Computes all the 4 score tests for YJ transformation

The transformations for negative and positive responses were determined by Yeo and Johnson (2000) by imposing the smoothness condition that the second derivative of zYJ(λ) with respect to y be smooth at y = 0. However some authors, for example Weisberg (2005), query the physical interpretability of this constraint which is oftern violated in data analysis. Accordingly, Atkinson et al (2019) and (2020) extend the Yeo-Johnson transformation to allow two values of the transformations parameter: λN for negative observations and λP for non-negative ones.

ScoreYJall computes: 1) the global t test associated with the constructed variable for λ=λP=λN.

2) the t test associated with the constructed variable computed assuming a different transformation for positive observations keeping the value of the transformation parameter for negative observations fixed. In short we call this test, "test for positive observations".

3) the t test associated with the constructed variable computed assuming a different transformation for negative observations keeping the value of the transformation parameter for positive observations fixed. In short we call this test, "test for negative observations".

4) the F test for the joint presence of the two constructed variables described in points 2) and 3.

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Ex in which positive and negative observation require different lambdas.`outSC`

=ScoreYJall(`y`

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`X`

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`Name, Value`

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Yeo, I.K. and Johnson, R. (2000), A new family of power transformations to improve normality or symmetry, "Biometrika", Vol. 87, pp. 954-959.

Atkinson, A.C. Riani, M., Corbellini A. (2019), The analysis of transformations for profit-and-loss data, Journal of the Royal Statistical Society, Series C, "Applied Statistics", https://doi.org/10.1111/rssc.12389

Atkinson, A.C. Riani, M. and Corbellini A. (2021), The Box–Cox Transformation: Review and Extensions, "Statistical Science", Vol. 36, pp. 239-255, https://doi.org/10.1214/20-STS778