Sums of Squares In
Unbalanced Analysis of Variance
This page gives links to the following material by Donald Macnaughton about numerator sums of squares in unbalanced analysis of variance:
Which Sums of Squares Are Best
Three fundamental concepts of science and statistics are entities, variables (which are formal representations of properties of entities), and relationships between variables. These concepts help to distinguish between two uses of the statistical tests in analysis of variance (ANOVA), namely
Two methods of computing ANOVA sums of squares are:
This paper evaluates the HTO and HTI methods of computing ANOVA sums for squares for fulfilling the two uses of the ANOVA statistical tests. Evaluation is in terms of the hypotheses being tested and relative power. It is concluded that (contrary to current practice) the HTO method is generally preferable when a researcher wishes to test the results of an experiment for evidence of relationships between variables.
To Obtain This Paper
This paper contains 22,000 words and 105 references. It is available in Adobe Portable Document Format (302 kilobytes) by clicking here. For information about the free PDF reader, click here. Click here if you have a problem viewing the PDF document.
Computing Numerator Sums Of Squares In Unbalanced Analysis Of Variance
The following documents and programs illustrate, in simple terms, the differences between five approaches to computing numerator sums of squares in unbalanced analysis of variance. The programs are written in SAS IML (Interactive Matrix Language) although a reader need not understand IML to understand the programs. The following documents are available:
The following SAS programs are available for downloading. (If a requested program file opens in your web browser, select "Save As" from the browser's File menu to save the file on a local drive.)
Reference: Searle, S. R. 1987. Linear Models for Unbalanced Data. New York: John Wiley.
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