Design and Analysis of Experiments with R
17 Dec 2014-
TL;DR: In this paper, the authors present an example of a two-factor Factorial Plan in R with fixed and random factors for estimating variance components of two-Factor Factorial Plans.
Abstract: Introduction Statistics and Data Collection Beginnings of Statistically Planned Experiments Definitions and Preliminaries Purposes of Experimental Design Types of Experimental Designs Planning Experiments Performing the Experiments Use of R Software Completely Randomized Designs with One Factor Introduction Replication and Randomization A Historical Example Linear Model for Completely Randomized Design (CRD) Verifying Assumptions of the Linear Model Analysis Strategies When Assumptions Are Violated Determining the Number of Replicates Comparison of Treatments after the F-Test Factorial Designs Introduction Classical One at a Time versus Factorial Plans Interpreting Interactions Creating a Two-Factor Factorial Plan in R Analysis of a Two-Factor Factorial in R Factorial Designs with Multiple Factors-Completely Randomized Factorial Design (CRFD) Two-Level Factorials Verifying Assumptions of the Model Randomized Block Designs Introduction Creating a Randomized Complete Block (RCB) Design in R Model for RCB An Example of a RCB Determining the Number of Blocks Factorial Designs in Blocks Generalized Complete Block Design Two Block Factors Latin Square Design (LSD) Designs to Study Variances Introduction Random Sampling Experiments (RSE) One-Factor Sampling Designs Estimating Variance Components Two-Factor Sampling Designs-Factorial RSE Nested SE Staggered Nested SE Designs with Fixed and Random Factors Graphical Methods to Check Model Assumptions Fractional Factorial Designs Introduction to Completely Randomized Fractional Factorial (CRFF) Half Fractions of 2k Designs Quarter and Higher Fractions of 2k Designs Criteria for Choosing Generators for 2k-p Designs Augmenting Fractional Factorials Plackett-Burman (PB) Screening Designs Mixed-Level Fractional Factorials Orthogonal Array (OA) Definitive Screening Designs Incomplete and Confounded Block Designs Introduction Balanced Incomplete Block (BIB) Designs Analysis of Incomplete Block Designs Partially Balanced Incomplete Block (PBIB) Designs-Balanced Treatment Incomplete Block (BTIB) Row Column Designs Confounded 2k and 2k-p Designs Confounding 3 Level and p Level Factorial Designs Blocking Mixed-Level Factorials and OAs Partially CBF Split-Plot Designs Introduction Split-Plot Experiments with CRD in Whole Plots (CRSP) RCB in Whole Plots (RBSP) Analysis Unreplicated 2k Split-Plot Designs 2k-p Fractional Factorials in Split Plots (FFSP) Sample Size and Power Issues for Split-Plot Designs Crossover and Repeated Measures Designs Introduction Crossover Designs (COD) Simple AB, BA Crossover Designs for Two Treatments Crossover Designs for Multiple Treatments Repeated Measures Designs Univariate Analysis of Repeated Measures Design Response Surface Designs Introduction Fundamentals of Response Surface Methodology Standard Designs for Second-Order Models Creating Standard Response Surface Designs in R Non-Standard Response Surface Designs Fitting the Response Surface Model with R Determining Optimum Operating Conditions Blocked Response Surface (BRS) Designs Response Surface Split-Plot (RSSP) Designs Mixture Experiments Introduction Models and Designs for Mixture Experiments Creating Mixture Designs in R Analysis of Mixture Experiment Constrained Mixture Experiments Blocking Mixture Experiments Mixture Experiments with Process Variables Mixture Experiments in Split-Plot Arrangements Robust Parameter Design Experiments Introduction Noise Sources of Functional Variation Product Array Parameter Design Experiments Analysis of Product Array Experiments Single Array Parameter Design Experiments Joint Modeling of Mean and Dispersion Effects Experimental Strategies for Increasing Knowledge Introduction Sequential Experimentation One-Step Screening and Optimization An Example of Sequential Experimentation Evolutionary Operation Concluding Remarks Appendix: Brief Introduction to R Answers to Selected Exercises Bibliography Index A Review and Exercises appear at the end of each chapter.
Citations
More filters
••
TL;DR: In this article, the authors examined the accuracy of communication using text-based messaging transmitted over WMN devices (TEXT-WMN) compared to voice transmitted over two-way radios (VOICE-TWR) in disaster simulations.
