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 learn nonreplicated experiments statistically simply because they're unusual with latest statistical tools which may be acceptable. research of Messy facts, quantity II info the statistical tools acceptable for nonreplicated experiments and explores how one can use statistical software program to make the mandatory computations possible

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By George A. Milliken, Dallas E. Johnson

Researchers frequently don't learn nonreplicated experiments statistically simply because they're unusual with latest statistical tools which may be acceptable. research of Messy facts, quantity II info the statistical tools acceptable for nonreplicated experiments and explores how one can use statistical software program to make the mandatory computations possible

Show description

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Extra info for Analysis of Messy Data, Volume II: Nonreplicated Experiments

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Test HOI: A! = 0 vs. Hal: X{ ^ 0 in the model yi} = n + Ti + ft + A! a^j + e/72. If one fails to reject //01, conclude the data are additive, and complete an analysis of the data accordingly. However, if one rejects #01, then test HQ2'- A2 = 0, A! ^ 0 vs. Ha: A2 * 0, A! * 0 in the model yu = V + Tf + ft + A! au yly. + A 2 a2i J2j + e// 3. If one fails to reject //02> conclude the appropriate model is the one given in (1), and complete the analysis accordingly. If one rejects //02, then test #03: A3 -0, A 2 ^ 0 , A!

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.

Ft, A, « ! , . . , a,, and y l9 . . 4). The maximum likelihood estimate of cr2 is (Z tjZ^-^\)/bt. However, this is a biased estimate of cr2. 1). 2) is not too badly biased when A ^ 0. The estimator a2 tends to be a conservative estimate of o2 ; that is, cr2 tends to overestimate a2 rather than underestimate a2. Although [(& - l)(t- 1) - v^o^lo2 is not distributed as a chi-square distribution, the constant (b - l)(t- 1) - vl provides some information as to how good cr2 might be as an estimate of cr2.

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