Designing experiments: randomization, replication, blocking

About this lesson

Algebra II › Statistical inference

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Designing experiments: randomization, replication, blocking

Warm-up

Three quick questions from earlier lessons.

Discover

To compare two fertilizers, you put fertilizer A on the sunny half of a field and B on the shady half. A grows better. What is the flaw?

  1. Sunlight, not the fertilizer, could explain the difference
  2. There is no flaw

Key idea

Principles of experimental design.

Comparison of treatments (often with a control or placebo group); random assignment of units to treatments; replication on enough units; blocking groups similar units first and randomizes within each block. With several factors, the treatments are all combinations of their levels.

Worked example

Test 2 doses × 3 diets on 60 rats.

Treatments: 2×3=62 \times 3 = 6
Each combination.
10 rats per treatment
Replication.
Shuffle the rats into the 6 groups
Random assignment.

Your turn, guided

Your turn: 3 temperatures × 4 times. Number of treatments.

1212
3 × 4.

Practice ★

  1. Why are 196 subjects assigned to the treatments at random?
    1. To balance other variables between the groups, so differences can be blamed on the treatment
    2. So the results apply to the whole population
    3. To give every subject the same chance of being in the study
  1. An experiment tests 2 fertilizer types at 5 watering levels, with every combination used. How many treatments are there?
  2. An experiment tests 3 fertilizer types at 4 watering levels, with every combination used. How many treatments are there?

Watch out!

Practice ★★

  1. A test of two diets on 115 adults first splits them into men and women, then randomizes diets within each group. What is this design?
    1. A randomized block design, blocking by sex
    2. A stratified random sample
    3. A completely randomized design

Exit ticket

Three questions to check you have got it.

  1. An experiment tests 2 fertilizer types at 5 watering levels, with every combination used. How many treatments are there?
  2. An experiment tests 3 fertilizer types at 4 watering levels, with every combination used. How many treatments are there?
  3. An experiment tests 4 fertilizer types at 4 watering levels, with every combination used. How many treatments are there?

Summary card

Experimental design

Compare · randomize · replicate · block. Treatments = combinations of factor levels.

Watch out: blocks (experiments) vs strata (samples).

End of the lesson

Next lesson: z-scores and the normal model Back to the chapter

Answers: Designing experiments: randomization, replication, blocking

A

  1. To balance other variables between the groups, so differences can be blamed on the treatment

B

  1. 1010
  2. 1212

C

  1. A randomized block design, blocking by sex

D

  1. 1010
  2. 1212
  3. 1616

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