Glossary - Cellular Potts Models: Multiscale Extensions and Biological Applications - page 215

When the scaling term is unknown and is replaced by an estimate based on
the data, the test statistic (under certain conditions) follows a Student's
t distribution. Among the most frequently used t-tests are
A one-sample location test of whether the mean of a normally dis-
tributed population has a value specified in a null hypothesis.
A two-sample location test of the null hypothesis that the means of
two normally distributed populations are equal. All such tests are
usually called Student's t-tests, though strictly speaking that name
should only be used if the variances of the two populations are also
assumed to be equal; the form of the test used when this assumption
is dropped is sometimes called Welch's t-test. These tests are often
referred to as \unpaired" or \independent samples" t-tests, as they
are typically applied when the statistical units underlying the two
samples being compared are nonoverlapping.
A test of the null hypothesis that the difference between two re-
sponses measured on the same statistical unit has a mean value of
zero. For example, suppose we measure the size of a cancer patient's
tumor before and after a treatment. If the treatment is effective, we
expect the tumor size for many of the patients to be smaller following
the treatment. This is often referred to as the \paired" or \repeated
measures" t-test.
A test of whether the slope of a regression line differs significantly
from 0.
Most t-test statistics have the form T = s , where Z and s are functions
of the data. Typically, Z is designed to be sensitive to the alternative
hypothesis (i.e. its magnitude tends to be larger when the alternative
hypothesis is true), whereas s is a scaling parameter that allows the dis-
tribution of T to be determined. As an example, in the one-sample t-test
Z = X p n , where X is the sample mean of the data, n is the sample size,
and is the population standard deviation of the data. In particular, in
the one-sample t-test, s is ^ =, where ^ is the sample standard deviation.
The assumptions underlying a t-test are that
Z follows a standard normal distribution under the null hypothesis.
ps 2 follows a 2 distribution with p degrees of freedom under the
null hypothesis, where p is a positive constant.
Z and s are independent.
Vascular endothelial growth factor (VEGF): A signal protein family
produced by cells that stimulates vasculogenesis and angiogenesis. The
most important member is VEGF-A. Other members are placenta growth
factor (PGF), VEGF-B, VEGF-C and VEGF-D. The latter ones were
discovered later than VEGF-A, and, before their discovery, VEGF-A was