STATISTICAL APPROACHES IN EXCELLENT RESEARCH METHODS is the 2019 Award Winning Book in Science/Nature/Environmental category in the just concluded 2019 NEXT GENERATION INDIE BOOK AWARDS that is sponsored by the INDEPENDENT BOOK PUBLISHING PROFESSIONALS GROUP in the United States.
This leading-edge book is an indispensable practical guide to the successful execution of research with particular attention to data analysis to arrive at indisputable findings, conclusions, and generalizations. Studying this book guarantees mastery knowledge for personally applying the most appropriate statistical tests accurately, swiftly, effortlessly and pleasurably in situations of data analysis. Statistical Approaches in Excellent Research Methods is a most clearly written modern and practical book with simple, direct, easy-to-understand and highly motivating information. It is a fresh approach to the teaching, learning and application of statistics as an exciting field that has very central and robust place in research in particular, and in virtually all spheres of human endeavor.
While Chapter 1 is an exploration of the fundamental concepts in inferential statistics, Chapter 2 presents all about descriptive statistics. Each of the inferential statistical tests that research could require is lucidly explained with its rationale, application and interpretation in Chapters 3 to 8. Information and Communication Technology (ICT) has so revolutionized all spheres of human endeavor to the extent that its effective and efficient use or otherwise in any area is synonymous with the success or failure, respectively, of that field. Chapters 9 to 12 are therefore dedicated exclusively to use of ICT in statistical analysis to ensure that every user of this book can personally apply IBM SPSS(R) Statistics skilfully and correctly in analysing all sorts of research data. Get a copy straightaway.
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Peter James Kpolovie is a professor of educational measurement and evaluation at the University of Port Harcourt. He is the Director of Academic Planning, Research and Control; and the former Head of Department of Educational Psychology, Guidance and Counselling at the University. His Ph.D. dissertation won National Universities Commission's Best Doctoral Thesis Award in 2002, and has been decorated with other awards of academic excellence. He also distinguished himself as an excellent administrator with his successful service in the Executive Council of Bayelsa State Government from 2003 to 2006, a period that the State recorded unparalleled infrastructural development. He authored innovative books that include, Excellent Research Methods (2016); Handbook of Research on Enhancing Teacher Education with Advanced Instructional Technologies (2015); and Educational Management in Developing Economies (2012) which are readily available online. His other great books are The Making of the United States of America: Lessons for Nigeria (2013); Test, Measurement and Evaluation in Education (2014); Educational Reforms without Evaluation Designs: Nigeria at risk (2012); Statistical Techniques for Advanced Research (2011); and Advanced Research Methods (2010). He has published over 150 journal articles. He can be reached through his Website, www.kpoloviepj.com or with the number, +2348137158851 or via E-mail, kpolovie@gmail.com.
PREFACE, xvii,
Chapter 1 FUNDAMENTAL CONCEPTS IN INFERENTIAL STATISTICS, 1,
Chapter 2 DESCRIPTIVE STATISTICS, 53,
Chapter 3 COMPARISON OF TWO MEANS WITH Z-TEST AND T-TEST, 118,
Chapter 4 COMPARISON OF MEANS WITH ANALYSIS OF VARIANCE (ANOVA), 165,
Chapter 5 COMPARISON OF MEANS WITH TWO-WAY ANALYSIS OF VARIANCE, 201,
Chapter 6 HYPOTHESIS TESTING WITH ANALYSIS OF COVARIANCE, 232,
Chapter 7 CORRELATION, 250,
Chapter 8 SIMPLE REGRESSION, 287,
Chapter 9 INFORMATION AND COMMUNICATION TECHNOLOGY IN DATA ANALYSES: IBM SPSS® STATISTICS IN ACTION, 303,
Chapter 10 CORRELATION AND REGRESSION ANALYSES, USING IBM SPSS® STATISTICS, 361,
Chapter 11 EXECUTION OF ANOVA, TWO-WAY ANOVA AND ANCOVA WITH IBM SPSS® STATISTICS, 407,
Chapter 12 NONPARAMETRIC STATISTICS WITH IBM SPSS® STATISTICS, 445,
REFERENCES, 490,
APPENDICES,
APPENDIX A Ten thousand random digits, 503,
APPENDIX B Areas of the normal curve, 507,
APPENDIX C Critical values for Student's t-distribution, 509,
APPENDIX D Critical values for the F-distribution, 510,
APPENDIX E Critical values for the studentized range a = 0.05, 524,
APPENDIX F Critical values for correlation coefficients, 526,
SUBJECT INDEX, 527,
FUNDAMENTAL CONCEPTS IN INFERENTIAL STATISTICS
Inferential statistics is the nucleus around which quantitative empirical research revolves (Kpolovie, 2011). There are specific definitions for terms that are crucial to statistical inference in this chapter. Such fundamental concepts that underlie research are examined here so that the application of different inferential statistical techniques will better be understood and learned with the greatest ease. Examples of the concepts include inferential statistics, population and sample, hypothesis, central limit theorem, normal curve, the level of significance, decision errors and two-tailed cum one-tailed tests.
