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I am explaining my results in my paper. I am looking for a word or phrase with similar meaning to 'statistical difference'.

If one performs a statistical test for a difference in the mean or median of two data samples, and the test rejects the null hypothesis (at some significance level alpha), then there is 'statistical difference' between the two samples. I am looking for another way to say this.

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    Which do you want? There's a (major) difference between "statistically different" and "statistically significant". – Hot Licks May 9 '17 at 13:00
  • First term. Significant difference, is not correct to say? – xava May 9 '17 at 13:05
  • @xava, you are using two different terms. In your question, you have "statistical difference" In your comment, you have "significant difference." Hot Licks has brought up a third term, "statistically significant." – rajah9 May 9 '17 at 13:23
  • The answer depends on what you are looking for and how you are using it. The most common term I've seen is the @HotLicks term, as in "The model is statistically significant with a p-value of .01." – rajah9 May 9 '17 at 13:25
  • No I am looking for similar terms to 'statistical difference' and was wondering if 'significant difference' is wrong to use. I am aware of the difference, for the first one the difference is based on a statistical test and the second one talks about the degree of the difference – xava May 9 '17 at 13:34
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You could simply say "significant difference." In my experience, "statistically" is typically implied prior to "significant." Also, you should never use the term "significant" except to mean statistically significant. If you want to say the difference is large, you would use another word, like "meaningful" or "substantial."

However, I would say that you don't even need to add a qualifier to the word "different" if the difference is statistically significant. You could just state the difference and report the results of the statistical test. If you are writing an academic paper and claim that two quantities are different, then the difference ought to be statistically significant. On the other hand, if you need to report a comparison for which a statistical test was negative, you would want to make sure to specify that the difference was not significant.

  • "Statistically significant" has a specific meaning in disciplines where statistical methods are employed to characterize data. One should avoid using the term unless you know for a fact that the basic computations involved in determining statistical "significance" have been performed and the resulting "p-value" is below about 5%. – Hot Licks May 10 '17 at 23:07
  • @HotLicks You should be able to tell from my answer that I'm familiar with the meaning of the phrase "statistically significant." I was curious about your claim that "statistically different" means something different than "statistically significant." If this is the case, what does "statistically different" mean? – Evan May 11 '17 at 1:44
  • "Statistically different" doesn't have a defined meaning in the same way that "statistically significant" does -- it's pretty much open to interpretation. But the OP needs to understand that using (or somehow implying) that some metric is "statistically significant" when in fact it has not been subjected to significance analysis could result in an academic report being considered to be fraudulent. – Hot Licks May 11 '17 at 1:55
  • I disagree strongly that the phrase "statistically different" has ambiguous meaning, at least in the context of a scientific manuscript. The phrase is less commonly used than "statistically significant," but not overwhelmingly so (453,000 vs. 2,060,000 hits on google scholar). And that is not just due to obscure publications. Top hits include very highly cited papers in Nature and Science. – Evan May 11 '17 at 2:28
  • Yeah, reviewing a few hits on Ngram it appears that "statistically different" is often used to mean "a difference which is statistically significant". So that term should be avoided as well, unless rigorous statistical analysis has been performed. – Hot Licks May 11 '17 at 2:35

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