Practical Research and Statistics

By K.J. Kovach and P.A. Richardson

The main aim of this new book is to provide a single, efficient, and effective source for college and university students to understand research development and learn, then apply, statistical concepts while developing a Research Proposal or Research Study using the American Psychological Association (APA) format.

It is a specialist text pa

• Language: English
• Publisher: Book Printing UK
• Release date: Mar 19, 2018
• ISBN: 9781911596332

Book preview

List of Tables

1.1   Research Process

1.2   Scales of Measurement

2.1   Research Proposal and Study Components

2.2   General Topics

2.3   Sample Types

3.1   Research Approaches

3.2   Quantitative Research Designs

4      Qualitative Research Designs

5.1   Data Collection Issues

5.2   Questionnaire Checklist

5.3   Additional Questionnaire Issues

5.4   Interviewing Guidelines

5.5   Focus Group Rules

6     Statistical Symbols and Formulas

10   Analysis of Variance Summary

List of Figures

Figure

1.1    Helical Concept

1.2    Research Process

1.3    Qualitative and Quantitative Data

1.4    Lower and Upper Limits

1.5    Introduction Summary Mind Map

2.1    Bloom's Taxonomy

2.2    APA Example Headings – Table of Contents

2.3    Hypotheses Symbols

2.4    Sampling Methods

2.5    Power

2.6    Type I & II Errors

2.7    Research Process & Report Mind Map

2.8    Review of Literature Mind Map

2.9    Methodology Mind Map

2.10  Statistics Mind Map

2.11  Completed Study Mind Map

3.0    Quantitative Designs Mind Map

4.1    Qualitative/Mixed Methods Mind Map

4.2    Qualitative Designs Mind Map

5.1    Data Collection Mind Map

5.2    Questionnaires Mind Map

5.3    Key Items Mind Map

5.4    Interviews Mind Map

5.5    Focus Group Mind Map

6.1    Normal Distribution

6.2    Tree Diagram

6.3    Descriptive Statistics Mind Map

6.4    Descriptive Presentations Mind Map

7.1    90% Distribution

7.2    t, z & CI Tests Mind Map

7.3    Confidence Intervals (CI) Mind Map

8.1    Bag of M&Ms

8.2    Chi Square Distribution

8.3    M&Ms Array

8.4    Skittles Array

8.5    Chi Square Mind Map

9.1    James Stevens

9.2    Scatter Plot

9.3    Correlation & Regression Mind Map

9.4    Correlation Mind Map

10.1  Formulas for Two-Way ANOVA

10.2  Two-Way ANOVA

10.3  Analysis of Variance Mind Map

11.1  Non-Parametric Tests Mind Map

11.2  Why Use? Mind Map

12.1  Report Writing Mind Map

12.2  Research Proposal Mind Map

List of Examples

Example

6.1    Mean, Mode, Median & Midrange

6.2    Weighted Mean

6.3    Grouped Mean

6.4    Percentiles

6.5    Quartiles

6.6    Variance & Standard Deviation

6.7    z-Score Analysis

6.8    Correlation, Scatterplot, Strength of Relationship

6.9    Box Plots

6.10  Stem and Leaf Plot

7.1    Critical t-values

7.2    t-test for Hypothesis Testing

7.3    Employee Salaries—t-test

7.4    t-test for Difference of Two Means (Independent Samples)

7.5    t-test for Difference of Two Means (Dependent Samples)

7.6    Standard Error of the Mean

7.7    z-test for One Mean

7.8    P-value

7.9    z-test for Two Means (Independent Populations)&

7.10   z-test for Sample Size

7.11   t-test for Confidence Interval (σ Unknown)

