# The Principles of Experimental Research

**By**

- K Srinagesh, Professor, Mechanical Engineering, University of Massachusetts, Dartmouth

The need to understand how to design and set up an investigative experiment is nearly universal to all students in engineering, applied technology and science, as well as many of the social sciences. Many schools offer courses in this fundamental skill and this book is meant to offer an easily accessible introduction to the essential tools needed, including an understanding of logical processes, how to use measurement, the doâ€™s and donâ€™ts of designing experiments so as to achieve reproducible results and the basic mathematical underpinnings of how data should be analyzed and interpreted. The subject is also taught as part of courses on Engineering statistics, Quality Control in Manufacturing, and Senior Design Project, in which conducting experimental research is usually integral to the project in question.

View full description### Audience

Undergraduate and first-year graduate students in most engineering disciplines taking required or optional course in â€śDesign of Experiments,â€ť â€śSenior Design Project,â€ť â€śCapstone Design Project,â€ť â€śEngineering Statistics,â€ť and other course related to experimental research, data analysis and statistical inference.

### Book information

- Published: December 2005
- Imprint: BUTTERWORTH HEINEMANN
- ISBN: 978-0-7506-7926-8

### Table of Contents

**1 Experimental Research in Science: Its Name and Nature**1.1 Defining Science 1.2 Science: Play or Profession 1.3 Science and Research 1.4 Varieties of Experimental Research 1.5 Conventional Researchers 1.6 Bibliography

**2 The Importance of Definitions**2.1 Toward Definition 2.2 Defining "Definition"2.3 Common Terms Used in Definitions 2.4 Varieties of Definitions 2.4.1 A. Direct and B. Indirect Definitions 2.4.2 C. Informal and D. Formal Definitions 2.4.3 E. Lexical and F. Stipulated Definitions 2.4.4 G. Nominal and H. Real Definitions 2.4.5 J. Definitions by Denotation2.4.6 K. Ostensive Definitions 2.4.7 L. Definitions by Genus and Difference 2.5 Need for Definitions 2.6 What Definitions Should and Should Not Do 2.7 References 2.8 Bibliography

**3 Aspects of Quantification**3.1 Quantity and Quality 3.2 The Uses of Numbers 3.3 An Intellectual Close-up of Counting 3.4 The Process of Measurement 3.5 Quantities and Measurements 3.6 Derived Quantities 3.7 Units for Measurement 3.8 Fundamental Quantities and Dimensions 3.9 Dimensional Analysis 3.10 Accuracy versus Approximation 3.11 Bibliography

**4 The Purpose and Principles Involved in Experimenting**4.1 The Purpose of Experimenting 4.2 Cause and Effect 4.3 Pertinence and Forms of Cause 4.4 Millâ€™s Methods of Experimental Inquiry 4.4.1 Method of Agreement 4.4.2 Method of Difference 4.4.3 Joint Methods of Agreement and Difference 4.4.4 Method of Residue 4.4.5 Method of Concomitant Variation4.5 Planning for the Experiment 4.6 Standardization of Test Material(s) 4.7 Reproducibility 4.8 Number of "Experiments"4.9 References 4.10 Bibliography

__Part II: Planning the Experiments__**5 Defining the Problem for Experimental Research**5.1 To Define a Problem 5.2 Relation of the Problem to Resources 5.3 Relevance of the Problem 5.4 Extent of the Problem 5.5 Problem: Qualitative or Quantitative? 5.6 Can the Problem Be Reshaped? 5.7 Proverbs on Problems 5.8 At the beginning 5.9 In Progress 5.10 At the End 5.11 References 5.12 Bibliography

**6 Stating the Problem as a Hypothesis**6.1 The Place of Hypothesis in Research 6.2 Desirable Qualities of Hypotheses 6.3 Bibliography

**7 Designing Experiments to Suit Problems**7.1 Several Problems, Several Causes 7.2 Treatment Structures 7.2.1 Placebo 7.2.2 Standard Treatment 7.2.3 â€śSubject-and-Controlâ€ť Group Treatment 7.2.4 Paired Comparison Treatment 7.2.5 Varying the Amount of One of the Two Factors 7.3 Many Factors at Many Levels, but One Factor at a Time 7.4 Factorial Design, the Right Way 7.5 Too Many Factors on Hand? 7.6 "Subjects-and-Controls" Experiments 7.6.1 Varieties within Subjects and Controls: Paired ComparisonDesign 7.6.2 Experiments with Humans 7.7 Combined Effect of Many Causes 7.8 Unavoidable (â€śNuisanceâ€ť) Factors 7.9 Bibliography

**8 Dealing with Factors**8.1 Designing Factors 8.2 Experiments with Designed Factors 8.3 Matrix of Factors 8.3.1 More Than Three Factors 8.4 Remarks on Experiments with Two-Level Factors 8.5 Response of Multifactor Experiments 8.6 Experiments with More Factors, Each at Two Levels 8.7 Fractional Factorials 8.8 Varieties of Factors 8.8.1 Quantitative versus Qualitative Factors 8.8.2 Random versus Fixed Factors 8.8.3 Constant and Phantom Factors 8.8.4 Treatment and Trial Factor 8.8.5 Blocking and Group Factors 8.8.6 Unit Factor 8.9 Levels of Factors 8.9.1 Levels of Quantitative Factors 8.9.2 Levels of Qualitative Factors 8.10 Bibliography

**9 Factors at More Than Two Levels**9.1 Limitations of Experiments with Factors at Two Levels 9.2 Four-Level Factorial Experiments 9.2.1 Main Effects and Interactions 9.3 Interactions 9.4 Main Effects 9.5 More on Interactions 9.6 More Factors at More Than Two Levels 9.6.1 Fractional Factorial with Three-Level Factors 9.7 Bibliography

