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 –
Control of as many aspects of the experiment as possible
Randomization of experimental units into treatments
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 :
Example – Roses
We 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.
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.
36 Rose Plants Group1: Regular soil Group2: Competitor’s soil Group3: New soil Randomize Measure the size and health of the roses
Example – 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
36 Rose Plants Randomize 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; Blocking
We may want to compare 2 different types of roses
We must block the plants into two groups first then randomize into treatments
36 Rose Plants Randomize 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 soil Randomize Block 18 Type 1 Roses 18 Type 2 Roses