7.12   t-test for Confidence Interval—Two Independent Samples

8.1    Test of Independence—Workforce Survey

8.2    Test of Equality

8.3    Goodness of Fit Test

9.1    t-values, Observed vs. Critical

9.2    Using Pearson Product Moment Correlation (PPMC)

9.3    Spearman Rank Order Correlation

10.1   ANOVA

10.2   Scheffé Test

10.3   Tukey Test

10.4   Tukey HSD for Example 10.3

10.5   Teaching Method Data Table

11.1   Sign Test – Paired Samples

11.2   Wilcoxon Rank Sum Test

11.3   Wilcoxon Signed-Rank Test

11.4   Kruskal-Wallis Test

11.5   Mann-Whitney U Test

12.1   Title Page

12.2   Abstract

12.3   Introduction

12.4   Extended Introduction

12.5   Review of the Literature

12.6   Methodology

12.7   Anticipated Results and Conclusions

12.8   Results, Analysis and Discussion, Summary and Conclusions

Preface

The main aim of this new text is to provide a single, efficient, and effective source for college and university students to understand research development and learn, then apply, statistical concepts while developing a Research Proposal or Research Study using the American Psychological Association (APA) format. It is a specialist text particularly well suited for introductory, accelerated, and short courses in this subject. After teaching over 30 years, the authors know that several different texts commonly must be bought or used in learning to develop a research proposal or research study. Additionally, many colleges and universities have combined various research and statistical courses into one course or program. Students, therefore, have to learn what research is and its many concepts, learn various descriptive and inferential statistics, and apply APA format for completed reports during one school term. Instructors as well as students easily appreciate that a detailed grasp of the above three components during a single university course would be a daunting task. Hence, the authors offer this practical integration and application of all three components into a single, recommended text, as an efficient, effective bridge to learning these complex areas. Mind Maps are used to help readers organize the many detailed concepts and techniques herein. These Mind Maps are presented with the central concept at or near the middle of the diagram and subordinate concepts and techniques arranged as branches clockwise from the upper right around to the upper left. For Instructors adopting this text, an Instructor Guide, chapter PowerPoint® files, and Test bank will be provided to facilitate the one course concept — email a request to [e-mail].

CHAPTER 1  INTRODUCTION

Learning Outcomes

After completing this chapter, the following Learning Outcomes should be met:

Define and understand what the scientific research process involves.

Discuss the differences between a Research Proposal and a Research Study.

Determine American Psychological Association (APA) reporting style and any organization’s specific requirements.

Formulate hypotheses development.

Differentiate between Quantitative, Qualitative, and Mixed research approaches.

Define key terms to include population, sampling, quantitative and qualitative data, and others.

Recall the four Scales of Measurement.

Explain ethics and copyright processes.

Introduction

Research is a process that involves collecting and analyzing data for a specific purpose. There is much more to research than developing information from raw data gathered at the early stages of the process, as ‘information’ needs to be formulated within a context. Leedy and Ormrod (2010, p. 2) defined research as a systematic process of collecting, analyzing, and interpreting information (data) in order to increase our understanding of the phenomenon about which we are interested. You [1] might have a theory about something and wish to test that theory, or you may have a question that requires answering. This is when the process starts; it soon becomes more complicated than many people—particularly new researchers—anticipate. The purpose of this text is to provide the reader with a practical guide to follow during a specific research process for an issue that results in developing a Research Proposal or a Research Study. Research is systematically explained as the reader is guided along a path that will lead to an efficient, effective research project. Many examples are also provided that help the reader visualize details in context and understand why research is a more complex process than simply collecting information and presenting the data[2].

Thought to Ponder: This text follows APA guidelines as modified for researchers who must provide academic reports. For example, university and college officials may require a Table of Contents, actual insertion of Tables and Figures, and separate Introduction and Review of the Literature chapters. APA formats are designed for publishers.

1.1  What is Research?

To begin, let’s review some key concepts of the research process. What does research involve?A person may have an idea or a question about something occurring in the workplace or a community, about a production plan, or about any other issue.

Thought to Ponder: It is widely accepted that ‘facts’ exist within the context of an implicit or explicit theory. Likewise, theories exist based on thoughts or observations of specific events, or facts.

