A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such a...

Bonferroni’s Adjustment (also known as Dunn’s procedure). This procedure is simple to use and can be applied in a wide variety of situations where alpha correction is needed (and is perhaps most appropriate for situations other than the post hoc situation discussed here). To obtain a corrected critical value the desired alpha is divided by the number of comparisons or tests performed and that v...

A general theory on rates of convergence in multiple regression is developed, where the regression function is modeled as a member of an arbitrary linear function space (called a model space), which may be niteor in nite-dimensional. A least squares estimate restricted to some approximating space, which is in fact a projection, is employed. The error in estimation is decomposed into three parts...

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An Excel sheet with both the data and the results can be downloaded by clicking here. The data correspond to an experiment where 4 new toothpaste formulas were each tested on 6 different patients in order to measure their effect on the whiteness of teeth. All patients had previously used the same toothpaste. Using the ANOVA function of XLSTAT we want to find out if the results differ according ...

We show that the one-way ANOVA and Tukey–Kramer (TK) tests agree on any sample with two groups. This result is based a simple identity connecting Fisher–Snedecor studentized probabilistic distributions proven without additional assumptions; in particular, standard assumptions (independence, normality, homoscedasticity (INAH)) are not needed. In contrast, it known for k>2 groups of observatio...

Abstract ANOVA—the workhorse of experimental psychology—seems well understood in that behavioral sciences have agreed-upon contrasts and reporting conventions. Yet, we argue this consensus hides considerable flaws common ANOVA procedures, these become especially salient the within-subject mixed-model cases. The main thesis is are model specification. specifications underlying use deficient from...