By George A. Milliken, Dallas E. Johnson
A best-selling reference for 17 years, research of Messy facts: quantity 1 has now been generally revised and taken completely modern. The authors have streamlined the presentation and included a few fresh advancements within the box, together with advances in random results versions and refinements to a number of comparability systems. most significantly, they've got thoroughly up-to-date fabric regarding software program and aspect how SAS-Mixed, SAS-GLM, and different applications can be utilized to enhance scan layout and version research. effortless to learn with strong examples and a comfy structure, this version will absolutely take its position as a favourite reference of scan designers and statisticians.
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Extra info for Analysis of messy data
7 1) Write down a model appropriate to describe the data. Describe each component of the model. 2) Estimate the parameters of the model in part 1. 3) Construct a 95% confidence interval about m1 - m2. 4) Use a t-statistic to test H0: m1 + m2 - m3 - m4 = 0 vs Ha: (not H0). 5) Use a F-statistic to test H0: m1 + m2 - m3 - m5 = 0 vs Ha: (not H0). 6) Use a t-statistic to test H0: (m1 + m2 + m3)/3 = (m4 + m5)/2 vs Ha: (not H0). 7) Use a F-statistic to test H0: m1 = m2 = m3 vs Ha: (not H0). 8) Use a F-statistic to test H0: (m1 + m2 + m3)/3 = (m4 + m5)/2, (m1 + m2 + m6)/3 = (m3 + m4 + m5)/3, and (m1 + m4 + m5)/3 - (m3 + m6)/2 vs Ha: (not H0).
The approximate denominator degrees of freedom for the distribution of Fc are Ï 2S Ô n = ÌS - r Ô0 Ó if S > r if S £ r The above process can be used to provide a test of the equal means hypothesis by selecting a set of t - 1 linearly independent contrasts of the mi. The SAS-Mixed procedure implements a version of this approximation to the denominator degrees of freedom associated with an approximate F statistic with multiple degrees of freedom in the numerator. SAS-Mixed can be used to fit models with unequal variances per treatment group or unequal variances in some other prespecified pattern using the REPEATED statement and specifying the GROUP = option.
Each of the recommended multiple comparison procedures as well as a few other popular procedures available for the one-way treatment structure of Chapter 1 are examined in the following discussion. Each of the procedures can also be used in much more complex situations, as will be illustrated throughout the remainder of this book. The parameter n used during the remainder of this book represents the degrees of freedom corresponding to the estimator of s 2. For the one-way case of Chapter 1, the error degrees of freedom are n = N - t.