Research & the Analysis of Research Hypotheses

TO:

Antonietta Russo who has encouraged me to create this book. Also with thanks to Dorothy Shields and Amita who got me started.

Copyright © 2014 by Kathleen Thomas Allan, Ph.D.. 539756

Library of Congress Control Number: 2014902074

ISBN:   Softcover         978-1-4931-6831-6

              Hardcover       978-1-4931-6830-9

              EBook             978-1-4931-6832-3

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner.

Rev. date: 02/28/2015

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PREFACE

The design of this book owes much to M. David Merrill, Ph.D., who in the 70’s was a professor at Brigham Young University. At the time, he was researching concepts for designing curriculum. He developed a method of designing instructional materials that used the principles of Rule – Example - Practice. The term rule covered such items as a mathematical rule, a classification paradigm, a descriptive category, or other information that gives the students a rule for understanding the main concept being taught. The term example covered the criteria showing how the rule worked. The term practice gave the student a way to perform an exercise, that is, in practicing with other variations of the example to gain experience in using the rule. For Merrill’s principles to be effective, the example must match the practice and the governing rule.

RESEARCH & THE ANALYSIS OF RESEARCH HYPOTHESES has been designed employing Merrill’s theories. The rule is described and defined in the portion of each unit of instruction labeled "

PURPOSE:" T

he example and matching practice are described in the portion labeled "

OBJECTIVES

: The body of the unit describes the rule in more detail giving examples as needed. Finally, there is an assignment" which requires the student to put the rule into practice. The two volumes provide a basis for doing a research study which graduate students can use as a model for their thesis or dissertation. Volume 1 covers basic principles and processes for doing a research study and Volume 2 covers the five major procedures for testing research data: the z-test, the t-test, the Pearson correlation test, the Spearman correlation test and the Chi Square test. Note:

‘Chi’ is pronounced Kai; the ‘Chi-Square’ symbol is: χ²

OUTLINE - VOLUME 1:

PREFACE:

SECTION 1: PRINCIPLES OF RESEARCH.

UNIT 1A: WHAT IS RESEARCH & WHY DO IT?

UNIT 1B: POPULATIONS & SAMPLE SIZES.

UNIT 1C: THE NATURE OF DATA.

UNIT 1D: THE HOW TO OF RESEARCH.

UNIT 1E: STAGES IN THE RESEARCH PROCESS.

SECTION 2: BASIC RESEARCH PROCESSES.

UNIT 2A: THE LITERATURE SEARCH.

UNIT 2B: RESEARCH HYPOTHESES.

UNIT 2C: DATA COLLECTION TECHNIQUES.

UNIT 2D: WRITING A RESEARCH PROPOSAL.

SECTION 3: BASIC CONCEPTS FOR DATA ANALYSIS.

UNIT 3A: PLAN FOR TESTING HYPOTHESES.

UNIT 3B: PROBABILITY AND FREQUENCY DISTRIBUTIONS.

UNIT 3C: PRELIMINARIES FOR TESTING INTERVAL DATA

OUTLINE - VOLUME 2:

SECTION 4: PROCEDURES FOR ANALYZING DATA.

UNIT 4A: FUNDAMENTALS OF ANALYSIS.

UNIT 4B: PLAIN & SIMPLE - THE Z-TEST.

UNIT 4C: THE COMMONEST TEST FOR ANALYZING INTERVAL DATA - THE T-TEST.

UNIT 4D: THE PEARSON PRODUCT MOMENT CORRELATION TEST.

UNIT 4E: TESTING ORDINAL DATA - THE SPEARMAN RANK ORDER CORRELATION TEST.

UNIT 4F: TESTING NOMINAL DATA – THE CHI-SQUARE TEST.

SECTION 5: THE FINAL REPORT

UNIT 5A: FORMING CONCLUSIONS.

UNIT 5B: COMPLETING YOUR FINAL REPORT.

SECTION 6: APPENDICES.

APPENDIX A: DO’S & DON’TS OF REPRESENTING DATA.

APPENDIX B: PROBABILITY & CHANCE.

APPENDIX C: CONDITIONAL PROBABILITY.

APPENDIX D: PERMUTATIONS & COMBINATIONS.

APPENDIX E: THE DISSERTATION WRITING PROCESS.

COURSE PURPOSE:

The two volumes of this text are required for completing this course. You will be required to practice the steps from developing an idea for your research to completing the final report. As you work through this text, your study should be a small one with a limited number of subjects and a single problem in the area of your graduate major; if you are a senior required to learn to do research, the problem can be in the area of your undergraduate major or the area you plan to major in when you enter graduate school.

Both volumes combined are designed to give each participant practice in all aspects of completing a small research study including a final report. Your report must include a section defining your objective for the research, a description of your research problem, that is, your main question, your theory about the solution, as well as why this problem is important. Your report must describe your plan for gathering information (data), how you will test your hypotheses, the results you obtain, and your report must include your conclusions and any questions the study has suggested for further research.

