The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 233

In certain instances, an element-by-element examination of each
growth matrix alongside the growth difference matrix is the best way
to digest the analytical output. Statistical tools can also help in assim-
ilating this information as shown below.
5.9.1 Statistical testing of similarity in growth pattern
Hypothesis testing for similarity in growth pattern
The range of the elements of the growth difference matrix just pre-
sented (0.671 - 0.991) indicates that the difference in facial growth in
these two species is not simply a matter of scale. Our previous discus-
sion suggests that there are significant differences in facial growth
patterns of these two species. If statistical testing for difference in
overall growth pattern is required or desired by the investigator, G obs
can be calculated following methods outlined above and detailed in
Chapter 4 for the two-sample case.
In this example, the Bootstrap reference sample is Macaca fascicu-
laris (the denominator). The histogram below provides the distribution
of 200 bootstrapped G statistics (each “*” represents the value of a sin-
gle bootstrapped G statistic) as well as the placement of G obs (signified
by the letter G in the figure) within this distribution. The probability
is given as 0.204 and G obs clearly falls within the central tendency of
the distribution. This means that we cannot reject the null hypothesis
that facial growth of Cebus apella is similar to the facial growth of
Macaca fascicularis . Here is a clear example where biologically inter-
pretable differences have been revealed using the growth matrices and
growth difference matrix analysis, but statistical hypothesis testing
suggests that the overall difference in growth is not significant.
We saw earlier that there were similarities in the pattern of facial
growth of these two species. Those linear distances that changed the
most and that changed the least were similar in the two species. Even
though the magnitudes of the changes differed greatly, the overall pat-
tern of growth is similar between the two species. From this
perspective the results of the G obs testing is not unexpected.