what does it mean for a variable to be statistically significant??
Could anyone give a complete answer to this question?
what does it mean for a variable to be statistically significant??
Could anyone give a complete answer to this question?
It means that it is a very unlikely result IF the variable in question had no effect; hence the "no effect" hypothesis is cast into doubt and the alternative hypothesis becomes more plausible.
I'm going to get a little technical in my explanation here, but it's for your benefit.
The concept of "significance" in hypothesis testing has a technical definition that often doesn't get explained (unfortunately) when the notion of "statistical signficance" is first learned, usually in the science classroom. Specifically, the "significance level" of a test is the probability that the test will produce a "Type I error." A Type I error occurs when we reject the null hypothesis when the null hypothesis is actually correct. A result is deemed "statistically significant" when we calculate that the probability that we observe a result at least as extreme as that which we calculated (assuming the null hypothesis is correct) is lower than the significance level.
Now, in layman's terms: a result is statistically significant when the result we observe is, under the null hypothesis, less probable than the event that our test produces a false positive in favor of rejecting the null hypothesis.
Colloquially (stat.), if somebody tell you that he/she found a statistically significant effect in some regression, he/she usually means that some variable x causally influences some variable y with a high probability.
Whether such a statement is appropriate is another matter entirely.