COURSE OBJECTIVES:

• Apply problem identification and problem solving skills in the real world.

• Define and/or describe all aspects of doing basic research.

• Identify a particular research question, form a hypothesis, and perform a literature search in the field of the research question.

• Evaluate professional literature in terms of its thesis, supporting evidence and suggestions for further research.

• Analyze the research literature that applies to your research question and write a paper describing how that research is relevant to your question and your hypothesis.

• Prepare a proposal for your research study to be submitted to your faculty advisor and department Chairman.

• Describe a research project/study to determine the validity of your hypothesis including data gathering and analysis.

• Gather appropriate data, analyze it using appropriate statistical tests described in this course, and illustrate the gathered data and analysis with appropriate graphics.

• Prepare and submit a publishable article describing your research and the results using the skills developed in fulfilling these course objectives.

TERMINAL OBJECTIVE FOR THE COURSE:

Write a report in the form of an article suitable for publication, reporting your research and the results, with a minimum standard of a B grade. Your Instructor may determine a different grade requirement.

SPECIFICATION FOR REPORTS & ASSIGNMENTS:

All Reports should be typed and double spaced. The reports for this course should be hand-in-hand with the student workbook and group discussion activities. Make sure spelling and grammar are correct. You will be required to get a minimum of a B Grade. Why a B Grade? You will have plenty of opportunities to improve all reports. And to be suitable for publication any standard below B would not be adequate.

ONLINE ACTIVITIES:

Through the various sections, you will be given a selection of URLs in order to learn how to use the Internet to get information about Research, Proposals, Thesis & Dissertation Writing and Statistical analyses. Take advantage of these as the various sites (and others) will be helpful when you begin to do other studies. {Note: some of these are stable, but others may change as the owners of the site make internal changes. This is inevitable. If this happens in this course, your instructor should be able to assist you to find others. Share information with other members of the course if you find any URLs without assistance.]

RESEARCH NOTEBOOK OR DIARY:

It is really important that whenever you are doing some activity that relates to your research, that you keep notes of what happens. This needs to be a small pocket notebook not your computer! You may get insights into the research, or find some unexpected problem, or discover something you hadn’t thought of. Whatever it is, if you don’t keep notes you will not remember the information that may add a special insight to your research paper. So…Get in the habit of carrying the research notebook/diary with you all the time. And USE it!

ASSIGNMENT WORKBOOK/COMPUTER FOLDER:

You need to keep your class notes, assignments, etc., in a workbook for this class or in a folder on your computer (keep it up to date). Always start a new page for each assignment. You will often be required to prepare handouts for the rest of the students in your class so they can review your work as part of a class discussion. Arrange for copying with your instructor.

• One major purpose of the group discussion is to enable each person in the class to improve their work.

o When critiquing, be honest but not unkind.

o No put-downs or derogatory remarks.

o Be helpful with suggestions for improvement.

TABLE OF CONTENTS

PREFACE

OUTLINE - VOLUME 1:

OUTLINE - VOLUME 2:

COURSE PURPOSE:

COURSE OBJECTIVES:

TERMINAL OBJECTIVE FOR THE COURSE:

SPECIFICATION FOR REPORTS & ASSIGNMENTS:

ONLINE ACTIVITIES:

RESEARCH NOTEBOOK OR DIARY:

ASSIGNMENT WORKBOOK/COMPUTER FOLDER:

SECTION 1: PRINCIPLES OF RESEARCH.

PURPOSE:

OBJECTIVES:

A BRIEF OUTLINE OF THE RESEARCH PROCESS:

UNIT 1A: WHAT IS RESEARCH & WHY DO IT?

PURPOSE:

OBJECTIVES:

INTRODUCTION:

LEARNING TO DO RESEARCH:

THE RELATIONSHIP BETWEEN RESEARCH & STATISTICS:

CHARACTERISTICS OF RESEARCH:

RESEARCH OBJECTIVES:

BEGIN THE PROCESS FOR YOUR RESEARCH STUDY:

UNIT 1A Assignment:

UNIT 1B: POPULATIONS & SAMPLE SIZES.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

WHAT IS A POPULATION?

CHRACTERISTICS OF POPULATIONS:

GENERALIZING STUDY RESULTS:

USING THE WHOLE POPULATION:

CERTAIN FACTORS MAY AFFECT SUBJECTS IN YOUR STUDY:

POPULATION VERSUS SAMPLE:

SAMPLE SIZE:

FACTORS USED IN DETERMINING SAMPLE SIZE:

DECIDING THE SIZE OF YOUR SAMPLE:

SELECTING YOUR SAMPLE:

UNIT 1B Assignment:

UNIT 1C: THE NATURE OF DATA.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

PARAMETRIC & NON-PARAMETRIC DATA:

USEFUL DEFINITIONS:

THE NATURE OF DATA:

NOMINAL DATA:

ORDINAL DATA:

INTERVAL DATA:

RATIONAL DATA:

IMPLICATIONS FOR GATHERING THESE TYPES OF DATA:

WHAT CATEGORIES OF INFORMATION CAN WE COLLECT?

