The word "sampling" carries the connotation that we are simply collecting pre-existing information from our objects of study. However, it is more common and often better practice for scientists to detect differences through a manipulative experiment, which is an attempt to create differences through changing factors in the environment. Although the term "experiment" is often used loosely for any scientific investigation, it is technically a term that is reserved for investigations that seek to determine causation. Framed in statistical terminology, in an experiment we attempt to increase variation due to one or more factors while decreasing the variation caused by all other factors by holding the other factors constant.
Factor. An experimental factor is a measurable quantity which varies and which may cause a change or variation in another measurable quantity. Examples could include: exposure to a drug, amount of water received, or season. Simple experiments investigate only a single factor, while more complex experiments investigate several factors simultaneously. A statistical analysis evaluates the effect of factors, so the list of "effects" in an analysis will correspond to the list of factors being tested. The factor is sometimes called the independent variable and the effect is sometimes called the dependent variable.
Replicate. Synonym: "individual" (in the case of observations rather than manipulations). A replicate is a single trial in an experiment, or a single measurement in an observation.
Sample. A set of replicates observed or measured in an experiment. The number of replicates is called the sample size (represented by N). A sample is assumed to be representative of a population, which is the set of all possible replicates.
Group. Replicates experiencing the same state of the experimental factor are members of a group. In a simple experiment, the control group includes replicates that are lacking the experimental factor. The treatment group includes replicates that experience the experimental factor.
In a more complex experiment, the term "treatment" is often used synonymously with "group". There is often no single group that can be identified as "the control". An experiment investigating the factor "season" could have treatment groups for summer, fall, winter, and spring.
Level. An experimental factor having two or more quantitative values is described as having several levels. For example, if the factor is exposure to a drug, there could be only two levels: "received drug" and "received placebo". There could be more than two descriptive levels such as absent, low, and high, or the levels could be numeric, e.g. 0 mg, 10 mg, 50 mg, and 200 mg.
In some cases, the experimental factor does not have discrete levels (i.e. it is a continuous factor). In that case, each data point includes a measurement of both the size of the experimental factor and the size of the response. For example, if an experiment is investigating the effect of light intensity on growth rate, each growth rate measurement would also have a measurement of the experimental factor (the light intensity). We refer to these as "regression-like" experiments because they are usually analyzed using linear regression (Section 6.3 of the Excel Reference and Statistics Manual).
A more complex experiment can also investigate more than one experimental factor at once. Such an experiment may be described as "2 factor" or "3 factor" (or "2 way" or "3 way"). For example, an experiment could simultaneously measure the effect of two factors, light intensity and water added, on growth rate. The light intensity factor would be continuous and the water added factor could have three levels, low, medium, and high.