Abstract: Background Communication failures secondary to damaged infrastructure have caused difficulties in coordinating disaster responses. Two-way radios commonly serve as backup communication for hospitals. However, text messaging has become widely adopted in daily life and new technologies such as wireless mesh network (WMN) devices allow for text messaging independent of cellular towers, Wi-Fi networks, and electrical grids. Objective To examine the accuracy of communication using text-based messaging transmitted over WMN devices (TEXT-WMN) compared to voice transmitted over two-way radios (VOICE-TWR) in disaster simulations. Secondary outcomes were patient triage accuracy, perceived workload, and device preference. Methods 2 × 2 Latin square crossover design: 2 simulations (each involving 15 min of simulated hospital-wide disaster communication) by 2 modalities (TEXT-WMN and VOICE-TWR). Physicians were randomized to one of two sequences: VOICE-TWR first and TEXT-WMN second; or TEXT-WMN first and VOICE-TWR second. Analyses were conducted using linear mixed effects modeling. Results On average, communication accuracy significantly improved with TEXT-WMN compared to VOICE-TWR. Communication accuracy also significantly improved, on average, during the second simulation compared to the first. There was no significant change in triage accuracy with either TEXT-WMN or VOICE-TWR; however, triage accuracy significantly improved, on average, during the second simulation compared to the first. On average, perceived workload was significantly lower with TEXT-WMN compared to VOICE-TWR, and was also significantly lower during the second simulation compared to the first. Most participants preferred TEXT-WMN to VOICE-TWR. Conclusion TEXT-WMN technology may be more effective and less burdensome than VOICE-TWR in facilitating accurate communication during disasters.
5 citations
••
TL;DR: In this article, a longitudinal analysis of 10 years of data from the Chitedze Agriculture Research Station in Malawi was performed to understand the joint effects of variations between the seasons and particular contrasts among treatments on yield of maize.
Abstract: Resilient cropping systems are required to achieve food security in the presence of climate change, and so several long-term conservation agriculture (CA) trials have been established in southern Africa – one of them at the Chitedze Agriculture Research Station in Malawi in 2007. The present study focused on a longitudinal analysis of 10 years of data from the trial to better understand the joint effects of variations between the seasons and particular contrasts among treatments on yield of maize. Of further interest was the variability of treatment responses in time and space and the implications for design of future trials with adequate statistical power. The analysis shows treatment differences of the mean effect which vary according to cropping season. There was a strong treatment effect between rotational treatments and other treatments and a weak effect between intercropping and monocropping. There was no evidence for an overall advantage of systems where residues are retained (in combination with direct seeding or planting basins) over conventional management with respect to maize yield. A season effect was evident although the strong benefit of rotation in El Nino season was also reduced, highlighting the strong interaction between treatment and climatic conditions. The power analysis shows that treatment effects of practically significant magnitude may be unlikely to be detected with just four replicates, as at Chitedze, under either a simple randomised control trial or a factorial experiment. Given logistical and financial constraints, it is important to design trials with fewer treatments but more replicates to gain enough statistical power and to pay attention to the selection of treatments to given an informative outcome.
5 citations
Cites background or methods from "Design and Analysis of Experiments ..."
...Other things being equal, the power of an experiment can be increased by increasing replication or adopting blocking (Lawson, 2014) or by incorporating covariates into the data analysis that account for some of the residual variation (Rudolph et al....
[...]
...Other things being equal, the power of an experiment can be increased by increasing replication or adopting blocking (Lawson, 2014) or by incorporating covariates into the data analysis that account for some of the residual variation (Rudolph et al., 2016)....
[...]
...The daewr package for the R platform (Lawson, 2014) provides functions for doing this....
[...]
••
TL;DR: In this paper, the authors proposed a cycle simplification methodology that seeks to reduce the driving cycle to a discrete set of stationary conditions, for which each operational calibration can be optimized, based on statistical analysis and modelling, and presented to select the most desirable operating condition that can be reached using an LCF.
5 citations
••
TL;DR: In this paper, a multiple nanoemulsion that encapsulates honeybee pollen extract has been designed and optimized as a natural complex matrix model using an iterative mathematical modeling method through a guided experimental design.
4 citations