On Oct 10, 7:06 am, djh <halitsk...@att.net> wrote: > For the test of the difference of 1S-1C and R1S-R1C at uL, I get > > 2-tailed p ~ 0.355484034 > > and for the test of the difference of 1S-1C and R1S-R1C at uH, I get > > 2-tailed p ~ 1.62136E-08 > > These may be correct (their difference certainly corresponds > ?directionally? to the difference from the incorrect ?ordinary? paired > t-test), but could you a take a moment and check the following to see > how I?m doing things for (Y,varY,dfY) at uL, to make sure I understood > your instructions correctly? > > For the computation of varY at uL, the two relevant columns are: > > uL > 1S-1C R1S-R1C > ?c1? ?cR1? > > a1 -0.045 -0.060 > a3 0.170 0.074 > b1 -0.122 -0.030 > b47 0.020 0.014 > c1 -0.006 -0.007 > c2 -0.118 -0.033 > > If we denote these columns by c1 and cR1 respectively for the sake of > exposition, the first step of your instructions say to compute Y as > follows: > > sum(c1) = -0.101 > sum(cR1) = -0.042 > Y = sum(c1) ? sum(cR1) = -0.059 > > The next step of your instruction requires computation of varY, which > I assume should be done as follows: > > 1) the sample variance of the values in c1 is 0.012 (call this > V(c1)) > 2) the sample variance of the values in cR1 is 0.002 (call this > V(cR1) > 3) so varY = (V(c1) + V(cR1)) / 4, where 4 = k**2 for k=2 > = (0.012 + 0.002)) / 4 > = 0.003474242 > > The next step of your instruction requires computation of dfY, which I > assume should be done as follows: > > 4) df-numerator = (V(c1) + V(cR1)) ** 2 > = (0.012 + 0.002) ** 2 > = 0.000193126 > > 5) df-denominator = (V(c1)**2)/5 + (V(cR1)**2)/5 > = 0.0000283196538188889 > > 6) df = df-num / df-den = 6.81949305487738 > > The next step of your instructions requires computation of t itself, > which I assume should be done as follows: > > 7) t = Y / sqrt(varY) > = -0.059 / 0.058942698 > = -1.000972162 > > And therefore, according to Excel?s 2-tailed t-dist function ?T.DIST. > 2T?: > > p ~ 0.355484034 > > Please either confirm that all the above is correct or let me know > where I went astray. > > Thanks very much as always for your patience with a novice.
Each of the 12 values in the table is the X in an (X, var_X, df_X) triple, and all 36 values are needed in order to do the test. The variance of sum(c1) ? sum(cR1) is the sum of all 12 var_X values, and the df is obtained using point 4.
The only time you get variances and df's the ordinary way is when you get the 1728 lowest-level means. Then var_X is the square of the standard error of the mean, and df = n-1. After than, ALL variances and df's are obtained using point 4.
For the record (and as I mentioned in passing in my post of 9/26 @ 9:33 pm), the df formula in point 4 is a special case of what is generally known as Satterthwaite's approximation. So all the t-tests can be referred to as "heteroscedastic t's using Satterthwaite df's".