One usually begins a research study with a broad general topic unless there is a specific topic relating to one’s work, business, school, or other known direction or interest. Of major importance to any researcher is one’s interest in the topic. Perhaps an employer, instructor, or other authority has assigned it, or it might stem from personal interest. Whatever the topic, it is usually general in form and one has to narrow the focus to a specific title. The study must be doable!

Information must be available to develop an Introduction and to accomplish a literature review. A researcher searches from the general to the specific. Using the topic, you have to narrow the focus to a specific target population, identify specific independent and dependent variables, and indicate the variables’ relationship(s). When pressed early in the process for a title, focus on a simple title that supports the topic you wish to study. A more complex or compounded title may include more than one independent variable. Separate hypotheses can often be developed from such complex titles; however, such complexity also often masks the need for more detailed, time-consuming research planning than you might have anticipated. Thus, it is advisable to keep your effort simple: "Take one piece of pie " at a time—study one variable at a time.

As an example, consider yourself sitting in an airport watching people walk by. Ever wonder why some people dress the way they do? Which suitcases are used more than others? How many people use specific airlines?Which airlines are preferred by holiday travelers and business travelers? The theories or questions you can develop are endless.

Thought to Ponder: In research, you need explicitly to allow for an inherent tendency to seek out facts that support a priori guesses, biases, pre-conceived ideas, etc.

From millennia, some, at times many, people have accepted declarations by those in authority or religious leaders; empiricism, however, brought change to people’s attitudes and methods of determining outcomes. Experience founded on science became prominent. Leedy and Ormrod (2010, p.7) emphasized that research is a helical concept, a spiraling that becomes smaller but is never ending: Research begets research ! As one reaches a finding in one study, further questions or issues develop. Perhaps the spiral becomes narrower, but the end is never reached. See Figure 1.1.

For example, in a business, a manager may wonder whether a new production process could be used to improve efficiency; if that is successful, might another process be even more successful? An airline manager may wonder whether a new flight route or different customer services would be more profitable. Counselors may wonder which treatment or intervention programs are most effective. Public administrators may discuss various optional corporate or government policies to recommend. Medical doctors may wonder if a different prescription would be more effective. Information experts may wish to develop more simplified technical programs, and on it goes. Whatever the profession or program, there will be questions or theories about programs, methods, and possible changes. Many professionals in every field use data for making changes. That word, change, is often used, but the real issue is whether the change makes a significant beneficial difference? Further, who decides that issue and the level of benefit ?

Thought to Ponder: You need to keep in mind that anyone can posit a theory yet no one can actually prove a theory; not all possible instances, especially future instances but also many prior instances, can be examined. However, you can disprove a theory by finding one or more instances that refute it. Thus, researchers strive to disprove theories, even ones they want to be correct. If no instances are found to disprove a theory, then that theory can be accepted, at least given current research efforts.

In research, you can never be 100% certain using sample data; therefore, you need to develop a plan of action to determine an outcome before it occurs. Research, then, is a systematic and scientific process to test one’s theory or answer one’s question. This concept is important. You can only refute or support, not prove, an alternate hypothesis or research hypothesis. Why?

When sampling is first used to support a theory, further sampling may change the initial finding or result. A scientific process is applied to develop the research plan and to follow detailed procedures. There are very specific actions to take in determining what data are necessary, how to collect the data, how to present those data, and then how to make a finding. Learning those details becomes a science, while practicing and improving upon these makes it an art form. Over time, you learn to become more effective, more efficient, and more satisfied with your progress in developing research skills and applying scientific steps. The application of a scientific approach, again, means that your efforts are subject to review, critique, replication efforts, and refutation as well as confirmation and approval.

Thought to Ponder: Sampling occurs when you cannot or do not collect data on 100% of the population of interest. One can and sometimes does inspect 100% of products delivered from vendors to confirm acceptable levels of quality. However, one seldom attempts to survey 100% of potential voters, even in local elections.

