Poster abstracts and manuscripts from the Third International ...

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"What sample size and sampling frequency are necessary to detect
a decrease of 20% in debris over five years?,,
The approach follows the outline of power analysis presented in
Muller et al. (1992). The multivariate linear model upon which
this analysis is based is a repeated measures model with one
within subject factor, time, that occurs at p time points (i.e.,
p-5 for annual surveys). Assumptions made are homogeneity of
variance (i.e., the error structure is the same between survey
units and, hence, between regions), independent survey units, and
that the debris on beaches can be modelled using a multivariate
normal distribution.
The null hypothesis is defined by: H,: 0 = 0 o
(axb)
where 0-CBU.B is the matrix of regional effects over time. Each
row of C defines a contrast among regions; it has dimension axq
(where a is the number of contrasts and q is the number of
regions). Each column of U defines a contrast among the time
periods; it has dimension pxb (where b is the number of contrasts
and p is the number of time points). Following Muller et al.
(1992) we will use the Pillai-Bartlett trace statistic (PB)
because of its robustness to violations of the ANOVA assumptions,
specifically, normality and constant variance. The distribution
of this test statistic when the null hypothesis is true can be
approximated by a central F-distribution. When the alternative
hypothesis is true, the test statistic has approximately a noncentral
F-distribution. The non-centralist parameter w (of the
non-central distribution) can be defined by the value of the test
statistic when the alternative is true.
In order to do a power analysis, we need to turn the question
into a null hypothesis- and decide on the contrast weights. We
are interested in whether or not the trend in each region is
decreasing by the stated percentage. In other words, are the
slopes of the lines for each region parallel and of a specific
value? We will be using linear orthogonal contrast weights. We
will set up the null hypothesis so that rejecting it means that
the decrease must be at least 20%. For annual surveys, this
translates to be H,:. The weighted average number of pieces of
debris at the last two time points is greater, than or equal to
80% of the weighted average number of pieces of debris at the