Randomized Block Design vs Completely Randomized Design
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Randomized block design
Collecting data and study design
A randomized block design first groups experimental units into blocks that are alike, then randomly assigns every treatment within each block.
Blocks are formed before any randomizing, using a variable you expect to affect the response, so units inside a block are similar on that variable. For example, to test two fertilizers on 40 plots that run from sunny to shaded, form 4 blocks of 10 plots by sunlight level, then randomly assign each fertilizer to 5 plots in every block. Because all treatments occur within every block, you can compare the treatments without variation from the blocking variable clouding the comparison. A matched pairs design is the two-treatment case: units are paired on an extraneous variable and one treatment is randomly assigned within each pair, or a single unit receives both treatments in a randomized order.
Completely randomized design
Collecting data and study design
In a completely randomized design, all experimental units are assigned to treatments entirely at random, with no blocking or prior grouping.
This is the simplest experimental design: one pool of units and one randomization. For example, write the names of 60 volunteers on identical slips, shuffle them, and deal 20 slips to each of three treatments. The treatment groups do not have to be the same size, though equal sizes usually give the cleanest comparison. The random assignment tends to balance extraneous variables across the groups and lets you argue for cause and effect.