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Chapter 1 Section 5. The Design of Experiments. 1. 2. 3. 4. Chapter 1 – Section 5. Learning objectives Define designed experiment Understand the steps in designing an experiment Understand the completely randomized design Understand the matched-pairs design. 2. 3. 4. 1.

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Chapter 1 Section 5

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Chapter 1 section 5

Chapter 1Section 5

The Design of

Experiments


Chapter 1 section 51

1

2

3

4

Chapter 1 – Section 5

  • Learning objectives

    • Define designed experiment

    • Understand the steps in designing an experiment

    • Understand the completely randomized design

    • Understand the matched-pairs design


Chapter 1 section 52

2

3

4

1

Chapter 1 – Section 5

  • Learning objectives

    • Define designed experiment

    • Understand the steps in designing an experiment

    • Understand the completely randomized design

    • Understand the matched-pairs design


Chapter 1 section 53

Chapter 1 – Section 5

  • Data can be collected in two main ways

    • Through sample surveys

    • Through designed experiments

  • Sample surveys lead to observational studies

  • Designed experiments enable researchers to control variables, leading to additional conclusions


Chapter 1 section 54

Chapter 1 – Section 5

  • A designedexperiment is a controlled study

  • The purpose of designed experiments is to control as many factors as possible to isolate the effects of a particular factor

  • Designed experiments must be carefully set up to achieve their purposes


Chapter 1 section 55

Chapter 1 – Section 5

  • Some variables in a designed experiment are controlled, those are the explanatoryvariables

  • These variables are also sometimes called the factors

  • Factors

    • Are part of a controlled environment

    • Has values that can be changed by the researcher

    • Are considered as possible causes


Chapter 1 section 56

Chapter 1 – Section 5

  • Examples of factors are

    • The dosage of a drug in a medical experiment

    • The type of teaching method in an education experiment

    • One drug by itself compared to that drug used in conjunction with another


Chapter 1 section 57

Chapter 1 – Section 5

  • The designed experiment analyzes the affects of the factors on the responsevariable

  • Response variables

    • Are not part of a controlled environment

    • Has values that are measured by the researcher

    • Measure the effects


Chapter 1 section 58

Chapter 1 – Section 5

  • Examples of response variables are

    • The blood pressures of the patients

    • The test scores for a class

    • The sizes of a cancerous tumor for patients


Chapter 1 section 59

Chapter 1 – Section 5

  • A treatment is a combination of the values of the factors

  • Examples of treatments

    • Giving one medication to one group of patients and a different medication to another

    • Using one type of fertilizer on a set of plots of corn and a different type of fertilizer on a different set of plots

    • Playing country music to one group of mice and rap music to another


Chapter 1 section 510

Chapter 1 – Section 5

  • The treatment is applied to experimentalunits (people, plants, materials, other objects, …)

  • When the experimental units are people, we refer to them as subjects

  • Subjects in an experiment correspond to individuals in a survey


Chapter 1 section 511

Chapter 1 – Section 5

  • An example of a designed experiment is to determine whether a new drug, Drug N, is more effective at treating high blood pressure than the existing drug, Drug E

  • Patients with high blood pressure are given either Drug N or Drug E

  • The blood pressures are measured one month later


Chapter 1 section 512

Chapter 1 – Section 5

  • For this experiment

    • Factor – the type of drug

    • Response variable – blood pressure

    • Treatment – given Drug N or Drug E

    • Experimental units / subjects – the patients

  • For this experiment

    • Factor – the type of drug

    • Response variable – blood pressure

    • Treatment – given Drug N or Drug E

    • Experimental units / subjects – the patients

  • If patients given Drug N have significantly lower blood pressures than patients given Drug E, we would wish to conclude that Drug N is more effective


Chapter 1 section 513

Chapter 1 – Section 5

  • Changes in behavior of subjects

  • Changes in behavior of subjects

  • For an experiment comparing a new drug to no treatment at all

    • If the subject knows that he or she is given a drug, he or she may feel better (the placebo effect)

  • Changes in behavior of subjects

  • For an experiment comparing a new drug to no treatment at all

    • If the subject knows that he or she is given a drug, he or she may feel better (the placebo effect)