INFERENTIAL STATISTICS
Inferential statistics is the science of using measurements of a sample to make dependable generalizations about important aspects of the measurement of a population. While a measure based on the observation of sample characteristics is called statistic and is usually symbolized with Roman alphabet like X with a bar (X) and S; a corresponding measure on the basis of a population characteristics is termed parameter and is usually symbolized with Greek alphabet such as ^ and a for mean and standard deviation, respectively (Kpolovie, 2014). Inferential statistics is employed for drawing of reasonable conclusions about the large group, called population by collecting and studying a portion of the population, called sample (Kpolovie, 2016). Unlike descriptive statistics that is concerned with collecting and describing data on only the observed individuals or events, inferential statistics is used for drawing of tentatively acceptable conclusions deductively about an entire population that may be infinite on the basis of data collected from a representative sample of that population. In other words, statistical inference refers to the conclusions drawn about a population, based on the information in a representative sample from the population. Thus, representative sample is a sine qua non criterion of inferential statistics because the accuracy of statistical inference can only be ensured or guaranteed when the data are drawn randomly from the population under investigation in such a meticulous way that every segment of the population is adequately and proportionally represented without bias in the sample (Cohen, 2008; Howell, 2002; McQueen and Knussen, 2006; Keller and Warrack, 2003; Aczel, 1999; Meltzoff, 2007; Crowl, 1996; Best, 1981; Blaxer, 2009; Kvanli, Pavur and Guynes, 2000; Bowerman, O'Connell and Hand, 2001; Breakwell, Hammond and Fife-Schaw, 2001 and Frank and Althoen, 1994).
The use of inferential statistics is of absolute importance in the social or behavioural sciences that deal with human beings who are composed of very complex interaction of emotions, motivations (intrinsic and extrinsic), learned behaviours and genetically determined actions to the extent that one cannot even be sure that the same individual will always behave in the same way (Kpolovie, 2016b). Under such circumstance, the exact situation about an entire population with respect to a variable of interest cannot be known ordinarily without quantitative, empirical and inferential investigations. It is even more so with the fact that humans are characterized by a great deal of imperfectly remembered experiences. It is only with research that adopts inferential statistics that data-based credible information about the actual situation of any variable in the whole population can be validly known. With inferential statistics, a manageable sample that is truly representative of the population is thoroughly studied with regard to a given variable; and whether or not a significant difference or relationship exists in both the sample and population is mathematically determined. The probability or likelihood that conclusions about the requisite characteristics of the sample are validly applicable to the population is only determinable with inferential statistics. In other words, inferential statistics employs inferential tests for determination of the level of confidence that can be placed in the results of the sample data, if the study had covered the population. In most cases, such statistical tests use a probability of or less than 0.05 (5 out of 100) or 0.01 (1 out of 100) to show that the apparent difference or relationship in the sample data is due merely to chance alone or purely to the manipulation or condition of the independent variable (Furr & Bacharach, 2014; Groth-Marnat & Wright, 2016; Cohen, Swerdlik & Sturman, 2013).
Inferential statistics can be satisfactorily defined as the entire body of quantitative techniques that enable the researcher to make appropriate generalizations from limited observations of a randomly drawn sample to the totality of the particular population from which the sample was taken. Research entails far more than collection, organization and quantitative description of data as presented in Chapter 2 to center on explanation, control, prediction and generalization (Kpolovie, 2011b; 2012). Research is more concerned with or places much greater emphasis on statistical inference than mathematical description because it is only with the statistical inference that conclusions, far-reaching interpretations, explanations, predictions, generalizations and control of phenomena for the satisfaction of human needs are done.
All the inferences about the population are from a representative sample, drawn randomly. But in spite of the randomization, a sample does not reflect characteristics of the parent population completely or with absolute fidelity because the characteristics of another similarly drawn sample from the population might not be perfectly the same with those of the first. Since the sample from which inferences are made about the population is usually not a perfect carbon copy of the population, the statistical techniques that are appropriate for data description are insufficient for the crucial task of making inferences about the population. Therefore, the leap of drawing inferences from sample to its population crosses the chasm...
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