Just some notes on non-integer degrees-of-freedom (I'll denote them by ft like the original poster, though the usual simbol is df) and t distribution in Excel:
1. Like Prof Koopman says, taking the conservative approach with truncated ft (like Excel does) should be OK. But doing a linear interpolation between the p-values you get with ft and ft+1 would be even better. You can implement it within a single formula.
2. A freely available add-in for Excel that has the t distribution function with non-integer ft is PopTools:
3. If you can, use Excel 2010 rather than any previous version. Excel 2007 (first version of the "New Excel") was well-intended, but a failure (to put things simply). Excel 2007 vs. 2010 is basically the same story as Windows Vista (failure) vs. Windows 7 (much much much better). The looong-due improvements in accuracy (and naming consistency) of Excel's core statistical functions in the 2010 version are documented in detail here:
(long URL so I had to break it into three lines to be able to post the message - reconstruct the URL carefully when pasting into web browser)
Best regards, Assist Prof Gaj Vidmar, PhD University Rehabilitation Institute, Republic of Slovenia
"Ray Koopman" wrote in news:email@example.com ...
On Jun 27, 4:57 pm, djh <halitsk...@att.net> wrote: > Regarding my previous post - once I have t and ft (degrees of > freedom), can I just use Excel's TDIST function as you've allowed > me to do before? > > Or does the special nature of your routine prohibit use of the > Excel function? > > On Jun 27, 6:44 pm, djh <halitsk...@att.net> wrote: > >> Ray - >> >> Due to my rank ignorance, I'm not clear on one point which you >> probably assumed I would understand. >> >> You wrote: >> >> "Then t = (sum d)/sqrt(sum vd), with degrees of freedom = >> >> ft = (sum vd)^2 / sum(vd^2/fd), analogous to each fd." >> >> and this implies to me that I go into a look-up table with t and ft >> to get p. >> >> But since you've specified the algorithm as a "hand-rolled" non >> standard routine, I'm not sure what t->p table to look for, i.e. >> which one to Google for or try to find in Minitab (which I have >> access to thru my wife now.) >> >> I think I asked you a question like this a while back, and you may >> have answered - if so, I apologize for asking again in this new >> context. >> >> Thanks again.
It uses the ordinary t-table but with non-integer degrees of freedom. TDIST won't give you the correct p unless ft happen to be an integer. You would give TDIST the absolute value of t and ask for the two- tailed p; TDIST would truncate ft to an integer, and the returned p would therefore be an upper bound for the true p. To get a lower bound, change ft to ft+1. My subjective guess is that if the sample sizes are always at least as big as those you've had so far then truncating ft to an integer is very unlikely to cause you to miss a result that would have been significant if you could get the true p.
With regard to the stepwise Bonferroni adjustment, the algorithm I gave was designed to be done by hand. If you're programming it then there are better ways. Here is one:
1. Sort the p-values, so that p <= ... <= p[n], keeping track of the comparison that each p[j] relates to.
2. Let k = smallest j for which p[j] > alpha/(n+1-j).
3. p, ..., p[k-1] are significant; p[k], ..., p[n] are not.