Harrogath wrote:
tickersu wrote:
Harrogath wrote:
This is not tricky. I think you missing some things.
Correlation coefficient can be from -1 to +1, so its center is Zero. If you check the T-test for testing correlation coefficient significance, you can see that the T-test can be negative too. So, if your calculated t is -1.7, your t critical value must be -2, not 2. Why? Because this is a two-tailed test. In this case, as the calculated t is higher than critical (remeber they are negatives), you FAIL to reject the Ho, or you accept the alternative hypotesis. Failing to reject the null doesn’t mean that you have evidence to support the alternative hypothesis. Failing to reject Ho means that you have insufficient evidence of the alternative hypothesis– Failing to reject Ho and finding evidence of the alternative hypothesis are mutually exclusive outcomes of the hypothesis test. …(A)
I prefer to use the absolute value of the calculated T and the critical values, so I dont get confused when they are negatives.
| calc. T | > | critical value | = Reject Ho (Sufficient statistical evidence of the alternative hypothesis) … (B)
| calc. T | < | critical value | = Fail to Reject Ho (insufficient evidence in favor of the alternative) … (C)
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Pro Tip Of The Day !
All T-test use n - 2 degrees of freedom. Not true, at all. … (D)
Regards
(A): I’m agree with your statement. Thats why we cannot say “Accept the alternative”, we say “Fail to reject the null”. I wrote it just to make it easier to differientiate from Fail to Reject Ho (this always a confusing part when learning Hyphotesis test” for students)
No, we say “Fail to reject the null” instead of “Accept the null”. It has to do with making a Type II error, for which we can’t easily assess the probability of occurrence. If I say “accept the alternative” this means I have evidence against Ho (reject Ho). You cannot both fail to reject Ho and accept the alternative at the same time.
(B): Isn’t it going against A) ?
No, see the previous reply. Remember, we have two “states of nature” for the test (Ho is assumed true, and we are searching for evidence of Ha). From our test, we either find evidence of the alternative or we do not. If we reject the null (Ho), we are saying that our evidence leads us to disagree with Ho, and the evidence supports the alternative.
(C): Ok with this, but be careful when replying like this, you can generate confusion. It seems you renaming what I wrote when in fact you are claryfing your statement (A)
I am rewriting what you wrote, not clarifying my statement. You said “Fail to reject Ho (accept the alternative)”. This isn’t correct, since these two ideas are mutually exclusive. Your statement is the equivalent of “I cannot disagree with Ho and I have evidence of Ha (disagreeing with Ho)”. I changed your statment to be correct. Failing to reject Ho means that you do not “accept” Ha (you have insufficient evidence to support Ha).
(D): At least, T-tests for slopes, intercept and other coefficients in regression analysis is done with n-2 df
This (df) is dependent on the number of estimated parameters in the regression (for your example). If you have an intercept and one independent variable (one estimated slope), then n-2 is correct (account for 1 intercept + 1 slope). If you have an intercept and two independent variables (two estimated slopes), then n-3 is correct (1 intercept + 2 slopes). In general, n-k-1 is the way to calculate degrees of freedom in one of these t-tests (n is sample size, k is coefficients estimated aside from the intercept, and 1 accounts for the estimated intercept).
Hope this helps!