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
I think this is what you’re getting at, I may be answering the wrong thing though: basically if it is found to be significant it means that in almost 100% of the cases X leads to or is directly causing Y. The t stat is just a way of quantifying the relationship of x and y for all of your hundreds or thousands of data points into one number. The math to get there is obviously complicated since its taking so many x/y pairs and reducing them all down to one number. So now we have a number representing the relationship, but how do we tell if its a random relationship or a causative one? We do that by proving that it ISN’T random, rather than proving that it IS causative. The critical value is then just the cutoff value on a standard bell curve (of all the possible relationships between two numbers) so that only 5% of the area is past that in the tiny little tip. If your t stat (number that represents the relationship of your two variables) is higher than the critical value (number that excludes 95% of all the known random relationships) then you can say that it is NOT a random relationship.
I hope this helped, that’s how I think of it at least.
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