Hodges et al (2007) proposed smoothed analysis of variance (ANOVA) and showed how to use it to smooth interactions in balanced, single-error-term ANOVAs. Besides avoiding discontinuous choices to include or exclude effects, smoothed ANOVA addresses three practical concerns: unreplicated designs, masking in effects with many degrees of freedom, and “subgroup analysis”. The present paper extends ...

32.1 Smoothed ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 32.1.1 Zhang et al.’s SANOVA proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 32.1.2 Maŕi-Dell’Olmo et al.’s SANOVA proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 32.2 Some Specific Application...

This paper aims at constructing stepwise test procedures based on the Bonferroni{ Holm principle for a multi{way ANOVA. Especially for the two{way ANOVA it is shown, that the procedures keep the multiple level. These theoretical results are supplemented by a simulation study to compare the multiple procedures regarding two power concepts and to learn about which of the introduced procedures is ...

This paper aims at constructing stepwise test procedures based on the Bonferroni Holm principle for a multi way ANOVA Especially for the two way ANOVA it is shown that the procedures keep the multiple level These theoretical results are supplemented by a simulation study to compare the multiple procedures regarding two power concepts and to learn about which of the introduced procedures is the ...

I present an active learning classroom exercise illustrating essential principles of one-way analysis of variance (ANOVA) methods. The exercise is easily conducted by the instructor and is instructive (as well as enjoyable) for the students. This is conducive for demonstrating many theoretical and practical issues related to ANOVA and lends itself to multiple possible configurations of ANOVA re...

ANOVA is one of the most important tools in comparing treatment means among different groups repeated measurements. The classical F test routinely used to if are same across groups. However, it inefficient when number or dimension gets large. We propose a smoothing truncation deal with this problem. It shown theoreticall...

Factorial models and analysis of variance have been a central pillar of statistical thinking and practice for at least 70 years, so the opportunity to revisit these topics to look for signs of new life is welcome. Given its lengthy history, Anova is an unpromising area for new development, but recent advances in computational techniques have altered the outlook regarding spatial factors, and co...

Modern society generates an incredible amount of data about individuals, and releasing summary statistics about this data in a manner that provably protects individual privacy would offer a valuable resource for researchers in many fields. We present the first algorithm for analysis of variance (ANOVA) that preserves differential privacy, allowing this important statistical test to be conducted...

In this example, we reanalyze the soybean yield data, but treat the explanatory variable as a categorical (ordinal) variable with 4 levels and use one−way anova to test for a significant SO2 effect. We can think of the data as samples from four different populations, corresponding to the SO2 concentration the chambers received, with possibly different means. In each treatment group we have 3 ob...

I. Definition and Applications...............................................................................2 II. Two-Way ANOVA prerequisites.......................................................................2 III. How to use the Two-Way ANOVA tool?...........................................................3 A. Parametric test, assume variances equal. .........................................