One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package ...extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.
Many psychologists do not realize that exploratory use of the popular multiway analysis of variance harbors a multiple-comparison problem. In the case of two factors, three separate null hypotheses ...are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14 % rather than 5 %, if the three tests are independent. We explain the multiple-comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus
F
test, control of the familywise error rate, control of the false discovery rate, and preregistration of the hypotheses.
From Many to One: Consensus Inference in a MIP Cressie, Noel; Bertolacci, Michael; Zammit‐Mangion, Andrew
Geophysical research letters,
28 July 2022, Volume:
49, Issue:
14
Journal Article
Peer reviewed
Open access
A Model Intercomparison Project (MIP) consists of teams who estimate the same underlying quantity (e.g., temperature projections to the year 2070). A simple average of the ensemble of the teams' ...outputs gives a consensus estimate, but it does not recognize that some outputs are more variable than others. Statistical analysis of variance (ANOVA) models offer a way to obtain a weighted frequentist consensus estimate of outputs with a variance that is the smallest possible. Modulo dependence between MIP outputs, the ANOVA approach weights a team's output inversely proportional to its variance, from which optimally weighted estimates follow. ANOVA weights can also provide a prior distribution for Bayesian Model Averaging of the MIP outputs when external evaluation data are available. We use a MIP of carbon‐dioxide‐flux inversions to illustrate the ANOVA‐based weighting and subsequent frequentist consensus inferences.
Plain Language Summary
There can be disagreement between different teams of scientists on the best way to model and hence estimate complex geophysical phenomena. Model Intercomparison Projects (MIPs) address this in a scientific manner, where a common protocol about data and certain basic geophysical features is agreed upon by the teams. The collection of the different teams' outputs is analyzed, often using the ensemble mean and a measure of the ensemble variability. However, the results may indicate that it is inappropriate to treat all teams' outputs equally, which can happen when some teams have superior models or better numerical approximations. It may also happen that some teams share code or their models have common features beyond those specified in the protocol. We adapt a statistical technique called the analysis of variance (ANOVA) to this complex setting, obtain optimal weights on the outputs, and then estimate those weights. This results in a statistically optimal (i.e., most precise) consensus summary of the MIP; other weights give less‐precise inferences. We call this inference framework for MIPs, Statistically Unbiased Prediction and Estimation‐ANOVA, and we apply it to a MIP designed to estimate the sources and sinks of carbon dioxide.
Key Points
Consensus inference is provided for Multiple Intercomparison Project (MIP) outputs when little or no evaluation data are available
The statistical analysis of variance method quantifies the MIP outputs' variabilities to obtain optimally weighted frequentist consensus inference
Variance parameters for optimal weighting of outputs and consensus inference are estimated using likelihood‐based methodology
Researchers often rely on analysis of variance (ANOVA) when they report results of experiments. To ensure that a study is adequately powered to yield informative results with an ANOVA, researchers ...can perform an a priori power analysis. However, power analysis for factorial ANOVA designs is often a challenge. Current software solutions do not allow power analyses for complex designs with several within-participants factors. Moreover, power analyses often need
η
p
2
or Cohen’s f as input, but these effect sizes are not intuitive and do not generalize to different experimental designs. We have created the R package Superpower and online Shiny apps to enable researchers without extensive programming experience to perform simulation-based power analysis for ANOVA designs of up to three within- or between-participants factors. Predicted effects are entered by specifying means, standard deviations, and, for within-participants factors, the correlations. The simulation provides the statistical power for all ANOVA main effects, interactions, and individual comparisons. The software can plot power across a range of sample sizes, can control for multiple comparisons, and can compute power when the homogeneity or sphericity assumption is violated. This Tutorial demonstrates how to perform a priori power analysis to design informative studies for main effects, interactions, and individual comparisons and highlights important factors that determine the statistical power for factorial ANOVA designs.
Aluminium alloy is the popular material in the world to produce lot of light weight parts with high strength, in additionally reinforcement is consider to these alloy is improve its strength. In this ...investigation consider the AA7050 aluminium alloy as a base material with reinforcement of Silicon Carbide (SiC) at various percentage level like as 0%, 4 % and 6 %. The wear of this composites are analysed through the design of experiments (Taguchi approach) for optimize the process parameters. This wear study is considered the parameters are Sliding velocity in m/s (1, 2 and 3), Sliding distance in m (1000, 1400 and 1800) and percentage of composition (0%, 43% and 6%). For this experimental investigation the sliding distance as most significant factor among three. The microstructure analysis demonstrated that there is a SiC particles which reduces wear of the samples.
This paper introduces the R package WRS2 that implements various robust statistical methods. It elaborates on the basics of robust statistics by introducing robust location, dispersion, and ...correlation measures. The location and dispersion measures are then used in robust variants of independent and dependent samples
t
tests and ANOVA, including between-within subject designs and quantile ANOVA. Further, robust ANCOVA as well as robust mediation models are introduced. The paper targets applied researchers; it is therefore kept rather non-technical and written in a tutorial style. Special emphasis is placed on applications in the social and behavioral sciences and illustrations of how to perform corresponding robust analyses in R. The R code for reproducing the results in the paper is given in the
Supplementary Materials
.
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