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 do’s and don’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.
Covers such essential fundamentals as "definitions," "quantification," and standardization of test materials
Shows students and professionals alike how to plan an experiment—from how to frame a proper Hypothesis to designing an experiment to accurately reflect the nature of the problem to "designing with factors."
Includes a separate section on the use of Statistics in Experimental Research, including overview of probability and statistics, as well as Randomization, Replication and Sampling, as well as proper ways to draw statistical inferences from experimental data.
Undergraduate and first-year graduate students in most engineering disciplines taking required or optional course in “Design of Experiments,” “Senior Design Project,” “Capstone Design Project,” “Engineering Statistics,” and other course related to experimental research, data analysis and statistical inference.
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 Statistics 15.3 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
- No. of pages:
- © Butterworth-Heinemann 2006
- 1st December 2005
- eBook ISBN:
- Hardcover ISBN:
Professor, Mechanical Engineering, University of Massachusetts, Dartmouth