Thanks to Kit Baum, there is a new update of -jonter- on SSC. This update
adds a couple of new options, and -jonter- now automatically corrects the
asymptotically normal test statistic, J*, for tied values in -varname-.
Tie-correction of J* should improve asymptotic p-values when users
apply -jonter- to ordered-category contingency tables. The actual
nonparametric test statistic, J, always has been corrected for ties, by
taking midranks. Permutation testing using J was (and is still) the way to
go if you're using -jonter- for these kinds of situations. Toward that end,
there is a new option, -jonly- that causes -jonter- to exit after
calculating only J. This pre-empts the computations involved in J* and
shortens execution time. This should cut overall time when using -jonter-
with -permute-.
In addition, the new version adds p-values for descending order. This
allows the use of -jonter- with inversely related variables without having
to manually reverse the order of one of the variables. The two-tailed
p-value is also reported, for when the user cannot legitimately employ a
one-tailed test. All three p-values are returned as scalars, just as are
both test statistics.
Last, there is a new option -continuity-, which adds a continuity correction
to the asymptotic test statistic (J*). The sources that I've run across
have been mixed about what kind of continuity correction to use for the
Jonckheere-Terpstra test. Unity is used by some and one-half by others.
The continuity correction used in this version of -jonter- is unity, but
simulations that I've done indicate that it doesn't matter much: both yield
test sizes and power the same as -ktau-, except when there is extensive
tying in -varname- ("extensive" meaning "as in a contingency table"), when
the unity correction tends to make the test more conservative than -ktau-,
and the one-half correction makes it only as conservative as -ktau-
(compared to -nptrend-, or to -jonter- without the correction). For those
who would like to use one-half for the continuity correction, the current
version of -jonter- also returns the denominator (SE of J) that goes into
J*, and you can use it (after running -jonter . . . continuity-) to back-out
the continuity correction from unity to one-half with the following code:
local Jstar = (r(Jstar) * r(se_Jstar) + sign(r(Jstar)) * 0.5) / r(se_Jstar)
and then use `Jstar' in -normal()- for calculation of p-values.
Bug reports and suggestions for further improvements are welcome. (I've
already noticed one goof-up--the inequality signs point in the wrong
direction for the one-tailed tests in the printout--but it's not worth
bugging Kit to upload a correction for that alone.)
Joseph Coveney
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