Posts Tagged ‘ Design of Experiments ’

One-Way ANOVA

September 11, 2012
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One-Way ANOVA Analysis of variance is a tool used for a variety of purposes. Applications range from a common one-way ANOVA, to experimental blocking, to more complex nested designs. This first ANOVA example provides the necessary tools to analyze data using this technique. This example will show a basic one-way ANOVA. I will save the

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Fractional Factorial Designs using FrF2

May 18, 2011
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The FrF2 package for R can be used to create regular and non-regular Fractional Factorial 2-level designs. It is reasonably straightforward to use. First step is to install the package then make it available for use in the current session: require(FrF2) A basic call to the main functino FrF2 specifies the number of runs in

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Generating Balanced Incomplete Block Designs (BIBD)

July 16, 2010
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The Balanced Incomplete Block Design (BIBD) is a well studied experimental design that has various desirable features from a statistical perspective. The crossdes package in R provides a way to generate a block design for some given parameters and test wheter this design satisfies the BIBD conditions. For a BIBD there are v treatments repeated r

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Design of Experiments – Block Designs

February 20, 2010
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Design of Experiments – Block Designs

In many experiments where the investigator is comparing a set of treatments there is the possibility of one or more sources of variability in the experimental measurements that can be accounted for during the design stage of the experimentation. For example we might be investigating four different pieces of machinery using say two different operators,

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Two-way Analysis of Variance (ANOVA)

February 15, 2010
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Two-way Analysis of Variance (ANOVA)

The analysis of variance (ANOVA) model can be extended from making a comparison between multiple groups to take into account additional factors in an experiment. The simplest extension is from one-way to two-way ANOVA where a second factor is included in the model as well as a potential interaction between the two factors. As an example

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One-way ANOVA (cont.)

February 12, 2010
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One-way ANOVA (cont.)

In a previous post we considered using R to fit one-way ANOVA models to data. In this post we consider a few additional ways that we can look at the analysis. In the analysis we made use of the linear model function lm and the analysis could be conducted using the aov function. The code used

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One-way Analysis of Variance (ANOVA)

February 3, 2010
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One-way Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA) is a commonly used statistical technique for investigating data by comparing the means of subsets of the data. The base case is the one-way ANOVA which is an extension of two-sample t test for independent groups covering situations where there are more than two groups being compared. In one-way ANOVA the data

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Design of Experiments – Blocking and Full Factorial Experimental Design Plans

December 6, 2009
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When considering using a full factorial experimental design there may be constraints on the number of experiments that can be run during a particular session, or there may be other practical constraints that introduce systematic differences into an experiment that can be handled during the design and analysis of the data collected during the experiment. Blocking

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Design of Experiments – Full Factorial Designs

December 1, 2009
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In designs where there are multiple factors, all with a discrete group of level settings, the full enumeration of all combinations of factor levels is referred to as a full factorial design. As the number of factors increases, potentially along with the settings for the factors, the total number of experimental units increases rapidly. In many

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Design of Experiments – Optimal Designs

November 29, 2009
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When designing an experiment it is not always possible to generate a regular, balanced design such as a full or fractional factorial design plan. There are usually restrictions of the total number of experiments that can be undertaken or constraints on the factor settings both individually or in combination with each other. In these scenarios computer

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