ExperimentImposing treatments on the

subjects in order to compare the results.

Explanatory variables are called factors and specific values of the explanatory variable are levels. These determine the treatments.

The objects on which the treatment is imposed on are called experimental units (human subjects).

Does the type of lighting or the type of music in a dentist’s waiting room have any effect on

the anxiety of a patient?• Types of music:

– pop

– classical

– jazz

• Levels of brightness– low

– medium

– high

• What are the factors?

• What could a possible response variable be?

• How many treatments are there?

• How many levels are there of each factor?

Type of music & Brightness level

3

9

Blood pressure, ...

Does the increase in the explanatory variable CAUSE the increase in the response variable?

YearNumber of Methodist Ministers in New England

Cuban Rum Imported to Boston (in barrels)

1860 63 8,376

1865 48 6,406

1870 53 7,005

1875 64 8,486

1880 72 9,595

1885 80 10,643

1890 85 11,265

1895 76 10,071

1900 80 10,547

1905 83 11,008

1910 105 13,885

1915 140 18,559

1920 175 23,024

1925 183 24,185

1930 192 25,434

1935 221 29,238

1940 262 34,705

The Beauty of ExperimentsJust because two variables have a relationship, that

doesn’t mean one causes the other – there is often a confounding variable at play!

BUT…long term well-designed experiments CAN be used to imply CAUSATION between the explanatory variable and the response variable.

Observational studies/ surveys can NOT!

http://tylervigen.com/

In which option can we conclude that the change in the explanatory variable CAUSES the biggest

change in the response variable?• Option 1: Students choose which group to join

• Option 2: Students are randomly assigned to a group.

• Students in Red Group– Do jumping jacks for two minutes

– Then measure heart rate

• Explanatory variable: type of activity (jogging or jj)

• Response variable: heart rate

Designing Good Experiments • Students in Blue Group

- Jog in place for two minutes- Then measure heart rate

3 Principles of Good Experimental DesignReplication--consistency to many subjects

Randomization--randomly assign subjects to treatment groups

Control/Comparison—having at

least two groups that can be

compared

“Differences in the response variable between groups, if enough to rule out natural chance variability, can then be attributed to the manipulation of the explanatory variable.” This will allow determination of cause and effect.

Ways to Randomize• Each subject draws out

of a bag a colored chip - each treatment is a different color

• Each subject is assigned a number - first set of random numbers produced go to one treatment and the rest to the other

• Each subject rolls a die - odds go to one treatment, evens to the other

• Each subject flips a coin - heads go one treatment, tails to the other

Control group--receives standard/traditional treatment OR no treatment at all OR a

Placebo -receives no active ingredient but subjects believe they are receiving treatment

Single Blind: subjects don’t know which treatment they receive

Double Blind: subjects and evaluators are “blind”; only the researcher has the “key”

Other Experimental Vocabulary

Completely Randomized Design• Randomly assign a treatment to each experimental

unit• The number of units assigned to each treatment is

as equal as possible• Randomization is expected to spread any

differences among units equally across all treatment groups

• Any significant difference in the two groups’ responses can be attributed to treatments used – therefore there are no confounding issues

Is weight training good for children? If so, is it better for them to lift heavy weights for a few repetitions or moderate weights a larger

number of times?

43 volunteers

14--Heavy load group

15--Moderate load group

14--Control group – no weights

Measure and compare muscular strength & endurance

Include: •Subjects•Random assignment•Explanatory(treatments)•Response

Randomly assigned to 3 treatment

groups

Block Designs to Reduce VariabilityBlock Design--divide units into

groups (blocks) in which the units in each block are similar to each other. Within each block randomly assign treatments (do multiple CRDs).

Block if you have reason to believe certain groups will have different results.

Matched-Pair Design—blocking on a unit: randomly assign either two matched units (identical twins) the treatments OR the same individual receives both treatments in random order

Blocking reduces variability.

