Coefficients for curve modeling are computed using probability distribution functions: polynomials, power functions, sinus, cosine, tangent, cotangent, logarithm, exponent or

arcsin, arccos, arctan, arcctg.

If the variance and mean of X and Y are the same (and they are usually close here), then M/1000 is equivalent to the standard correlation coefficient r, except that the

arcsin transformation (applied to a measure of Mielke 1991) means that the deviation from unity asymptotes to the square root of mse, rather than mse itself.

The

arcsin [square root of x] transformation was used to normalize the fraction of cells in the S phase of the cell cycle, fraction of cells in the G2-M phases of the cell cycle, and RSG1.

[[phi].sub.1] = [pi] +

arcsin [[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]] - [[beta].sub.0], [[phi].sub.2] = 2[pi] -

arcsin [[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]] - [[beta].sub.0].

[alpha](i) =

arcsin [2 (dx(i) - [dx.sub.-90]/[dx.sub.+90] - [dx.sub.-90] - 0.5)], (1)

[DELTA][phi] = 2 x

arcsin [[a.sub.z]/[2 x [R.sub.v] x cos [[alpha].sub.v]]] (13)

7: [F.sub.6,23] = 1.08, P = 0.41, with

arcsin transformation).

Demographic data were tested for normality, and transformed when necessary; proportions were transformed by

arcsin [check]p (Zar, 1999).

d = 2R X

arcsin ([square root of [haversin([DELTA][PHI]) + cos [[phi].sub.1]cos [[phi].sub.2]haversin([DELTA][phi])]])

Analyses.--I compared the among-year differences of A) percent daily loss in mass while nest-guarding (

arcsin transformed) and B) percent daily gain in mass subsequent to release (

arcsin transformed) with one-way ANOVAs, using proportional values to accommodate for the differences in size of the spiders.

and rewriting the "

arcsin" as an "arctan" form, we obtain the new integral