What exactly does it mean when a result is statistically significant vs. insignificant? When we compare, for example, a t-stat and the critical t-value, I know we either reject or fail to reject the null hypothesis based on whether the t-stat is less than or greater than the t-value. What exactly does it mean when the t-stat is greater than the critical t-value? What even is the “t-stat” and “critical t-value” in layman terms?
After doing enough problems, I’m sure I’ll get it, but I don’t like _not_ being able to explain this to myself simply – which indicates that I haven’t understood it well enough. Can someone please dumb all of this down for me and truly explain it to me like I’m a child?
In: Mathematics
Statistically, “significant” means that the data supports rejecting the null hypothesis and that the the chances are very low that it’s a coincidence. “Insignificant” means either that the data supports the null hypothesis, or that it’s weak enough that it might be a coincidence.
Since coin-flipping is the go-to situation for probability, consider the following situation: You’re told that a coin is a fair coin (null hypothesis), but you’re not allowed to hold it or look at it. Someone repeatedly flips it for you, and the result is heads every time. At what point do you decide that you were lied to, and the coin actually has heads on both sides? 5 flips? 10? 100?
IRL you could, of course, look at the coin to see if there’s a tails side. But if, for example, you wind up with 99 heads and 1 tails, you can be pretty sure the coin is biased, whereas 5 heads and 1 tails wouldn’t do it because that could easily happen with a fair coin. Somewhere in between is the line between significance and insignificance, and that (I think) is what the critical t-value represents.
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