On Sun, 20 Aug 2000, jkroger wrote in part:
> I want to show that in some conditions, the difference between the length
> of A's response and B's response is greater than in other conditions:
> duration(A) - duration(B) is significantly greater in some conditions.
>
> I tried a t-test for each condition, subtracting B from A at each interval
> and using a t-test to determine if the resulting sample differed from 0.
Yes, but this does not address the question you said you want to show:
which is not that d(A) - d(B) differs from zero, but that
(d(A) - d(B)) in condition 1 (say) > (d(A) - d(B)) in condition 2.
(As an aside, using a t-test would be arguably appropriate for a planned
comparison; but it is much too sensitive for pursuing comparisons that
were suggested by the fall of the data, so to speak, which I gather is
the case in the present instance.)
Presumably you have the mean durations for each cell of the design from
the ANOVA you mentioned in a subsequent post, and appropriate error mean
squares for testing assorted null hypotheses (or constructing confidence
intervals, or both). Plug these into a post hoc contrast analysis (I'd
recommend the method of Scheffe', since the phenomenon appears to be one
you noticed in analyzing the data, not one you anticipated) for the
contrast
d(A1) - d(B1) - d(A2) + d(B2)
(where for the hypotheses the d's represent population means, and for
the analysis one would substitute the observed sample means), for which
the null hypothesis is that the value of the contrast is zero and your
conjecture is that the value is positive (although, since it IS a post
hoc contrast, you should test it against a two-sided alternative
hypothesis).
You may in fact have a number of such conjectures that you want
to pursue; the virtue of the Scheffe' method (and criterion) is that the
Type I error rate is "experimentwise".
On Sun, 20 Aug 2000, jkroger wrote:
> I have two timecourse measures, A and B. At 20 consecutive intervals, A
> and B are measured, and the results are plotted. Both signals rise quickly
> to about the same height, then fall. Sometimes A stays elevated longer.
>
> There are eight separate trials (representing eight conditions), producing
> eight pairs of curves.
>
> I want to show that in some conditions, the difference between the length
> of A's response and B's response is greater than in other conditions:
> duration(A) - duration(B) is significantly greater in some conditions.
>
> I tried a t-test for each condition, subtracting B from A at each interval
> and using a t-test to determine if the resulting sample differed from 0.
> Unfortunately, in a couple conditions where it appears the A response is
> about the same as the B response, but the t-test is so sensitive that even
> small differences between A and B produce significance. The t value for
> the condition (#1) which it is important to demonstrate has a longer A
> duration (as is clearly obvious on inspection) is over 38. The conditions
> in which A - B is minimal still have significant t's of 5 or 8 (when a p
> of .05 requires a t of around 2).
>
> So according to the test I've chosen, A-B in almost all of the conditions
> is significant. What test will allow me to reveal the much greater
> significance of condition #1 relative to the others? I thought of
> chi-square (sum(A), sum(B) for all intervals; crossed with 1-8), but as
> chi-square is for frequency data, I'm not sure if it's applicable here.
>
> Thanks for any guidance,
> Jim
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