Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
When faced with the same variables in different groups or indifferentin different datasets, it is usually more valuable to treat them consistently than to optimize in terms of what seems best to suit particular skewness or kurtosis. Typically a scale -- in terms of either a transformation or a link function -- should be chosen consistently on substantive or scientific grounds (e.g. physical, biological, economic). Most often that means working on logarithmic scale.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
When faced with the same variables in different groups or indifferent datasets, it is usually more valuable to treat them consistently than to optimize in terms of what seems best to suit particular skewness or kurtosis. Typically a scale -- in terms of either a transformation or a link function -- should be chosen consistently on substantive or scientific grounds (e.g. physical, biological, economic). Most often that means working on logarithmic scale.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
When faced with the same variables in different groups or in different datasets, it is usually more valuable to treat them consistently than to optimize in terms of what seems best to suit particular skewness or kurtosis. Typically a scale -- in terms of either a transformation or a link function -- should be chosen consistently on substantive or scientific grounds (e.g. physical, biological, economic). Most often that means working on logarithmic scale.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
When faced with the same variables in different groups or indifferent datasets, it is usually more valuable to treat them consistently than to optimize in terms of what seems best to suit particular skewness or kurtosis. Typically a scale -- in terms of either a transformation or a link function -- should be chosen consistently on substantive or scientific grounds (e.g. physical, biological, economic). Most often that means working on logarithmic scale.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
When faced with the same variables in different groups or indifferent datasets, it is usually more valuable to treat them consistently than to optimize in terms of what seems best to suit particular skewness or kurtosis. Typically a scale -- in terms of either a transformation or a link function -- should be chosen consistently on substantive or scientific grounds (e.g. physical, biological, economic). Most often that means working on logarithmic scale.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of (0, 1)$(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of (0, 1) indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.
Skewness and kurtosis in the sense of moment-based measures are just one possible choice of measures of "skewness" or "kurtosis" in some Platonic sense. To be less cryptic, there are vague concepts of asymmetry and tail weight of distributions that can be made precise and quantified in many different ways. Moment-based measures can be, for example, over-sensitive to outliers and they pose more subtle problems in being limited as functions of sample size, so that a sample may not be able to exhibit the skewness and kurtosis of its parent family.
Skewness and kurtosis can be calculated for counted or measured variables regardless of whether values are negative, zero or positive, but the Box-Cox power family in its simplest form usually presupposes positive or at least non-negative values.
Similarly skewness and kurtosis can be calculated for bounded variables -- such as those observed on, or mappable to, $(0, 1)$ or $[0, 1]$ -- but if transformations make sense for the latter they are usually of different form, e.g. logit rather than logarithm. An even more extreme case is that of $(0, 1)$ indicator variables which often exhibit extreme skewness but which cannot be transformed in any useful way.
Such a formulation places even more stress in the wrong place than do naive or over-simplified treatments of Box-Cox by arguing or implying that getting closer to normal marginal distributions is the main deal. On the contrary, even for regression-type models it's at most conditional distributions being close to normal that is some kind of ideal. More generally, what is most valuable about a transformation -- if it is valuable at all -- is likely to be getting closer to (in rough order of importance) additivity, linearity, homoscedasticity and symmetry -- with normality as a special case of the latter being least important of all ideal conditions (often unfortunately stated as assumptions).
Transformations divide the statistical world, and this community too. There are leading members here who never saw a transformation they didn't dislike -- and leading members too who are very positive about transformations being often useful when carefully chosen (above all for visualizing data or results). But there is perhaps slowly and steadily growing recognition that (in jargon introduced with generalized linear models) using link functions other than identity is in many ways a deeper and more helpful way to deal with awkward (e.g. skewed or long-tailed) outcomes. A canonical example here is Poisson regression which does not entail transforming an outcome but respects the scale of the outcome by estimating positive mean functions. Transformations can still make sense for predictors.
I take from the Box and Cox analysis two main ideas, neither quite original even at the time, but both pushed well in their paper: (a) the most common transformations aren't a ragbag of small mathematical tricks but form a family (b) the data themselves can indicate a transformation that may be appropriate, or (just as valuable) that a range of transformations may be appropriate. It's notable that their empirical examples are used to motivate logarithmic and reciprocal transformations that would have seemed sensible to experienced practitioners any way. What I think is contrary to the spirit of their paper is any idea that you can and should automate choice of transformation or that there are calculations that will indicate that power 0.123 or whatever is the transformation to use. Their intent aside, in 60 years since their paper (1964), other methods have emerged strongly that offer other solutions in different ways given awkward distributions.