Biology Reference
In-Depth Information
MANOVA Multivariate analysis of variance. A method for testing the hypothesis that samples do not differ in
their means; MANOVA differs from ANOVA in that the means are multidimensional vectors. See also General
Linear Models (GLM), ANOVA, ANCOVA and MANCOVA (Chapters 8, 9).
Map A mathematical function relating X to Y by stating the correspondence between elements in X and Y. Each
element in X is placed in correspondence with one element in Y. Multiple elements in X may map to the same ele-
ment in Y (landmark configurations differing only in rotation for example would all map to the same shape). A
map is written as: f : X
Y where f is the map from the set X to the set Y.
Matrix A rectangular array of numbers (real or complex). The numbers in a matrix are referred to as elements of
the matrix. The size of a matrix is always given as the number of rows followed by the number of columns; e.g. a
4
-
2 matrix has four rows and two columns.
Mean Also known as the average; an estimate of the center of the distribution calculated by summing all observa-
tions and dividing by the sample size.
Median An estimate of the center of a distribution calculated such that half the observed values are above and
the other half are below.
Metric A non-negative real-valued function,
D
(
X, Y
), of the points
X
and
Y
in a space such that:
3
1. The only time that the function is zero is when
X
and
Y
are the same point, i.e.
D
(
X, Y
)
0, if and only if
X
Y
5
5
2. If we measure from
X
to
Y
, we get the same distance as when we measure from
Y
to
X
,so
D
(
X, Y
)
D
(
Y, X
)
5
for all
X
and
Y
3. The triangle inequality holds true. The triangle inequality states the distance between any two points,
X
and
Y
,
is less than or equal to the sum of distances from each to a third point,
Z
,so
D
(
X, Y
)
D
(
X, Z
)
D
(
Y, Z
), for
#
1
all
X, Y
and
Z
.
Multiple regression Regression of a single (univariate) dependent variable on more than one independent vari-
able. See also Multivariate regression, Multivariate multiple regression, Regression.
Multivariate analysis of variance See MANOVA.
Multivariate multiple regression Regression of several dependent variables on more than one independent vari-
able. In morphometrics, this method is used to regress shape (the dependent variables) onto multiple independent
variables. See also General Linear Models, Multiple regression, Multivariate regression, Regression.
Multivariate regression Regression of several dependent variables onto one independent variable. In morpho-
metrics, this method is used to regress shape onto a single independent variable, such as size. The coefficients
obtained by multivariate regression are the same as those estimated by simple bivariate regression of each depen-
dent variable on the independent variable. However, the statistical test of the null hypothesis differs. See also
General Linear Models, Multiple regression, Multivariate multiple regression, Regression (Chapters 8, 9).
Non-uniform Non-isotropic, or localized, not Uniform; Non-affine. See Non-uniform deformation.
Non-uniform deformation The component of a deformation that is not uniform. In contrast to a uniform defor-
mation, which leaves parallel lines parallel and has the same effect everywhere across a form, a non-uniform
deformation turns squares into trapezoids or diamonds (shapes that do not have parallel sides) and has different
effects over different regions of the form. Most deformations comprise both uniform and non-uniform parts. The
non-uniform component can be further subdivided, see Partial warps (Chapter 5).
Normalize To set the magnitude to one. Normalizing a vector sets the length of the vector to one; this is done by
dividing each component of the vector by the length of the vector, calculated by taking the square root of the
summed squared coefficients.
Null hypothesis, or null model Usually, the hypothesis that the factor of interest has no effect beyond that
expected by chance. For example, in an analysis of allometry, the null hypothesis being tested by regression of
shape on size is that shape does not depend on size (i.e. isometry). Similarly, in a comparison of two means using
Hotelling's
T
2
-test, the null hypothesis is that the two groups do not differ beyond what is expected by chance.
Orange Book Bookstein, F.L. (1991).
Morphometric Tools for Landmark Data. Geometry and Biology
. Cambridge
University Press. See also Black Book, Blue Book, Red Book and White Book.