  • For an experiment comparing a new drug to an existing drug

    • If the subject knows which drug he or she is given, that may change his or her behavior


Chapter 1 section 514

Chapter 1 – Section 5

  • To avoid the effects of subject behavior

    • Subjects not given any medication are often given a placebo such as a sugar tablet

    • The subjects will not know which treatment they get

  • To avoid the effects of subject behavior

    • Subjects not given any medication are often given a placebo such as a sugar tablet

    • The subjects will not know which treatment they get

  • To avoid the effects of researcher behavior

    • The researchers are not told which drug they are administering

  • To avoid the effects of subject behavior

    • Subjects not given any medication are often given a placebo such as a sugar tablet

    • The subjects will not know which treatment they get

  • To avoid the effects of researcher behavior

    • The researchers are not told which drug they are administering

  • When both the subjects and the researchers do not know which treatment, this is called double-blind


Chapter 1 section 515

3

4

1

2

Chapter 1 – Section 5

  • Learning objectives

    • Define designed experiment

    • Understand the steps in designing an experiment

    • Understand the completely randomized design

    • Understand the matched-pairs design


Chapter 1 section 516

Chapter 1 – Section 5

  • Conducting an experiment involves considerable planning

  • Conducting an experiment involves considerable planning

  • Planning steps

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

    • Determine the number of experimental units

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

    • Determine the number of experimental units

    • Determine the level of each factor

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

    • Determine the number of experimental units

    • Determine the level of each factor

  • Implementation steps

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

    • Determine the number of experimental units

    • Determine the level of each factor

  • Implementation steps

    • Conduct the experiment

  • Conducting an experiment involves considerable planning

  • Planning steps

    • Identify the problem

    • Determine the factors

    • Determine the number of experimental units

    • Determine the level of each factor

  • Implementation steps

    • Conduct the experiment

    • Test the claim


Chapter 1 section 517

Chapter 1 – Section 5

  • Identify the problem

  • The first step in planning an experiment (or in most any project at all) is to identify the problem

  • The identification would include

    • The general purpose of the experiment

    • The response variable

    • The population

  • This is also referred to as the claim


Chapter 1 section 518

Chapter 1 – Section 5

  • Determine the factors

  • The second step in planning an experiment is to determine the factors to be studied

  • The factors could be identified

    • By subject matter experts

    • By the purpose of the experiment

    • Using results from previous studies

  • Factors must be identified as either fixed, controlled, or uncontrolled


Chapter 1 section 519

Chapter 1 – Section 5

  • Determine the number of experimental units

  • In general, the more the experiment units, the more effective the experiment

  • The number of experimental units

    • Could be limited by time

    • Could be limited by money

  • There are techniques to calculate the number of experimental units (to be covered later)


Chapter 1 section 520

  • Determine the level of each factor

  • Three ways to deal with the factors

    • Control – fix the levels at a constant level (for factors not of interest)

  • Determine the level of each factor

  • Three ways to deal with the factors

    • Control – fix the levels at a constant level (for factors not of interest)

    • Manipulate – set the levels at predetermined levels (for factors of interest)

  • Determine the level of each factor

  • Three ways to deal with the factors

    • Control – fix the levels at a constant level (for factors not of interest)

    • Manipulate – set the levels at predetermined levels (for factors of interest)

    • Randomize – randomize the experimental units (for uncontrolled factors not of interest)

  • Determine the level of each factor

  • Three ways to deal with the factors

    • Control – fix the levels at a constant level (for factors not of interest)

    • Manipulate – set the levels at predetermined levels (for factors of interest)

    • Randomize – randomize the experimental units (for uncontrolled factors not of interest)

  • Randomization decreases the effects of uncontrolled factors, even ones not identified

Chapter 1 – Section 5

  • Determine the level of each factor

  • Three ways to deal with the factors


Chapter 1 section 521

Chapter 1 – Section 5

  • Conduct the experiment

  • The subjects are assigned at random to the treatments

    • When a treatment is applied to more than one experimental unit, this is called replication

