• Variance Stabilizing Transformations:
• When analyzing proportional data ($p$) where observations follow a binomial distribution, the variance is proportional to $p(1 - p)$, which depends heavily on the mean.
• Angular / Arcsine Transformation:
• The variance-stabilizing transformation for binomial proportions or percentages is the sine inverse transformation ($f(p) = \arcsin(\sqrt{p})$ or $\sin^{-1}\sqrt{p}$).
• This stabilizes the variance to a constant value of approximately $\frac{1}{4n}$ (in radians), satisfying the homoscedasticity assumption of ANOVA.
• Other Transformations:
• Square root transformation ($\sqrt{x}$ or $\sqrt{x + 0.5}$): Used for count data following a Poisson distribution.
• Logarithmic transformation ($\log x$): Used when standard deviation is proportional to the mean.
• Fisher's $z$-transformation: Used to normalize the sample correlation coefficient $r$.
• Conclusion: The appropriate transformation is Sine inverse transformation (Option 2).

Correct option: (2) Sine inverse transformation