Randomized Block Design

43 volunteers blocked by age

21-- Children aged 5-10

7--Heavy

22-- Children aged 11-16

Measure & compare between groups

7--Moderate

7--Control

7--Heavy

8--Moderate

7--Control

Measure & compare between groups

Block by age because we believe younger children might have different results than older children

Randomly assigned to 3 groups

Randomly assigned to 3 groups

Matched Pair Design

43 volunteers

21—Heavy load for six weeks, rest two weeks, moderate load for six weeks

22 – Moderate load for six weeks, rest two weeks, heavy load for six weeks

Measure increases in strength & endurance & compare between groups

Randomly assigned to

2 groups

Quitting Smoking w/Nicotine PatchesRecruited 240 smokers (volunteers) at Mayo Clinic

from 3 large cities

Randomly assigned 22-mg nicotine

patch or placebo patch for 8 weeks.

All attended counseling before, during, and after.

Double-blind

After 8-wk (1 yr), 46% (27.5%) of nicotine patch group quit smoking and 20% (14.2%) of placebo group quit.

Quitting Smoking w/Nicotine Patches

• What are the experimental units?

• What are the treatments?

• What was the explanatory variable?

• What was the response variable?

• How was randomization applied?

• How was control applied?

• How was replication applied?

• Is this an experiment or an observational study?

• How would you summarize the results of this experiment?

• 240 volunteers• Patches• Type of patch• Whether or not they quit• Assigned patch

randomly• Placebo patch • About 120 in each group• Experiment

• The nicotine patch worked!

Which type of experiment?

• A baby-food producer claims that her product is superior to that of her leading competitor, in that babies gain weight faster with her product. As an experiment, 30 healthy babies are randomly selected. For two months, 15 are fed her product and 15 are feed the competitor’s product. Each baby’s weight gain (in ounces) was recorded.

• Completely Randomized Design • Randomly assign babies to treatments.

Have 15 red and 15 blue chips in a bag and draw one for each baby. Reds get her product, blues get the competitor’s product.

• Or …Assign each baby a number 01-30. Generate 15 distinct random numbers in this range to get her product. The rest get the competitor’s product.

• Compare the weight gain of the babies after the two month period.

Which type of experiment?

• Is the right hand of right-handed people generally stronger that the left? Paul Murky of Murky Research designs an experiment to test this question. He fastens an ordinary bathroom scale to a shelf five feet from the floor, with the end of the scale projecting out from the shelf. Subjects squeeze the scale between their thumb and their fingers on the top. A scale, which reads in pounds, will be used to measure hand strength.

• Matched Pairs Design

• Randomly assign ½ of the people to test right and then left hand, and the other ½ to test left hand first, and then right hand.

• Make sure the participants cannot read the scale so they don’t influence themselves into trying to “top their score”.

• Compare the differences in hand strength.

Which type of experiment?

• An agronomist wishes to compare the yield of five corn varieties. The field, in which the experiment will be carried out, increases in fertility from north to south.

• Block design• Block the field on

location since fertility increases from north to south. (each color is one block)

• Randomly assign each plot within the block to 1 of the 5 corn varieties (1-5).

• Compare the yield of corn from each of the plots of land.

Randomization in ALL Studies

• In Observational Studies

– Randomize selection of subjects

• In Experiments

– Randomize assignment of treatment

Using Random number table to randomize assigning treatments

• 15487 45195 56420 02314 41265 03798 23185 15770 21468 02172 39741 01468 15647 04841 54970 32670

• Suppose you have 3 treatments for 30 subjects • Option 1: Assign subjects a number and first 10 numbers chosen

get treatment A, second 10 get B and the rest get C.

• Option 2: Assign the treatments a number or range of numbers (A is 1-3, B is 4-6, C is 7-9, ignore 0) and each subject gets the next treatment that comes up. Stop when there are 10 in each treatment group.