arcsine

To assess the ability of the different materials to absorb moisture from the air, moisture levels (%) were transformed to arcsine square root prior to analysis with 1-way ANOVA.

The proportion was transformed by arcsine square root to improve normality of the residuals.

Parameters (a) Variables df (b) F Substrates 1, 16 417.07 Destruction Embryonic stages 3, 16 1337.29 Embryonic stages x Substrates 3, 16 207.72 Substrates 1, 16 0.14 Viability Embryonic stages 3, 16 18.80 Embryonic stages x Substrates 3, 16 1.71 Parameters (a) Variables P Substrates < 0.001 Destruction Embryonic stages < 0.001 Embryonic stages x Substrates < 0.001 Substrates 0.708 Viability Embryonic stages < 0.001 Embryonic stages x Substrates 0.206 (a) Both parameters were transformed to arcsine in order to meet the assumptions of normality and homogeneity of variances.

The percentage of fruits per size class was transformed using the arcsine square root of x/100 equation.

The proportion "p" can be made nearly "normal" if the square root of p is multiplied by the arcsine (Ott, Longnecker, and Ott 2001; Osborne 2002).

Prior to statistical analysis, the hyperhydricity (%) data were transformed into arcsine to improve the normality of the data distribution.

The decision ANOVA was run using the Arcsine Transformation because some of the percentages were less than 25%; however Table 3 presents the ANOVA using the percentages for ease of interpretation.

With the aim of improving the performance of such CIs, four transformation functions (logit, probit, arcsine root, and complementary log-log) are selected and applied to the maximum likelihood estimate of R, and the resulting CIs are empirically compared in terms of coverage probability and expected length.

To determine pooled proportions, the variances of the raw proportions (r/n) were stabilized using a Freeman-Tukey-type arcsine square root transformation [22]: y = arcsine [[square root of (r/(n + 1))]] + arcsine [[square root of (r + 1)]/(n + 1)], with a variance of 1/(n + 1), where n is the denominator for population size.

Prior to analyses, pods inflated/flower (IP/F) and seeds matured/flower (S/F) of a plant were arcsine [square root of (xi)] transformed, and counts of flowers/ plant were log10 (x + 1) transformed to meet assumptions of parametric analysis (Zar, 1984).

For a real Gaussian process Van Vleck and Middleton [13] have shown that the autocorrelation coefficient ([R.sub.t] with t = [t.sub.2] - [t.sub.1]) of the output from a hard limiter is related with the input autocorrelation coefficient (here denoted r) by the well-known arcsine law:

However, further attention was given only to mortality data, and mortality data (proportional) was normalized by transforming into arcsine of the square root prior to statistical analysis and data from each colony.

The proportion of morphologically normal oocytes, in vitro matured and fertilized over the various groups was compared by Duncan's New Multiple Range Test (DNMR test) on arcsine transformed data.

You can look up the angle in a trig table, or use a scientific calculator's arcsine key.