A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero. Notationally, consider a set of variables . Then the linear combination is a contrast if . There is a reason for why I chose to use as the symbol for the variables in […]
A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero. Notationally, consider a set of variables . Then the linear combination is a contrast if . There is a reason for why I chose to use as the symbol for the variables in […]
Fractional factorial designs use the notation; unfortunately, this notation is not clearly explained in most textbooks or web sites about experimental design. I hope that my explanation below is useful. is the number of levels in each factor; note that the notation assumes that all factors have the same number of levels. If a factor has […]
Consider again an experiment that seeks to determine the causal relationships between factors and the response, where . Ideally, the sample size is large enough for a full factorial design to be used. However, if the sample size is small and the number of possible treatments is large, then a fractional factorial design can be used instead. Such a […]
A common problem in statistics is determining whether or not the means of 2 populations are equal. The independent 2-sample t-test is a popular parametric method to answer this question. (In an earlier Statistics Lesson of the Day, I discussed how data collected from a completely randomized design with 1 binary factor can be analyzed […]
In a recent “Machine Learning Lesson of the Day“, I discussed the difference between a supervised learning model in machine learning and a regression model in statistics. In that lesson, I mentioned that a statistical regression model usually consists of a systematic component and a random component. Today’s lesson strictly concerns the systematic component. An […]
An experimenter may seek to determine the causal relationships between factors and the response, where . On first instinct, you may be tempted to conduct separate experiments, each using the completely randomized design with 1 factor. Often, however, it is possible to conduct 1 experiment with factors at the same time. This is better than […]
My last lesson introduced the matched pairs experimental design, which is a special type of the randomized blocked design. Let’s now talk about how to analyze the data from such a design. Since the experimental units are organized in pairs, the units between pairs (blocks) are not independently assigned. (The units within each pair are […]
The matched pairs design is a special type of the randomized blocked design in experimental design. It has only 2 treatment levels (i.e. there is 1 factor, and this factor is binary), and a blocking variable divides the experimental units into pairs. Within each pair (i.e. each block), the experimental units are randomly assigned to the […]
A completely randomized design works well for a homogeneous population - one that does not have major differences between any sub-populations. However, what if a population is heterogeneous? Consider an example that commonly occurs in medical studies. An experiment seeks to determine the effectiveness of a drug on curing a disease, and 100 patients are recruited […]
