Statistical Models for Landmark Coordinate Data - An Invariant Approach to Statistical Analysis of Shapes - page 62

assume that the variability around the mean can be modeled by a
Normal distribution with mean 0 and variance

2 . We also assume that
the individuals are independent of each other. For this particular case,
this assumption means that the individuals are not siblings or other-
wise related.
The simple statistical model presented for the relationship between
height and weight includes all of the following considerations: lineari-
ty of the relationship, Normal variability, and individuals that are
independent of each other. The validity of each component of the model
can be debated. If a component is changed, a new statistical model is
obtained.
Notice that data do not enter into the discussion of the model. A
model is formulated using the intuition of the scientist and whatever
previous experience and knowledge (s)he may have. Once a model is
formulated, the data are used to determine those parameters of the
model that are most compatible with the observations. This process is
called “estimation of the parameters.” Many different methods may
exist for the estimation of the parameters. A method is any technique
used in the analysis of data.
While conducting any scientific study, a model should be specified
first. Following the specification of a model, methods should be devised
or chosen for estimating the parameters of the model and for conduct-
ing any other relevant data analysis. A particular method is judged as
good or bad, correct or incorrect, only in relation to its efficacy under a
particular model. An evaluation of the conclusions of any scientific
analysis of data must consider the validity of the model and the cor-
rectness of the method.

3.1 Statistical models

“The ubiquity of noise is why statisticians and statistics are useful to science
— if there is no noise, no uncertainty, then there is no need for us or it.''
Holland (1992)

There is variation among biological organisms. No two individuals, no
matter how closely related, are exactly the same. Even if two individu-
als are twins or clones, variability between the phenotypes exists due
to the individual's interactions with the environment. To describe this
variability and to enable proper statistical comparison of groups, a
method for estimating variability within a population is needed.
The first and most important step in the statistical analysis of land-