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An Analysis of Transformations

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TLDR
In this article, Lindley et al. make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's.
Abstract
[Read at a RESEARCH METHODS MEETING of the SOCIETY, April 8th, 1964, Professor D. V. LINDLEY in the Chair] SUMMARY In the analysis of data it is often assumed that observations Yl, Y2, *-, Yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.

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Citations
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Journal ArticleDOI

Structural diversity promotes productivity of mixed, uneven-aged forests in southwestern Germany

TL;DR: Structural and species diversity acted as direct and independent drivers of stand productivity, with structural diversity being a slightly better predictor, and the positive effects of species diversity and structural diversity on forest productivity and ecosystem dynamics are highlighted.
Journal ArticleDOI

Children who read words accurately despite language impairment: who are they and how do they do it?

TL;DR: For a subset of children seen at 4 and 6 years, early phonological skills were equally poor in those later classified as LI or LI + DX, and reading comprehension, however, is constrained by LI.
Journal ArticleDOI

Dynamic averaging of rainfall‐runoff model simulations from complementary model parameterizations

TL;DR: In this paper, the authors present a method to combine models to produce a more satisfactory streamflow simulation, on the basis of two different parameterizations of the same model, by using a seasonal index to weigh the two simulations, providing good efficiency in both low and high flows.
Posted Content

A critical review of literature on the hedonic price model

TL;DR: The applicability of the hedonic price model to the housing market is critically examined in this paper, where a list of common housing attributes used in the estimation of the price models and their effects on housing prices are identified.
References
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Book

Theory of probability

TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.
Journal ArticleDOI

Theory of Probability.

TL;DR: In this paper, the authors introduce the concept of direct probabilities, approximate methods and simplifications, and significant importance tests for various complications, including one new parameter, and various complications for frequency definitions and direct methods.
Book ChapterDOI

Properties of Sufficiency and Statistical Tests

TL;DR: In this article, the structure of small sample tests, whether these are related to problems of estimation and fiducial distributions, or are of the nature of tests of goodness of fit, is considered further.
Journal ArticleDOI

The use of transformations.

Bartlett Ms
- 01 Mar 1947 - 
TL;DR: In this paper, the authors summarize the transformations which have been used on raw statistical data, with particular reference to analysis of variance, and the usual purpose of the transformation is to change the scale of the measurements in order to make the analysis more valid.
Journal ArticleDOI

One Degree of Freedom for Non-Additivity

John W. Tukey
- 01 Sep 1949 - 
TL;DR: The present writer is usually much more concerned with and worried about non-additivity, and until recently has suffered from the lack of a systematic way to seek it out, and then to measure it.