Cocatre-Zilgien J.H. & Delcomyn F. (1988). Empirical evaluation of
two-sample statistical tests for differences of stepping phase during insect
walking. Biol. Cybern. 59:367-377.
Abstract. In order to determine which statistical tests can validly be applied
to data that describe a temporal relationship between two or more repetitive
movements by an animal, we evaluated empirically seven two-sample that seemed
potentially useful: Student's t test, the Watson Williams test for means, the
variance ratio F test, the Watson Williams test for the concentration parameter
k, the Wallraff test, the Mann Whitney test and the Watson U2 test. Evaluations
were carried out on the timing (phases) of bursts of muscular activity in one
leg relative to those in another during free walking in cockroaches. Each
statistical test was evaluated by dividing randomly a single parent set of data
into two subsets, each subset containing about half the original data set. This
division was repeated 400 times, thus generating 400 pairs of subsets. Each
statistical test was used separately on the pairs of subsets to test the null
hypothesis that the two samples of each pair came from the same population; this
procedure generated 400 statistics for each test, one for each pair of subsets.
An estimate of the reliability of each statistical test was obtained by
comparing the number of times the test actually indicated a significant
difference between subsets to the number of times it might be expected to do so
(20 out of 400 when tested at the 5% level of significance). This procedure was
repeated on ten different sets of data. The outcome of the evaluation suggested
that, from an empirical point of view, Student's t, the Mann Whitney, the
Wallraff and the Watson U2 tests may be useful in assessing differences among
the data we analyzed. The variance ratio F test and the Watson Williams test for
the concentration parameter k were clearly not usable. The Watson Williams test
for means might be useful in some circumstances. Performing an arcsine
transformation of the data did not significantly alter these results. Possible
causes of the inapplicability of some of these tests to phase data are
discussed.
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