When talking about experimental designs do you ever get bewildered by the terms response, factor, and level? If so you are not alone. However, getting the definition of these terms is absolutely critical to ensure that the experimental design is not ruined in the initial planning and execution phases.
In this article, I will present definitions for these terms, synonyms, and point out ways to avoid getting it wrong. Along the way we will also define discrete, continuous, categorical, binary, and ordinal - some other commonly misused terms.
Examples of response variables could be the number of scoops of ice cream sold, the height of a corn plant, the patient's pain score after surgery, or the score on a standardized knowledge test.
Responses can be either continuous or discrete.
Continuous responses are somewhat easier to conceptualize. Continous responses take a value that theoretically could take on any possible value in a range of portion of the number line. An example would be height, blood pressure, temperature.
Factors are the variables in the study that we believe will influence the results.
Factors can also be called independent variables, explanatory variables, manipulator variables, or risk factors.
Examples of factors may be an antibiotic given to a patient, a teaching session given to a student, the type of triage system being used, or the age of a person taking a driving test.
Factors too can be either continuous or discrete.
An example of a continuous factor might be
When factors are discrete, again either binomial, ordinal, or categorical, the values that they can take are called levels.
Example of levels of a factor may be such things as the type of antibiotic given, triage system used, or the presence or absence of a training session.
Why is it so important to know all these tedious definitions? Choosing the right statistical test to analyze your data depends directly on knowing the response, factors, and levels for the experimental data. Choosing this statistical test correctly means sailing through the power calculation, study design, data collection, and analysis. Getting it wrong can mean hours and hours of needless work and - in the worst case - an experiment that is unsalvageable.