Experimental design
You can impose a treatment on purpose. How do you set up the comparison so that a difference in the results can only have come from the treatment or from chance?
Where you are 6 inside
What this area is about
An experiment imposes treatments and measures what happens, which is what lets it show cause and effect. That only works if the plan keeps everything else out of the comparison. This area is that plan, built from four ideas: control, randomization, replication and blocking.
How these fit together
The vocabulary. Experimental units and treatments names the parts: units, factors and their levels, treatments, and the response variable.
The principles. A control group, often given a placebo and kept blind, sets the baseline. Random assignment lets chance alone split the units into groups, so that nothing else steers who gets which treatment.
The designs. A completely randomized design assigns all units by chance alone, with no grouping first, and adds replication, enough units per treatment for a real difference to show. Blocking groups units that are alike before randomizing within each group; matched pairs is its smallest case.
Reading the result. Comparing treatments by re-randomizing asks whether the difference between groups is bigger than the luck of the assignment would usually produce.
A path through it
Units and treatments first, then the control group, then random assignment, then the completely randomized design, then blocking. Re-randomizing comes last, once hypotheses and simulated sampling distributions are familiar.
Finish here and paired data analyzes the matched pairs design that blocking builds.