Sentence examples for power transformations from inspiring English sources

This data preprocessing was introduced by Tukey (1957) as a family of power transformations such that the transformed values are a monotonic function of the observations over admissible range.

Figure 2 contrasts the two different power transformations along with non-transformed data on interaction effects.

To do this, we performed multiple linear regression on phylogenetically independent contrast values estimated using the ape package in R. Before contrasts were estimated variables were transformed as necessary with power transformations to meet normality assumptions of phylogenetically independent contrast methods.

Data were transformed when necessary using logarithmic and power transformations in order to avoid the effects of highly inter-correlated, leading to multi-collinearity among Y1 to Y5 with Z.

Quantitative data were transformed towards normal distribution using Box-Cox power transformations.

Wherever necessary and to ensure normality of residuals was satisfied, data was transformed prior to analysis using Box-Cox power transformations [ 46], i.e. x' = (xp –1)/p, where p is the power maximizing normality likelihood obtained with the 'bcPower' function from the 'car' package in R. Visual inspection of the residuals indicated no violation of assumptions of homoscedasticity.

As sensitivity analyses, QALYs will be estimated using the SF-6D and individual utilities obtained using the e-TTO and visual analogue scale (transformed using a power transformation).

Therefore, the Box-Cox power transformation provides a powerful tool for developing parsimonious models (i.e. applying linear mixed modeling) for data representation and interpretation.

To obtain normally distributed residuals, SCC was transformed using the Box-Cox power transformation ((SCC-0.0816351-1)/-0.0816351).

TG levels were transformed using a logarithmic transformation (see Supplementary Material for a power transformation approach).

The non-transformed response vector was then obtained through the inverse of power transformation function (2)Y ijk = (ϒ i j k λ * λ +1)(1/λ) with the power transformation parameter being fixed at 0.4.