Treatment vs Experiment

A factor is an explanatory variable the experimenter sets, and its levels are the settings that variable can take. A treatment is one complete combination: one level of every factor, imposed on an experimental unit. With a single factor the treatments are simply its levels. With two factors the number of treatments is the product of the two level counts.

A bakery tests two oven temperatures, 190 and 210 degrees Celsius, crossed with three rising times of 30, 60 and 90 minutes. That is $2 \times 3 = 6$ treatments, running from 190 degrees for 30 minutes through to 210 degrees for 90 minutes. Six, not the two factors and not the $2 + 3 = 5$ levels. With 48 loaves available, $48/6 = 8$ loaves receive each treatment, and the response is loaf height in centimeters after baking.

The sentence that costs points: "the treatment group got the new gel and the control group got nothing, so there was one treatment." Whatever the control group receives, a placebo, the current standard product, or no gel at all, is one of the conditions being compared, which is why a well-designed experiment compares at least two treatment groups. A treatment is also a condition rather than a set of units: the 8 loaves baked at 210 degrees for 90 minutes are a treatment group, and the treatment is the baking recipe they got.

Treatments exist only where somebody imposes them. In an observational study the groups compared are formed by what the subjects were already doing, so those are levels of a variable that got recorded, not treatments, and that is exactly why such a study cannot carry a causal claim on its own.

Factors, levels and treatments are the vocabulary of topic 1.13 Experimental Design, and a design description that never names the treatments precisely has not described the experiment.

An experiment imposes something. The researcher assigns conditions called treatments to experimental units and then measures a response, which is the line between an experiment and an observational study, where the groups assemble themselves. The course names four marks of a well-designed experiment: comparison of at least two treatment groups, random assignment of treatments to units, replication, meaning more than one unit per treatment, and direct control of extraneous variables.

A store tests two checkout layouts on 200 shoppers, using a random number generator to send 100 to each. Mean checkout time comes out at 84 seconds under layout A and 97 seconds under layout B, a difference of 13 seconds. Because chance decided who met which layout, no systematic difference in basket size or shopping habit is expected to pile up on one side, so a gap that size, if it is larger than chance variation would ordinarily produce, is fairly credited to the layout.

"It was an experiment, so it proves cause and effect" hides two separate conditions inside one word. Imposing a treatment is what makes a study an experiment. Random assignment is what makes its comparison causal, and the two do not always travel together. Give layout A to the morning shift and layout B to the afternoon shift and you have imposed treatments, so it is still an experiment, but time of day now moves in lockstep with layout and no causal reading is available.

The causal claim also has a limit on who it covers. Random assignment supports a conclusion about the units in the study, and extending that to a wider group takes random selection, a different act at a different stage; scope of inference works through the combinations.

Everything else in experimental design is machinery for those four marks: blocking to pull a known nuisance variable out of the comparison, a control group and a placebo to supply a baseline, and blinding to keep expectations from leaking into the response. Replication means many units per treatment, not repeating the whole study, which is the vocabulary slip the exam catches most often here.