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Equation Entry

This document describes the entry of equations into the Stat-Ease simulator.

Note: For more examples of entering simulation equations, see here.

Standard polynomials in terms of the factors can be entered. These take the form of intercept + coefficients times a term.

Polynomial Example

50 + 6A + 7B – 15AB

Categoric factors have two forms. These examples are based on a three-level factor A and a four-level factor B and their interaction.

50 + {6,-2}A + {-2,-1,1}B + {12, -4, 8, -3, -1,0}AB

This method is shorter and matches the simulator for version 8 and earlier.

50+6 * A[1]-2 * A[2]-2 * B[1]-1 * B[2]+1 * B[3]+12 * A[1]B[1]-4 *
A[2]B[1]+8 * A[1]B[2]-3 * A[2]B[2]-1 * A[1]B[3]+0 * A[2]B[3]

This version matches Stat-Ease 9 and later ANOVA model output.

Functions must be entered using lower case letters; variable IDs can be either lowercase or capitals

Functions take the form of <function name>(function or factor ID or number). The parentheses are required.

Name	Explanation
sin	sine function
cos	cosine function
tan	tangent function
asin	arcsine function
acos	arccosine function
atan	arctangent function
sinh	hyperbolic sine function
cosh	hyperbolic cosine function
tanh	hyperbolic tangent function
asinh	hyperbolic arcsine function
acosh	hyperbolic arccosine function
atanh	hyperbolic arctangent function
log2	logarithm to the base 2
log10	logarithm to the base 10
log	logarithm to the base 10
ln	logarithm to base e (2.71828…)
exp	e raised to the power of x
sqrt	square root of a value
sign	sign function -1 if x<0; 1 if x>0
rint	round to nearest integer
abs	absolute value
min	min of all arguments
max	max of all arguments
sum	sum of all arguments
avg	mean value of all arguments
logit	log(p/(1-p)), 0 < p < 1
ilogit	inverse logit (see also: sigmoid, expit, logistic function)

To enter the absolute value of the sin function for A * B:

abs(sin(a*b)) - or - abs(sin(A*B)) - or even - abs(sin(A*b)) are all equivalent.

The following table lists the default binary operators supported by the parser.

if-then-else operations as follows:

(x ? y : z) – Evaluate x, if x is true, do y, if x is false do z. Both the “if true” and “if false” actions must be specified.

Constant	Description
_pi	pi
_e	Euler’s number
_c	Speed of light in vacuum \((m*s^{-1})\)
_h	Planck’s Constant \((J*s)\)
_hbar	Reduced Planck’s Constant \((J*s)\)
_G	Newtonian constant of gravitation \((m^3kg^{-1}s^{-2})\)
_k_B	Boltzmann constant \((J*K^{-1})\)
_N_A	Avogadro constant \((mol^{-1})\)
_epsilon_0	Electric constant or vacuum permittivity \((F*m^{-1})\)
_mu_0	Magnetic constant or vacuum permeability \((N*A^{-2})\)