I can’t keep straight the rules the for deciding if a result is statistically significant or not. If t critical is less than calculated t, accept or reject the null hypothesis? And is this true in all cases?

For statistical significance, if caluclated T > +critical T or calulated T < -Critical T, Reject the null that it is not statitically significant , That means it IS statistically significant!

Does it help if you ask the question “How many standard deviations away am I ?”. If you’re close to the hypothesized value (often zero) you can’t reject the null, you can’t determine whether the value you’re looking at is to be considered similar to the null (often zero). The critical value is often “twoish” something (around 2). Also: think about if it’s a one-tailed or two-tailed test, in the latter case it’s symmetrical so you can’t simply say it should be “less than” the critical to fail to reject. The area under the curve, on the outside (ie further away from zero) should add up to the significance level, e.g. add up to 5% with 2.5% in each tail.

I hope I got this right.

Could someone remind me of what was the trick when the F-test shows significance but none of the parameter’s t-statistics are significant enough? The one-tailed F-test shows how well the independent variables as a group explains the variation in a dependent variable, rejection of the null with the F-test shows that at least one of the variables is significant enough. But if the t-test shows insignificance in every variable, you have multicollinearity, but the higher degree of correlation between some or all of the variables makes it impossible to know which one contributes so the t-tests show insignificance.If one or more variables are omitted, the variation in the dependent variable will show on one or more of the remaining variables which will now also come out showing significance in their t-tests, which they didn’t before - before dropping one or more independent variables that is.

what ‘trick’ are you asking about, you pretty much just explained multicollinearity and how to detect and correct for it…

wawa it is multicollinearity