EVALUATING THE INFORMATION WE COLLECT:

UNIT 1C Assignment:

UNIT 1C Assignment Feedback:

UNIT 1D: THE HOW TO OF RESEARCH

PURPOSE:

OBJECTIVES:

INTRODUCTION:

APPROACHES TO RESEARCH:

DEFINING BASIC RESEARCH METHODOLOGIES:

DESCRIBING YOUR METHODOLOGY:

UNIT 1D Assignment:

UNIT 1E: STAGES IN THE RESEARCH PROCESS.

PURPOSE:

OBJECTIVES:

THE RESEARCH PROCESS:

UNIT 1E Assignment:

SECTION 2: BASIC RESEARCH PROCESSES.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

THE RESEARCH PROPOSAL:

UNIT 2A-1: THE LITERATURE SEARCH.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

THE LITERATURE SEARCH PROCESS:

UNIT 2A-2: SEARCHING ERIC FOR ARTICLES

(ERIC: Educational Resources Information Center)

PURPOSE:

OBJECTIVES:

INTRODUCTION:

EDUCATIONAL LEVEL:

SEARCHES:

BASIC SEARCH:

ADVANCED SEARCH:

EXAMPLE OF USING THE THESAURUS:

MY ERIC:

UNIT 2A-2 Assignment:

UNIT 2B: RESEARCH HYPOTHESES

PURPOSE:

OBJECTIVES:

IMPORTANCE OF GOOD HYPOTHESES:

UNIT 2B-1: WHAT IS A RESEARCH HYPOTHESIS?

PURPOSE:

OBJECTIVES:

INTRODUCTION:

HUMAN NATURE:

THE FORMATION OF INFORMAL HYPOTHESES:

THE NEXT STEP IN YOUR RESEARCH STUDY:

DEFINING THE RESEARCH HYPOTHESIS:

UNIT 2B-1 Assignment:

UNIT 2B-2: CONVERTING PROBLEM STATEMENTS INTO HYPOTHESES.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

NULL & ALTERNATIVE HYPOTHESES:

AIMS OF RESEARCH:

TAILS ON A CURVE:

REGION OF ACCEPTANCE:

TESTS OF HYPOTHESES:

TYPE I AND TYPE II ERRORS:

HYPOTHESES FOR ONE- & TWO-TAIL TESTS:

WRITING YOUR HYPOTHESES:

UNIT 2B-2 Assignment:

UNIT 2C: DATA COLLECTION TECHNIQUES.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

NEED FOR PRIVACY:

IMPLICATIONS FOR GATHERING DATA:

DESCRIBING THREE TYPES OF RESEARCH DATA:

INTERVIEW TECHNIQUES FOR GATHERING DATA:

GATHERING DATA THROUGH SURVEYS AND QUESTIONNAIRE INSTRUMENTS:

TYPES OF SURVEYS:

CONDUCTING A SURVEY:

TYPES OF QUESTIONS:

THE FORMAT OF THE QUESTIONNAIRE:

COMPLETENESS CHECKS:

COLLECTING DATA:

WAYS OF RECORDING DATA:

UNIT 2C Assignment:

UNIT 2D: WRITING A RESEARCH PROPOSAL.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

ORGANIZING THE RESEARCH PROPOSAL:

CONTENTS OF THE RESEARCH PROPOSAL:

YOU HAVE EVERYTHING YOU NEED TO WRITE THE PROPOSAL!

COLLECTING YOUR DATA FOR YOUR STUDY:

UNIT 2D Assignment:

SECTION 3: PREPARING FOR DATA ANALYSIS.

PURPOSE:

OBJECTIVES:

PRELIMINARIES FOR ANALYSIZING DATA:

UNIT 3A-1: DECISION ERRORS: Type I & Type II.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

TYPE I AND TYPE II ERRORS.

TESTING THE HYPOTHESIS OF NOT GUILTY:

TESTING THE HYPOTHESIS OF NOT INNOCENT:

DECISION ERRORS:

THE PROBABILITY OF MAKING TYPE I OR TYPE II ERRORS:

FACTORS AFFECTING POWER:

DECISION RULES:

USING A P-VALUE:

REGIONS OF ACCEPTANCE OR REJECTION:

UNIT 3A-1 Assignment:

UNIT 3A-1 Assignment Feedback:

UNTI 3A-2: FOUR STEPS FOR TESTING HYPOTHESES.

