AP Statistics5.2 Designing Experiments

Design a comparative experiment and a completely randomized experiment

Understand the 3 principles of experimental design

Understand cautions about experimentation

Learning Objective:

experimental units – individuals on which the experiment is done

subjects – human experimental units

treatment – specific experimental condition applied to the units

Definitions

explanatory variable – attempts to explain the observed response

response variable – measures an outcome of the experiment

  factors – explanatory variables in an

experiment

level – specific value of a factor

placebo – “dummy” treatment/no treatment; e.g. getting sugar pill instead of actual medicine

control group – group that receives the dummy treatment

bias – systematically favoring certain outcomes

randomization – use of chance to divide experimental units into groups

statistically significant – an observed effect so large that it would rarely occur by chance

placebo effect – subjects respond favorably to getting any treatment – response to dummy treatment

Answer: The liners are the experimental units. The heat applied to the liners is the factor; the levels are 250F, 275F, 300F, and 325F. The force required to open the package is the response variable.

Example : 5.27 p. 268

The experimental units are the batches of the product; the yield of each batch is the response variable.

There are two factors: temperature (with 2 levels) and stirring rates (with 3 levels), for a total of 6 treatments.

 

Since two experimental units will be used for each of the 6 treatments, we need 12.

 

Example: 5.29 p. 268

60 rpm 90 rpm 120 rpm

50 degrees 1 2 3

60 degrees 4 5 6

treatment observe response

***problems with lurking variables (such as

the placebo effect) since there is no control group to establish a “baseline” measurement***

Simple Experiment

*****problems with bias in assigning individuals to treatment groups; e.g. put all of the more sickly patients in the control group so the treatment group looks better*****

Comparative Experiment

Randomized Comparative Experiment

Control the effects of lurking variables (use a control group)

Randomization – randomly allocate units to treatment groups (so you’re not “stacking the deck” in favor of one particular treatment)

Replication – take a large enough group size so that you can see the results repeatedly (this reduces the chance variation in the results; therefore, results are more likely to be statistically significant)

Principles of Experimental Design

How much difference in the responses of the control and treatment groups is enough to be convincing that the treatment really works? Experiments give good evidence to establish cause-and-effect, but the outcomes of randomized experiments do depend on chance. We cannot say that any difference in responses is due to the treatment. Some differences in response would appear even if we used the same treatment on all subjects, because everyone is not exactly the same. By randomly assigning subjects to groups, we eliminate the possibility of systematic differences between the groups, but there will still be chance variation. It is through statistical inference, using the laws of probability, that we decide whether the observed difference in responses between the control and treatment groups is too large to occur as a result of chance alone. This is called statistical significance.

Statistical Significance

Lack of blindness – If the experimenter assessing the responses

to treatments knows which treatment was given, he/she may bias the results (consciously or unconsciously); if a subject knows that they got the placebo treatment, they may under-report their response

Lack of realism – subjects or treatments or setting of an experiment may not realistically duplicate the conditions we want to study

Cautions about Experimentation

Answer: Because the experimenter knew which subjects had learned the meditation techniques, he (or she) may have had some expectations about the outcome of the experiment: if the experimenter believed that meditation was beneficial, he may subconsciously rate that group as being less anxious.

Example: 5.38 p. 279

Double-blind – neither the subjects nor the people (evaluators) measuring the response to treatments knows which treatment the subject got; helps eliminate bias

 

Other Experimental Designs

choose blocks of two units that are as closely alike as possible and randomly select which one receives the treatment OR one subject/unit who receives two treatments in random order (a person serves as their own control)

Matched Pairs Design

Each subject is exposed to both treatments

Paired Design

Block design – units are separated in to blocks (groups of units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments, e.g. blocking by gender or race); random assignment of units to treatments is carried out separately within each block