Design of Experiments: General Block Design

October 12th, 2013

In some experiments, where the aim is to compare a set of treatments, there are one or two sources of variation that can be accounted for at the design stage of a study. The statistical technique that is used in these situation is blocking and it can be used to reduce the variance of pairwise treatment comparisons. Read the rest of this entry »

Design of Experiments: Blocking, Confounding and Interactions

September 27th, 2013

In a previous post we considered some general points about experimental design. In this post we will look at some other common considerations when planning an experiment, specifically blocking, confounding and interactions. Read the rest of this entry »

Design of Experiments: General Background

June 2nd, 2013

The statistical methodology of design of experiments has a long history starting back with the work of Fisher, Yates and other researchers. One of the main motivating factors is to make good use of available resources and to avoid making decisions that cannot be corrected during the analysis stage of an investigation. Read the rest of this entry »

Fractional Factorial Designs using FrF2

May 18th, 2011

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. Read the rest of this entry »

Generating Balanced Incomplete Block Designs (BIBD)

July 16th, 2010

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. Read the rest of this entry »

Design of Experiments – Block Designs

February 20th, 2010

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, who would be expected to display different degrees of competence with the equipment. Or we might not be able to run all of the experimental combinations in one session so we would want to take into account systematic differences that are due to experiments in the various sessions. Read the rest of this entry »

Two-way Analysis of Variance (ANOVA)

February 15th, 2010

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. Read the rest of this entry »

One-way ANOVA (cont.)

February 12th, 2010

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. Read the rest of this entry »

One-way Analysis of Variance (ANOVA)

February 3rd, 2010

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. Read the rest of this entry »

Design of Experiments – Blocking and Full Factorial Experimental Design Plans

December 6th, 2009

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. Read the rest of this entry »