Much of the meaning of terms depends on context. Terminology Much of the meaning of terms depends on context.

Experimental unit In the context of a CRD- Completely Randomized Design, they are single entities of a sample drawn from a population to which treatments are applied. For a CRD they are usually tested once if we only have one type of response variable. They may be subjects, samples of material, etc.

CRD-Completely Randomized Design A sample is randomly drawn from a population. Experimental units from the sample are randomly assigned to treatment groups. Order of applying treatments is random. Order of post-treatment testing is random. Basically, randomization is used to eliminate systematic bias at every stage of the experiment.

Replicate or replication In the context of a CRD, a replicate is another observation or data point taken from a different experimental unit for a given treatment or treatment combination. A replicate of an entire experiment is generally considered a Block. On occasion an experimenter will take replicate (adjective) measurements from the same experimental unit, especially if the measurement system has a lot of variation, such as radioactive counts.

Block In Statistics, “Block” can be used as a noun or verb, much like the use of the term “Replicate” (note the pronunciation of “Replicate”). Generally when used as a noun, Block refers to an entire replication of an experiment. On occasion, an author may use block to refer to an experimental unit such as subject (you may have noticed that Dr. Tom doesn’t like this).

Block, continued….. When used as a verb, “to block on factor X” means that we expect factor X may influence the response to a treatment. So if we block on factor X, that means that we can isolate, or control for, the effect of factor X on the response from the effects of other treatments. For example, “The experimenter Blocked on Gender…”, so Gender is a term in the model, though not a treatment. Gender is in the model since it can influence the effect of treatments considered.

Block as a noun examples. Generally a block is a replication of an entire experiment. It may occur at a different time, a different location, under different conditions, etc. Each block has different experimental units. Experimental units within blocks are more similar than experimental units between blocks. The term Block in the model is used to control for between Block variation.

Block as a verb examples: To block on gender means we take gender into account in the design and analysis of an experiment so that it is not confounded with treatment. Gender will be a term in the model. To block on source of material means we take source of material into account in the design and analysis of an experiment so that it is not confounded with treatment. Source of material will be a term in the model.

Experimental units and experimental subunits An experimental unit may be divided into experimental subunits. For example, a sample of homogeneous material may be divided into subsamples. The variation of subsamples from within a sample is less than the variation between different samples.

Whole plot and split plot In Experimental Design, whole plots are experimental units assigned to treatments (or treatment conditions) called whole plot treatments. Split plots are experimental subunits assigned to other treatments (or treatment conditions) called split plot treatments. Usually, whole plots are nested within whole plot treatments. Text has different examples. Split plots are assigned to split plot treatments in such a way that the whole plot is crossed with the split plot treatment.

Split plots and controlling for variation If a whole plot is split and the split plots are assigned to different treatments, these treatment comparisons control for the whole plot to whole plot variation. Whole plot treatment comparisons are less sensitive than split plot treatment comparisons. Whole plot treatment comparisons are like independent sample t-tests. Split plot treatment comparisons are like paired t-tests.

Split plots and repeated measures (terminology comes from Agriculture). You can think of subject as a whole plot. If each subject is assigned to only one Group, then Group is a whole plot treatment. Group is also a between subjects term. If subject is crossed with Test, Test is a split plot treatment. Test is also called a within subjects term. Split plot terms control for subject to subject variation, so split plot treatments have more sensitive F-tests than whole plot treatments.