__Part III: The Craft Part of Experimental Research__**10 Searching through Published Literature**10.1 Researcher and Scholar 10.2 Literature in Print 10.3 Overdoing? 10.4 After the Climb 10.5 Bibliography

**11 Building the Experimental Setup**11.1 Diversity to Match the Need 11.2 Designing the Apparatus 11.2.1 Seeking Advice 11.3 Simplicity, Compactness, and Elegance 11.4 Measuring Instruments 11.5 Calibration 11.6 Researcher as Handyman 11.7 Cost Considerations 11.8 Bibliography

__Part IV: The Art of Reasoning in Scientific Research__**12 Logic and Scientific Research**12.1 The Subject, Logic 12.2 Some Terms in Logic 12.3 Induction versus Deduction 12.4 References 12.5 Bibliography

**13 Inferential Logic for Experimental Research**13.1 Inferential Logic and Experimental Research 13.2 Logical Fallacies 13.2.1 Fallacies of Ambiguity 13.2.2 Fallacies of Irrelevance 13.3 Argument 13.3.1 Categorical Propositions 13.3.2 Forms of Categorical Propositions 13.3.3 Conventions, Symbolism, and Relations among CategoricalPropositions 13.4 Diagrammatic Representation of [AQ: Categorical?]Propositions 13.5 Categorical Syllogisms 13.5.1 Structures of Syllogisms 13.5.2 Validity of Syllogisms 13.5.3 Venn Diagrams for Testing Syllogisms 13.6 Ordinary Language and Arguments 13.7 References 13.8 Bibliography

**14 Use of Symbolic Logic**14.1 The Need for Symbolic Logic 14.2 Symbols in Place of Words 14.3 Conjunction 14.4 Truth Tables 14.5 Disjunction 14.6 Negation 14.7 Conditional Statements 14.8 Material Implication 14.9 Punctuation in Symbolic Logic 14.10 Equivalence: "Material" and "Logical" 14.10.2 Logical Equivalence 14.11 Application of Symbolic Logic 14.11.1 Ordinary Language to Symbolic Language 14.12 Validity of Arguments 14.13 Reference 14.14 Bibliography

__Part V: Probability and Statistics for Experimental Research__**15 Introduction to Probability and Statistics**15.1 Relevance of Probability and Statistics in Experimental Research 15.2 Defining the Terms: Probability and Statistics 15.2.1 Probability 15.2.2 Statistics15.3 Relation between Probability and Statistics 15.4 Philosophy of Probability 15.5 Logic of Probability and Statistics 15.6 Quantitative Probability 15.6.1 Relative Frequency Theory 15.7 Nature of Statistics 15.8 Measures of Central Tendency (Average) 15.8.1 Arithmetic Average (Sample Mean) 15.8.2 Weighted Mean 15.8.3 Median 15.8.4 Mode 15.9 Measures of Dispersion 15.9.1 Range 15.9.2 Mean Deviation 15.9.3 Coefficient of Dispersion 15.9.4 Standard Deviation 15.10 Tabular Presentations of Statistical Data 15.11 Grouping the Data 15.12 Graphical Presentations of Data 15.12.1 Histogram 15.12.2 Frequency Polygon 15.12.3 Cumulative Frequency Distribution 15.13 Normal Distribution Curve 15.14 Frequency Distributions That Are Not Normal 15.15 References 15.16 Bibliography

**16 Randomization, Replication, and Sampling**16.1 Need for Randomization 16.2 Applications of Randomization 16.3 Methods of Randomization 16.4 Meaning of Randomization 16.5 Replication 16.6 Samples and Sampling 16.7 Notions of Set 16.8 Permutations and Combinations 16.8.1 Permutations 16.8.2 Combinations 16.9 Quantitative Statement of Randomization 16.10 Sampling Methods 16.10.1 Simple Random Sampling 16.10.2 Cluster Sampling 16.10.3 Stratified Sampling 16.10.4 Systematic Sampling 16.10.5 Multistage Sampling 16.11 Bibliography

**17 Further Significance of Samples**17.1 Inference from Samples 17.2 Theoretical Sampling Distribution of X 17.3 Central Limit Theorem 17.4 Standard Normal Distribution 17.5 Frequency Distribution and Probability Function 17.6 Standard Normal Curve 17.7 Questions/Answers Using the APSND Table 17.8 Bibliography

**18 Planning the Experiments in Statistical Terms**18.1 Guiding Principles 18.2 Some Preliminaries for Planned Experiments 18.2.1 Sample Size 18.2.2 Minimum Acceptable Improvement 18.3 Null and Alternate Hypotheses 18.3.1 Null Hypothesis in an Experiment 18.3.2 Alternate Hypothesis 18.3.3 Risks Involved: a and b Errors 18.3.4 Sample Mean X: Its Role in the Design 18.3.5 Hypotheses Based on Other Parameters 18.4 Accepting (or Rejecting) Hypotheses: Objective Criteria 18.5 Procedures for Planning the Experiments 18.5.1 Criterion Values 18.6 Other Situation Sets 18.7 Operating Characteristic Curve 18.8 Sequential Experimenting 18.9 Concluding Remarks on the Procedures 18.10 Bibliography

**19 Statistical Inference from Experimental Data**19.1 The Way to Inference 19.2 Estimation (From Sample Mean to Population Mean) 19.2.1 Interval Estimation 19.2.2 Variations in Confidence Interval 19.2.3 Interval Estimation of Other Parameters 19.3 Testing of Hypothesis 19.4 Regression and Correlation 19.4.1 Regression Analysis 19.4.2 Measuring the Goodness of Regression 19.4.3 Correlation Coefficient 19.5 Multiple Regression 19.6 Bibliography