Applied Statistics

Appendix BSymbolism

In part, we use different notation to other mathematical disciplines. We do not use capital letters as in probability theory to denote random variables but denote them by bold printing. We do this not only to distinguish between a random variable F with F‐distribution and its realisation F but mainly because linear models are important in this book. In a mixed model in the two‐way cross classification of the analysis of variance with a fixed factor A and a random factor B is the model equation with capital letters written as:

This looks strange and is unusual. We use instead

Functions are never written without an argument to avoid confusion. So p(y) is often a probability function but p a probability. Further is f(y) a density function but f the symbol for degrees of freedom.

Sense	Symbol
Rounding up function	⌈x⌉ = smallest integer ≥x
Binomial distribution with parameters n, p	B(n,p)
Chi‐squared (χ2)‐distribution with f degrees of freedom	CS (f)
Determinant of the matrix A	|A|, det(A)
Diagonal matrix of order n	D(a1. … . an)
Direct sum of the sets A and B	A ⊕ B
Identity matrix of order n	In
(n x m)‐matrix with only zeros	0nm
(n x m)‐matrix with only ones	1nm
Euclidian space of dimension n and 1 respectively (real axis), positive real ...