DOE training, or design of experiment, intends to help scientists, engineers, and decisions makers to design effective experiments, evaluate the results of the experiments properly and efficiently, and finally to be able to come up with a logical, correct conclusion that answer their questions, for which they performed the experiments.
Importance of Experiments
The characteristics of an experiment vary with the factors of the experiment, the methods used in each step of it, the treatments applied, and the evaluated outcomes.
- Experiments give us the opportunity to directly compare various methods on the same variable(s)
- Experiments help us to stay away from having a compromised judgment towards specific methods (or treatments)
- Experiments help reducing the judgment errors
- Experiments allow us to simulate an actual situation in the lab without having to deal with unexpected incidents and/or out-of-control circumstances. The fact that we perform experiments under strictly controlled conditions allow us to focus on the targeted variables and be able to properly assume that any outcome is the direct result of the changes we cautiously made in the experiment.
Characteristics of Effective Experiments
- Demonstrate very small systematic errors
- Are accurate and clear
- Provide reasonable error approximation
- Present a wide range of rationality
- Treatments: various methods to be compared in regards to effectiveness on the targeted variable
- Experimental units: the elements on which we test the treatments.
- Responses: the results we get due to applying a certain treatment on an experimental unit.
- Randomization: the employment of an established, implicit probabilistic method to allocate certain treatments to units.
- Response units: the real substances whose response is measured
Randomization and Design
As mentioned above, the characteristics of an experiment vary by the treatments and experimental units applied, how the treatments are allocated to units, and the results and responses are measured. An experiment is called randomized when the techniques through which the treatments are assigned to units includes an identified, well-studied probabilistic structure. The probabilistic structure is what is referred to as a randomization. An experiment can demonstrate various randomized specifications along with the delegation of treatments to units. You should know that randomization is one of the most crucial components of a well-planned experiment.
The major reasons why randomization is crucial is as following:
- Randomization avoids confusion
- Randomization can construct the foundation of inference
Various Types of Randomization
- Physical randomization
- Numerical randomization
- The paired t-test
- Two-sample t-test
- Randomization p-value
- Randomization null-hypothesis
- Statistical methods, e.g. ANOVA
What is Completely Randomized Design (CRD)?
The most straightforward randomized experiment to compare the effect of multiple treatments on certain variables (units) would be the Completely Randomized Design.
Where there are A number of treatments and B number of units to apply in the experiment, then the structure of the CRD would be illustrated as:
Sample size =b1, b2, b3, …, ba, where b1+b2+…+ba= B
Sample b1 is randomly chosen for treatment 1, then sample b2 is randomly chosen to obtain the treatment B-b1, and so on.
CRDs are the easiest, most understandable, most easily evaluated designs.
Preliminary Exploratory Analysis
Performing a preliminary exploratory or graphical analysis of the data before any official modeling, testing, or approximation can often save a lot of time and money. Such preliminary analysis include:
- Clear informative statistics including tools, medians, standard errors, interquartile ranges
- Diagrams, including stem and leaf diagrams, box-plots, and scatter-plots
- The above procedures used individually on each treatment category
Variance assessment indicates that each category of treatments don’t demonstrate the same mean response. However, an ANOVA cannot alone make this statement that treatments are different or in what ways they vary. In order to get to that conclusion, the treatment means, or equivalently, need to be considered at the treatment effects. One technique to evaluate treatment effects is called a contrast.
While ANOVA plays as the background to shed some light on the data, it won’t provide adequate light to reveal all the details. A contrast allows you to concentrate on a certain, thin specification of the data. However, the contrast demonstrates a narrow focus that it won’t provide the big picture. By applying multiple contrasts, you can hang around your focus to discover more details. Wise use of contrasts requires selecting appropriate contrasts so that they reveal useful features of your data.
In the case of having multiple relevant tests or interval approximations at the same time, multiple comparisons or simultaneous inference becomes important. The problem of multiple comparisons is one of error rates. Every test or confidence interval possesses a Type I error rate, which is controllable by the experimenter.
If all the tests are considered as a whole unit, then you can calculate an integrated Type I error rate for the whole unit of tests or intervals. When the unit consists of multiple true null hypotheses, the likelihood of one or more of these true null hypotheses is declined would go up, and the chance of any Type I errors in the unit become pretty large. Multiple comparisons protocols manage Type I error rates for units of tests.
Multiple Comparisons Methods
- The Bonferroni technique
One of the simplest methods associated with the multiple comparisons would be the Bonferroni technique, which is broadly applicable in multiple comparisons processes.
- The Scheffe technique
The Scheffe ́ technique is used for contrasts generating synchronized self-assurance intervals for any and all contrasts, consisting of contrasts recommended by the data. Thus Scheffe ́ is the suitable method for analyzing contrasts obtained from data interfering. Such appears to be an error rate control, arbitrarily many comparisons, even ones recommended from the data analysis! The disadvantage of this great protection is the low power. Hence, the Scheffe ́ method is used in those conditions where there is a contrast recommended by the data, or many contrasts that cannot be managed by other techniques.
- Pairwise Comparisons
A pairwise comparison is a contrast that evaluates the difference between two treatment tools
Random effects are another technique to designing experiments and modeling data. Random effects are perfect for the treatments with random samples chosen from a diverse population of possible treatments. They are also suitable for random sub-sampling from populations. Models associated with random effects models make similar types of breakdowns into general mean, treatment effects, and random error, yet these models postulate that the treatment effects are random variables. Plus, the concentration of implication is on the population, not the single treatment effects.
The reason why random effects should be applied is that you intend to draw interpretations about the population from which the treatments were chosen. In particular, you want to understand the variation in the treatment effects. Therefore, you need to design an experiment that considers variation in a population by looking at the variability that rises when the population is sampled. In other words, random effects come to play when variances and variability are being investigated.
A block of units is a series of units that are coherent in some sense. They could be field diagrams placed in the similar general area, or are samples assessed at about the same time, or are units that originated from an individual supplier. Such resemblances in the units themselves will result in predicting that units inside a block might also share similar responses. So during constructing blocks, coherency of the units inside blocks is intended to accomplish, but units in various blocks could be different. The Randomized Complete Block design (RCB) is the basic blocking design.
An RCB is used to enhance the strength and accuracy of an experiment by reducing the error variance. This reduction in error variance is accomplished by exploring groups of units that are coherent (blocks) and, in effect, replicating the experiment separately in the various blocks. The RCB is an efficient design when you are dealing with an individual source of unimportant variation in the responses that you can determine early and apply to divide the units into blocks. Blocking is performed at the time of randomization; you can’t build blocks after the experiment is over.
How Can You Learn More?
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