PURPOSE:

OBJECTIVES:

INTRODUCTION:

PROCESS FOR TESTING HYPOTHESES:

ANALYZING & INTERPRETING DATA:

BASIC ANALYTICAL TESTS:

UNIT 3A-2 Assignment:

UNIT 3B: BASIC CONCEPTS FOR DATA ANALYSIS.

PURPOSE:

OBJECTIVES:

DECISIONS RULES AND ERRORS:

UNIT 3B-1: PROBABILITY.

PURPOSE:

OBJECTIVE:

INTRODUCTION:

PROBABILITY & PROBABILITY DISTRIBUTIONS:

A TREE DIAGRAM:

WHAT IS A CUMULATIVE PROBABILITY?

RELATIVE FREQUENCY:

CONDITIONAL PROBABILITY:

UNIT 3B-1 Assignment:

UNIT 3B-2: FREQUENCY DISTRIBUTIONS

PURPOSE:

OBJECTIVES:

INTRODUCTION:

THE FREQUENCY DISTRIBUTION AND FREQUENCY TABLE:

A FREQUENCY ARRAY:

THE TALLY SHEET:

CLASS, CLASS INTERVALS, AND FREQUENCIES:

USING CLASS INTERVALS:

NORMAL DISTRIBUTION:

AN EXAMPLE OF POTENTIALLY SKEWED DATA:

UNIT 3B-2 Assignment:

UNIT 3C: PRELIMINARIES FOR TESTING INTERVAL DATA.

PURPOSE:

OBJECTIVES:

FLOW CHART - ANALYZING INTERVAL DATA:

3C-1: MEASURES OF CENTRAL TENDENCY - MEAN, MEDIAN & MODE

PURPOSE:

OBJECTIVES:

INTRODUCTION:

I CAN READ YOUR MIND!

THE MEAN, MEDIAN, AND MODE:

THE MEAN:

CALCULATING THE MEAN:

FREQUENCIES:

DETERMINING THE MEDIAN:

SUMMARY FOR CALCULATING THE MEDIAN:

WHEN TO USE MEDIAN OR MEAN:

THE MODE:

MORE THAN ONE MODE:

SUMMARY - DIFFERENCES BETWEEN MEAN, MEDIAN, AND MODE:

UNIT 3C-1 Assignment:

UNIT 3C-1 Assignment Feedback:

UNIT 3C-2: MEASURES OF SPREAD - RANGE, VARIANCE & STANDARD DEVIATION

PURPOSE:

OBJECTIVES:

INTRODUCTION:

THE RANGE & GROSS OUTLIERS:

EXPLAIN WHY AN OUTLIER EXISTS:

THE VARIANCE:

CALCULATING THE VARIANCE:

STANDARD DEVIATION:

EXAMPLE USING THE ALGORITHM:

PITFALLS WHEN ADDING GRAPHICS:

FINAL EXAMPLES:

UNIT 3C-2 Assignment:

UNIT 3C-2 Assignment Feedback:

PREVIEW: VOLUME 2

SECTION 1: PRINCIPLES OF RESEARCH.

PURPOSE:

Research isn’t just a matter of looking something up, writing a description of what you found, and giving your opinion of the effects and/or benefits of your findings. While those may be elements of research, what is needed from seniors and graduate students is something a lot more formal; something that is guided by a specific question or set of questions in a particular educational field of study. Formal research is the process of collecting, organizing, analyzing, and interpreting data for the purpose of gaining insight, increasing understanding of the research question, and presenting the results to our colleagues. Your ultimate aim is to satisfy not just yourself but others in the same field as yourself. Your questions must address concepts or ideas that will benefit or improve practices in your field of study and assist in increasing understanding of the principles and standards within your field.

The first vital component in doing research is to have a good, working plan. There are a lot of elements required for a quality plan. You must properly define the problem you are interested in and define any specialized terms that are essential to the area of your study. In addition, you must be able justify your investigation of this particular problem. You must determine the methodology you will use to complete your investigation (what you will do and how you will do it). Part of determining the methodology requires knowledge of populations and samples. You must also be certain that the data you collect will enable you to reach valid conclusions. In order to do that, you need to understand the nature of data, that is, what types of data may be sought, how they are similar and how they differ. Then you must convert your problem definition into a hypothesis, an explanation or theory of why the problem exists. The next stage is gather the data and analyze it to determine if your hypothesis does explain your question.

The major purpose of doing research is to add to the body of knowledge for your major field. What this means is that the data you collect must be analyzed and, yes, it does use a tool called statistics. But it is simply a tool. Once analyzed, conclusions are drawn and you write your final report. All these activities are an integral part of the research process.

OBJECTIVES:

• Determine what research is and why it needs to be done.

• Define the meaning of population and sample as far as research is concerned.