    • Replication is useful for accuracy, to further decrease the effects of uncontrolled factors

  • Collect and process the data


Chapter 1 section 522

Chapter 1 – Section 5

  • Test the claim

  • This is inferential statistics

  • Techniques of inferential statistics are studied in chapters 9 through 14


Chapter 1 section 523

1

2

4

3

Chapter 1 – Section 5

  • Learning objectives

    • Define designed experiment

    • Understand the steps in designing an experiment

    • Understand the completely randomized design

    • Understand the matched-pairs design


Chapter 1 section 524

Chapter 1 – Section 5

  • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random

  • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random

  • An example

    • A farmer wants to test the effects of a fertilizer

    • We choose a set of plants to receive the treatment

    • We randomly assign plants to receive different levels of fertilizer

  • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random

  • An example

    • A farmer wants to test the effects of a fertilizer

    • We choose a set of plants to receive the treatment

    • We randomly assign plants to receive different levels of fertilizer

  • This has similarities to completely random sampling


Chapter 1 section 525

Chapter 1 – Section 5

  • We control as many factors as we can

    • Amount of watering

    • Method of tilling

    • Soil acidity

  • We control as many factors as we can

    • Amount of watering

    • Method of tilling

    • Soil acidity

  • Randomization decreases the effects of uncontrolled factors

    • Rainfall

    • Sunlight

    • Temperature


Chapter 1 section 526

Chapter 1 – Section 5


Chapter 1 section 527

1

2

3

5

4

Chapter 1 – Section 5

  • Learning objectives

    • Define designed experiment

    • Understand the steps in designing an experiment

    • Understand the completely randomized design

    • Understand the matched-pairs design

    • Understand the randomized block design


Chapter 1 section 528

Chapter 1 – Section 5

  • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment

  • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment

  • A matched pair design requires

    • Units that are paired (twins, the same person before and after the treatment, …)

    • Only two levels of treatment (one for each of the pair)

  • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment

  • A matched pair design requires

    • Units that are paired (twins, the same person before and after the treatment, …)

    • Only two levels of treatment (one for each of the pair)

  • An example

    • A subject before receiving the medication

    • The same subject after receiving the medication


Chapter 1 section 529

Chapter 1 – Section 5

  • Test whether students learn better while listening to music or not

    • Match students by IQ and gender (to control those factors)

    • Randomly choose one of each pair (to decrease the effects of other uncontrolled factors

    • Assign that one to a quiet room and the other to a room with music (the treatment)

    • Administer the test and analyze the test scores


Chapter 1 section 530

Chapter 1 – Section 5


Chapter 1 section 531

Chapter 1 – Section 5

  • An example

    • We are testing the effects of treatments A, B, and C on soybean plants

    • Assume that group 1 is treated with A and group 2 is treated with B

    • Assume that Chemgro plants have higher yields than Pioneer plants

    • Assume that group 1 has more Chemgro plants (happens because of randomization) than group 2


Chapter 1 section 532

Chapter 1 – Section 5

  • If group 1 (treatment A) has higher yields than group 2 (treatment B)

    • Is this because treatment A is more effective than B?

    • Is this because there are more Chemgro plants in group 1?

  • If group 1 (treatment A) has higher yields than group 2 (treatment B)

    • Is this because treatment A is more effective than B?

    • Is this because there are more Chemgro plants in group 1?

  • It is not possible to distinguish

    • The effects of Treatment A versus B

    • The effects of Chemgro versus Pioneer

  • If group 1 (treatment A) has higher yields than group 2 (treatment B)

    • Is this because treatment A is more effective than B?

    • Is this because there are more Chemgro plants in group 1?

  • It is not possible to distinguish

    • The effects of Treatment A versus B

    • The effects of Chemgro versus Pioneer

  • When two effects cannot be distinguished, this is called confounding


Summary chapter 1 section 5

Summary: Chapter 1 – Section 5

  • The planning for designed experiments is crucial to the success of the experiment

  • A double-blind implementation of experiments reduces the amount of changes in behavior

  • There are different good methods for assigning treatments to experimental units

    • Completely random

    • Matched-pairs

    • Randomized blocks


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