Applied Statistics Lesson of the Day – Basic Terminology in Experimental Design #1

The word “experiment” can mean many different things in various contexts. In science and statistics, it has a very particular and subtle definition, one that is not immediately familiar to many people who work outside of the field of experimental design. This is the first of a series of blog posts to clarify what an experiment is, how it is conducted, and why it is so central to science and statistics.

 

Experiment: A procedure to determine the causal relationship between 2 variables – an explanatory variable and a response variable.  The value of the explanatory variable is changed, and the value of the response variable is observed for each value of the explantory variable.

  • An experiment can have 2 or more explanatory variables and 2 or more response variables.
  • In my experience, I find that most experiments have 1 response variable, but many experiments have 2 or more explanatory variables.  The interactions between the multiple explanatory variables are often of interest.
  • All other variables are held constant in this process to avoid confounding.

Explanatory Variable or Factor: The variable whose values are set by the experimenter.  This variable is the cause in the hypothesis.  (*Many people call this the independent variable.  I discourage this usage, because “independent” means something very different in statistics.)

Response Variable: The variable whose values are observed by the experimenter as the explanatory variable’s value is changed.  This variable is the effect in the hypothesis.  (*Many people call this the dependent variable.  Further to my previous point about “independent variables”, dependence means something very different in statistics, and I discourage using this usage.)

Factor Level: Each possible value of the factor (explanatory variable).  A factor must have at least 2 levels.

Treatment: Each possible combination of factor levels.

  • If the experiment has only 1 explanatory variable, then each treatment is simply each factor level.
  • If the experiment has 2 explanatory variables, X and Y, then each treatment is a combination of 1 factor level from X and 1 factor level from Y.  Such combining of factor levels generalizes to experiments with more than 2 explanatory variables.

Experimental Unit: The object on which a treatment is applied.  This can be anything – person, group of people, animal, plant, chemical, guitar, baseball, etc.

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