Chapter 1: The Nature of Statistics

1.5Experimental Designs

Observational Studies & Designed Experiments

• Purpose of a study is to investigate whether a relationship exists between two characteristics

• Essential to distinguish between two types of procedures: observational studies and designed experiments

Observational Study

• Researchers observe characteristics and take measurements

• i.e. A sample survey

• Reveals causation

Designed Experiment

• Researchers impose treatments and controls and then observe characteristics and take measurements

• Can reveal only association

Principles of Experimental Design• Following principles allow a researcher to conclude

that differences in the results of an experiment not reasonably attributable to chance are likely caused by the treatments

• Control– Some method should be used to control for effects due to

factors other than the ones of primary interest• Randomization– Subjects should be randomly divided into groups to avoid

unintentional selection bias in constituting the groups (make groups as similar as possible)

• Replication– A sufficient number of subjects should be used to ensure

that randomization creates groups that resemble each other closely and to increase the chances of detecting differences among the treatments when such differences actually exist

Important method of control is to compare several treatments

• Placebo– Involved in one of the most common experimental

situations– An inert or innocuous medical substance

• Treatment group– Receives the specified treatment

• Control group– Receives the placebo

Experimental Units

• The individuals or items on which the experiment is performed in a designed experiment

• “Subject”– When the units are human beings

Other definitions…

• Response variable– Focus of a question in a study or experiment

• Factor– explanatory variable manipulated by the experimenter– Each factor can have different levels, called treatments

Example 1.12• The Golden Torch Cactus, a columnar cactus native to

Argentina, has excellent landscape potential. William Feldman and Frank Crosswhite, two researchers at the Boyce Thompson Southwestern Arboretum, conducted a thorough investigation of the optimal method for producing these cacti. The researchers examined, among other things, the effects of a hydrophilic polymer and irrigation regime on weight gain. Hydrophilic polymers are used as soil additives to keep moisture in the root zone. For this study, the researchers chose Broadlead P-4 polyacrylamide, abbreviated P4. The hydrophilic polymer was either used or not used, and five irrigation regimes were employed: none, light, medium, heavy, and very heavy.

• Identify the:– Experimental units

– Response variable

Example 1.12• The Golden Torch Cactus, a columnar cactus native to

Argentina, has excellent landscape potential. William Feldman and Frank Crosswhite, two researchers at the Boyce Thompson Southwestern Arboretum, conducted a thorough investigation of the optimal method for producing these cacti. The researchers examined, among other things, the effects of a hydrophilic polymer and irrigation regime on weight gain. Hydrophilic polymers are used as soil additives to keep moisture in the root zone. For this study, the researchers chose Broadlead P-4 polyacrylamide, abbreviated P4. The hydrophilic polymer was either used or not used, and five irrigation regimes were employed: none, light, medium, heavy, and very heavy.

• Identify the:– Factors

– Levels of each factor

Example 1.12• The Golden Torch Cactus, a columnar cactus native to

Argentina, has excellent landscape potential. William Feldman and Frank Crosswhite, two researchers at the Boyce Thompson Southwestern Arboretum, conducted a thorough investigation of the optimal method for producing these cacti. The researchers examined, among other things, the effects of a hydrophilic polymer and irrigation regime on weight gain. Hydrophilic polymers are used as soil additives to keep moisture in the root zone. For this study, the researchers chose Broadlead P-4 polyacrylamide, abbreviated P4. The hydrophilic polymer was either used or not used, and five irrigation regimes were employed: none, light, medium, heavy, and very heavy.

• Identify the:– treatments

Example 1.12None Light Medium Heavy Very heavy

No P4 No waterNo P4

Light waterNo P4

Medium waterNo P4

Heavy waterNo P4

Very heavy waterNo P4

With P4 No waterWith P4

Light waterWith P4

Medium waterWith P4

Heavy waterWith P4

Very heavy waterWith P4

Definitions…• Response variable– The characteristic of the experimental outcome that is to be

measured or observed• Factor– A variable whose effect on the response variable is of

interest in the experiment• Levels– The possible values of a factor

• Treatment– Each experimental condition– For one-factor experiments: treatments are the levels of the

single factor– For multifactor: each treatment is a combination of levels of

the factors

Completely Randomized Design

• All the experimental units are assigned randomly among all the treatments

• Most commonly used and simplest design• Not always the best

• Randomized block design– Experimental units that are similar in ways that are expected

to affect the response variable are grouped in blocks– Random assignment of units to the treatments is made block

to block

Example 1.13

• Suppose that we want to compare the driving distances for five different brands of golf ball. For 40 golfers, discuss a method of comparison based on:

• A. Completely randomized design

• B. Randomized block design

Practice Problems

• P. 29-30

• 1.38-1.53