Experimental Design

Experimental DesignExperimental Design

Experiments – manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels.

 Experimental Units – individuals on which

the experiment is done

Subjects – human experimental units

Factor – a variable whose levels are controlled by the experimenter. Experiments attempt to discover the effects differences in factor levels may have on the responses of the experimental units

Level – the specific values that a factor can have

Treatments – a specific experimental condition that is a combination of levels of each factor

Principals of Experimental Design – 1.Control of as many aspects of the

experiment as possible

2.Randomization of experimental units into treatments

3.Replication over as many experimental units as possible or replication on another sample of the population of interest.

Control Group – experimental unit that is assigned the baseline treatment, be it no treatment, the default treatment, or placebo

Placebo – a treatment known to have no effect, a dummy treatment.

 Blinding – subjects are unaware of what

treatment they are receiving.  Double-Blinding – subjects and

administrators/judges are all unaware of which treatment is being given

Matched pairs – two subjects with equal characteristics are given different treatments and compared together.

 Block – used when groups of experimental

units are similar. Randomization is then used within each block

Confounding – when levels of one factor are associated with the levels of another factor so their effects cannot be separated

The best experiments are usually:RandomizedDouble-blindComparativePlacebo-controlled

Example – RosesExample – RosesWe have developed a new type of potting

soil specifically designed for rose plants.We need to design a completely

randomized experiment to show that the soil does increase the size and health of roses grown in otherwise similar circumstances.

Response Variable: The size and health of the roses grown

Treatments: The factor is soil. We’ll grow roses in three different levels; some with regular soil, some with the leading competitor's soil, and some with the new soil. There are three treatments.

Experimental Units: We’ll obtain 36 rose plants of the same variety from a local grower.

Experimental Design:Control: the roses will be grown near each

other so that they will get similar amounts of sun, rain, and be grown in the same temperature environments. The plants will be weeded and watered the same amount.

Randomness: We will number each plant and using a random number generator we will randomly assign into three groups.

Replicate: There are 12 plants in each treatment.

Experimental Design:

36 Rose Plants

Group1: Regular soil

Group2: Competitor’s soil

Group3: New soil

Ran

dom

ize

Measure the size and health of the roses

Example – 2 Factors; WateringExample – 2 Factors; Watering

From the original we also want to check how watering may effect the size and health of the roses.

We now have 2 factors: soil and amount of water.

For the watering we will let some only get water from nature, the others we will water once a day in the morning.

This creates 6 treatments

Experimental Design:

36 Rose Plants

Ran

dom

ize

Measure the size and health of the roses

Group1: 6 Regular soil, no water

Group2: 6 Regular soil, water

Group3: 6 Competitor’s soil, no water

Group4: 6 Competitor’s soil, water

Group5: 6 new soil, no water

Group6: 6 new soil, water

Example – 1 Factor; BlockingExample – 1 Factor; Blocking

We may want to compare 2 different types of roses

We must block the plants into two groups first then randomize into treatments

Experimental Design:

36 Rose Plants

Ran

dom

ize

Measure the size and health of the roses

Group1: 6 Regular soil

Group4: 6 Regular soil

Group2: 6 Competitor’s soil

Group5: 6 Competitor’s soil

Group3: 6 new soil

Group6: 6 new soilRan

dom

ize

Blo

ck

18 Type 1 Roses

18 Type 2 Roses