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RegisterOne or two-tailed? [General Statistics]
Dear Ol'Pirate,
The formula for the two-tailed CI is that given above (using a critical tvalue(1-alpha/2, df)).
The formula for the one-tailed interval (upper or lower) differs from that in using tval(1-alpha, df). This is the dual to the two one sided tests (TOST) procedure.
Using alpha=0.05 in the one-sided case both CIs are identical if using alpha=0.1 in the two-sided case. This is why it is said that the usual (two-sided) 90% CIs are operationally equivalent to the TOST procedure.
But in no case the critical value has to be derived with 1-2*alpha.
Lets take alpha=0.05, df=10, EXCEL 2010:
❝ aren't both right?
The formula for the two-tailed CI is that given above (using a critical tvalue(1-alpha/2, df)).
The formula for the one-tailed interval (upper or lower) differs from that in using tval(1-alpha, df). This is the dual to the two one sided tests (TOST) procedure.
Using alpha=0.05 in the one-sided case both CIs are identical if using alpha=0.1 in the two-sided case. This is why it is said that the usual (two-sided) 90% CIs are operationally equivalent to the TOST procedure.
But in no case the critical value has to be derived with 1-2*alpha.
❝ Because of symmetry tval(1-alpha, df) = tval(1-alpha/2, df) if we are clear about the circumstances.
❝ If I remember correctly MS Excel does it a little different from everyone else among the commonly used programs?
Lets take alpha=0.05, df=10, EXCEL 2010:
1-alpha 1-alpha/2
R qt(0.95,10) =1.8124611228 qt(0.975,10) =2.228138852
SAS tinv(0.95,10) =1.8124611228 tinv(0.975,10) =2.228138852
EXCEL t.inv(0.95,10) =1.812461123 t.inv(0.975,10)=2.228138852
but
EXCEL t.inv.2s(0.95,10)=0.064298146 t.inv.2s(0.975,10)=0.032130806 Kappes!
(Kappes = Kohl = cabbage = nonsense in the speech of the Ruhr district)
but
EXCEL t.inv.2s(0.1 ,10)=1.812461123 t.inv.2s(0.05,10)=2.228138852—
Regards,
Detlew
Regards,
Detlew
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Ing. Helmut Schütz