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).

Mortality of mosquito larvae was analyzed by ANOVA, previous

arcsin data transformation, to detect significant differences among treatments and controls.

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