# Analysis of Messy Data, Volume II: Nonreplicated Experiments by George A. Milliken, Dallas E. Johnson By George A. Milliken, Dallas E. Johnson

Researchers frequently don't examine nonreplicated experiments statistically simply because they're surprising with present statistical tools that could be appropriate. research of Messy info, quantity II info the statistical tools acceptable for nonreplicated experiments and explores how one can use statistical software program to make the necessary computations possible

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13 Type I and Type III Analysis of Variance Tables from SAS® GLM. V. 0343 There have been several extensions of these types of tests to other interaction models by using different functions to model the interaction terms and also to other designs such as the rc-way cross-classified treatment structures and Latin square treatment structures. Milliken and Graybill (1970) introduced a generalized procedure which allows one to use any known function of the main-effect parameters to model the interaction.

This is additional support for the claim that there is no interaction in the first three rows of this data set. 3083. All of these are significant at the 5% level, indicating that there is no other subset of three rows which is free of interaction. Another possible method of analysis is to perform Tukey's singledegree-of-freedom test for interaction to two rows at a time. This was done for all possible pairs of rows in the above example. The values of Tukey's F statistics for testing for nonadditivity in the pairs of rows (1,2), (1,3), .

8 MANDEL'S BUNDLE-OF-STRAIGHT-LINES MODEL 23 Step 2. 10) i = 1,2, . . 10) is a simple linear regression model with an intercept at zero and hence a/ = S 7 ft^ 7 /Z j§72, which is algebraically equivalent to a, = Z 7 /3/(yo - y. -)/E /372. The regression sum of squares from the z'th model is SSREG, = X &« /S # = a? Z # 7 7 i - 1,2, . . Z\$ 7 7 7 The sum of squares due to #0: o^ = a2 = • • • = a r is obtained by pooling the SSREG over all / and is given by ssHo = XssREGi = Z ^ Z ^ ' ' 7 The residual sum of squares from all models is obtained by pooling the SS/j.