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
At it’s most basic form it’s that you have some results for something (say someone’s age and whether they voted for Biden or Trump). Now a trend you might see in those results is that older people were more likely to vote for Trump and younger people were more likely to vote for Biden. So you might make a Null hypothesis to test this. The null hypothesis is always negative, as if there’s no real trend so might be “age has no effect on how a person votes”.
If you test this out statistically, it will be statistically significant if the trend is not just random. That age actually does affect how a person votes. In that case, you can reject the null hypothesis and say there’s a true link between age and voting pattern.
The t-test is just a way to measure how different your results are to what you would expect if there was no real trend at all. If the t-value is above a critical value then the difference between your measured results and what the results would look like if things were random is big enough to be confident that your trend is statistically significant.
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