# Design Principals

Design Principals- In using DOE it is essential to identify and define critical concepts, which includes:

• Randomization – this is an essential component of any experiment that is going to have validity. If you are doing a comparative experiment where you have two treatments, a treatment and control for instance, you need to include in your experimental process the assignment of those treatments by some random process. An experiment includes experimental units.
• Replication – It is the square root of the estimate of the variance of the sample mean. The width of the confidence interval is determined by this statistic. Our estimates of the mean become less variable as the sample size increases. Replication is the basic issue behind every method we will use in order to get a handle on how precise our estimates are at the end. We always want to estimate or control the uncertainty in our results. We achieve this estimate through replication.
• Blocking – is a technique to include other factors in an experiment that contribute to undesirable variation by creatively using various blocking techniques to control sources of variation that will reduce error variance. For example, age and gender are factors that contribute to the variability and make it difficult to assess systematic effects. By using these as blocking factors, you can both avoid biases that might occur due to differences between the allocation of subjects to the treatments, and as a way of accounting for some noise in the experiment.
• Multi-factor Designs – It is contrary to the scientific method where everything is held except one factor which is varied. The one factor at a time method is a very inefficient way of making scientific advances. It is much better to design an experiment that simultaneously includes multiple factors that may affect the outcome. These may be blocking factors that deal with parameters or they may just help you understand the interactions or the relationships between the factors that influence the response.
• Confounding – It is usually avoided but in building complex experiments we sometimes can use confounding to our advantage. We will confound things we are not interested in order to have more efficient experiments for the things we are interested in. This will come up in multiple factor experiments later on. We may be interested in main effects but not interactions so we will confound the interactions in this way in order to reduce the sample size, and thus the cost of the experiment, but still has good information on the main effects.
• Power – The equivalent to one minus the probability of a Type II error (1-β). A higher power is associated with a higher probability of finding a statistically significant difference. Lack of power usually occurs with smaller sample sizes.
• The Beta Risk- (i.e., Type II ErrororConsumer’s Risk) is the probability of failing to reject the null hypothesis when there is a significant difference (i.e., a product is passed on as meeting the acceptable quality level when in fact the product is bad). Typically, (β) = 0.10%. This means there is a 90% (1-β) probability you are rejecting the null when it is false (correct decision). Also, the power of the sampling plan is defined as 1-β, hence the smaller the β, the larger the power.
• Sample Size – The number of sampling units in a sample. Determining the sample size is a critical decision in any experiment design. Generally, if the experimenter is interested in detecting small effects, more replicates are required than if the experimenter is interested in detecting large effects. Increasing the sample size decreases the margin of error and improves the precision of the estimate.
• Balanced Design – A design where all treatment combinations have the same number of observations. If replication in a design exists, it would be balanced only if the replication was consistent across all the treatment combinations. In other words, the number of replicates of each treatment combination is the same.
• Order – The order of an experiment refers to the chronological sequence of steps to an experiment. The trials from an experiment should be carried out in random run order. In experimental design, one of the underlying assumptions is that the observed responses should be independent of one another (i.e., the observations are independently distributed). By randomizing the experiment, we reduce bias that could result by running the experiment in a “logical” order.
• Interaction effect – The interaction effect for which the apparent influence of one factor on the response variable depends upon one or more other factors. The existence of an interaction effect means that the factors cannot be changed independently of each other.

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