1.2  Research Process.

The research process generally follows a nine-step format: See Table 1.1 and Figure 1.2. Specific details of the Research Proposal or Study will be covered later, but a brief review of the nine steps follows. First, one begins with a question or problem. Second, an operational definition(s) must be created to specify the issue. Third, an Introduction provides the basis of the topic, from the general to the specific so that the reader understands the focus and purpose of the study. It is also used to define terms as necessary.

After this, a Review of the Literature (Step Four) provides a more detailed review of the pros, cons, and neutral aspects of the topic. Slightly different than APA format is the separation of the Introduction and Review of the Literature (these are usually combined for published articles). The literature review for academic purposes then becomes a more in-depth review of those prior efforts to explore the pros, cons, and neutral aspects of the topic. Current sources (less than 10 years old) and authorities long standing (consider the classics, e.g., Freud) are presented without bias. Bias simply means skewing the data intentionally or unintentionally from the actual estimate. Ending this fourth step would be the presentation of one’s theory, or hypothesis. A hypothesis is a tentative assumption made to test its logical or empirical consequences (Merriam-Webster’s Collegiate Dictionary, 2003). For qualitative researchers, one may present a Research Hypothesis or a Research Question. For quantitative researchers, the null and alternate hypothesis are presented (details of each will be presented later).

Figure 1.2   Research Process

The Fifth step, Methodology,is an explanation of the research: This is a critical step. Any reader should be able to replicate the study by following the information provided. Various subcomponents for this heading will be covered later in the text. Once the methodology has been formulated, data are collected as planned (Step Six). Step Seven is the presentation of the data, or Results. Analysis of the results then becomes Step Eight, and this is completed without bias. Lastly, Step Nine is the Summary and Conclusions.

1.3  Key Terms.

Many important terms must be understood prior to commencing the research process. To begin, the target population must be selected: This is the group of people under study. From this target population, a sample or samples can be used to collect data to test your theory or hypothesis. Types of samples will be reviewed later. Data, or values of a variable (an attribute or characteristic), can be qualitative or quantitative. Qualitative data are categorical or can be encompassed within groupings:for example, colors of a car, gender, or preference ratings. A number can be qualitative if it just relates to a category or description, such as rating a teacher on a scale of 1 to 5. Quantitative data are numerical and can be discrete or continuous. Discrete data are basically whole values or numbers that can be counted:for example, 1, 2, and 3. Continuous data can be measured and have infinite values:for example, 10, 10.5, 10.75, and 10.752. These variables are illustrated in Figure 1.3.

An important aspect of continuous data is that values exist within numeric boundaries. A whole number, for example, is deemed to be entered between upper and lower boundaries which exist at 0.5 unit above and below the number. For example, 44 has a lower limit of 43.5 and an upper limit of 44.5. Examples are seen in Figure 1.4.

1.3.1   Scales of Measurement.

All data fall under one of four scales of measurement: (a) nominal, (b) ordinal, (c) interval, and (d) ratio. Based on the type of data obtained, you can present various descriptive statistics and use different inferential tests. Equate each scale above to one of four properties, respectively: (a) name, (b) magnitude, (c) equal intervals, and (d) true zero. For example, nominal is categorical or name only. Ordinal measurement has name and order or ranking (magnitude). Interval scale has (a) name, (b) magnitude, and (c) equal intervals. The last category is ratio which has (a) name, (b) order, (c) equal interval, and (d) a true zero. See Table 1.2.

Figure 1.3   Qualitative and Quantitative Data

Figure 1.4  Lower and Upper Limits

Thought to Ponder: When representing continuous data that have been grouped for easier presentation, you may find a collected datum or value that rests on both limits; therefore, you have to choose where to place the value. Place it in the next upper class. For example, if there are two classes identified as 40 - 50 and 50 - 60, and the value obtained is 49.5, place the value in the higher grouping. (This implements a ‘rounding up’ strategy.) The better way to present classes would be to use ‘less than’ symbols: for example, 40 < 50 and 50 < 60, and so forth. This identifies specific limits. Note too that the ability to round up requires that data be collected to one decimal or place value more than