In Do We Really Need the S-word? in 'American Scientist', the author Megan D. Higgs writes
Did the people who introduced the word’s use in statistics intend for it to be interpreted according to its current everyday meaning? The answer is not simple. In his 2001 book The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, David Salsburg contends the word carried much less weight in the late 19th century, when it meant only that the result showed, or signified, something. Then, in the 20th century, significance began to gather the connotation it carries today, of not only signifying something but signifying something of importance. The coinciding of this change in meaning with a steady increase in its use by more scientists with less statistical training has had a big impact on the interpretation of scientific results. My sentiments echo Salsburg’s: “Unfortunately,” he writes, “those who use statistical analysis often treat a significant test statistic as implying something much closer to the modern meaning of the word.”
I did some searching on Google, but unfortunately, most results are about the term "Historical significance", and I failed to find a definitive reference about the change in the meaning of "significant".
Can you tell me about more about the meaning change, like when and why did it happen?