Question

By Cristie McClendon, Scott Greenberger, and Stacey Bridges

Reading Quantitative Research

Essential Questions

1. What types of research problems are suitable for quantitative research?

2. How does a researcher select a quantitative design?

3. What are the GCU core designs for quantitative research?

4. How does one select appropriate measures or instruments for quantitative research?

5. What sampling approaches are used in quantitative research?

6. What are the most common approaches used in quantitative data analysis?

Introduction Quantitative research is frequently used in the social sciences because it is quick, relatively inexpensive, and

considered a valid method of inquiry by researchers and academicians. The goals of quantitative research are

to describe the attributes of a group of people, to measure differences between groups, to determine if a

relationship exists between variables, or to predict if one event or factor causes another.

Quantitative studies contain measurable and quanti�able data, a

statistically appropriate sample, use of statistical techniques, and

a structured data collection plan to ensure that the study can be

replicated. Additionally, quantitative studies require the use of

valid and reliable instruments, surveys, or databases to quantify

variables. The research method is deductive, very structured, and

in�exible as often the goal of the researcher is to generalize or

apply the results to other groups and populations besides those

participating in the study. Ultimately, quantitative research offers a systematic and structured process for

answering research questions (Balnaves & Caputi, 2001).

Critically Reading Quantitative Research

Doctoral learners must go through a process of learning how to critically read empirical research. While

reading is a familiar skill to learners, at the doctoral level, it takes on new depth as learners transition to the

mindset of a researcher. The required reading materials will be more dif�cult to read, take more time, and

require learners to improve their reading ef�ciency and critical-thinking skills. Having ample time built in for

reading is crucial to the success of a doctoral student. Reading is the foundation to a dissertation research

project. The �rst 2 years before a proposal is accepted will be spent reading peer-reviewed articles,

dissertations, books, and other scholarly sources that can potentially contribute to the dissertation project. At

the same time, the reading of these materials directly contributes to subject matter expertise of the learner

helping to make him or her an expert in the �eld of study. Unfortunately, there is not a speci�c number of

Schedule enough time to read

critically.

resources that a learner must read to transform into an expert. The reading process in a doctoral program is an

ongoing, self-directed, independent project that begins in the �rst course and does not end until the

dissertation is approved. Even then, the learner who has transitioned to a researcher will continue to read on

the topic in the years after graduation in order to remain current with the literature. Those who also become

published scholars will continue to contribute to the literature with their own publications.

Successful completion of a doctoral dissertation requires signi�cant amounts of independent, critical reading

on the research topic. This allows the doctoral researcher to become familiar with the scope of the topic and to

identify problem spaces within the existing literature that become the source of the dissertation research.

Researchers read research differently in order to save time, often employing a nonlinear approach.

Nonetheless, doctoral learners should schedule enough time

to critically read a research article. Articles should be read for

relevance, critique, and reference sourcing, which takes time,

as many articles will need to be read multiple times to garner

a reasonable understanding. Quinton and Smallbone (2006)

offered additional information regarding how to develop a critical approach.

Reading Quantitative Research

Learners intending to examine large samples to generalize outcomes to a population or a subpopulation should

familiarize themselves with quantitative research frameworks. In order to critique a source, understanding the

research framework is needed. This chapter provides information on quantitative research frameworks to

assist learners in identifying quantitative research and understanding the multiple techniques encountered

when reading research. The article “Step-by-Step Guide to Critiquing Research. Part 1: Quantitative Research”

by Coughlan, Cronin, and Ryan (2007) provides in-depth coverage of critiquing research to supplement the

discussion of quantitative research frameworks. McGregor (2008) offered a summary of how to critique an

article in Figure 1.1 (https://methods-sagepub-com.lopes.idm.oclc.org/book/understanding-and-evaluating-

research/i1401.xml). The following information is intended to serve as a starting point for learners as they

strive to improve their reading skills to gather sources for their dissertations. Broad techniques are provided

along with resources for learners to further explore information independently.

Following is a process of reading for relevancy and reading strategically to evaluate �ndings. It includes

information on how to review the references. Although, reading research saves the researcher time in the

early phases of the research project, a researcher should expect to read the article more than once as the

research project progresses.

Determine Relevance of the Article

While being able to distinguish an empirical article from a nonempirical source is an important skill to learn,

it is also meaningful to look further into the types of articles and papers that can be encountered when reading

literature on a topic. Any doctoral learner that has searched the library for sources can attest that there are

multiple types of articles that can be found in peer-reviewed journals. The �rst chapter of the Publication

Manual of the American Psychological Association (2020) details the diversity of sources that can be found in

a typical journal. What learners may be most familiar with are scienti�c journal articles that report original

research, also known as primary research. There are also methodological and theoretical articles that describe

advancements in theories or methods and do not present research. Literature reviews and meta-analyses

review or synthesize the �ndings from primary research. Some additional types of articles that are published

in journals include white papers, book reviews, reports, and letters to the editors; these types of articles are not

considered primary research and do not factor into the discussion of identifying parts of research articles.

Parts of an Empirical Article

Title

Abstract

Key Words

Introduction

Methods

Results

Discussion

Conclusion

Author Information

Regardless of the methodology of a study, when evaluating a source, a learner should determine the credibility

and rigor of the work. Understanding how to evaluate sources now can save time when making design

choices for dissertation research. A learner must �rst decide if an article is relevant to add to the reading list.

The �rst page of an article contains the most important sections of an article to determine relevancy to a

current research project.

Publication Information: The publication information includes where the article was published.

What type of source is this? Is it original, peer-reviewed, empirical research? For more information,

view the video "Finding Empirical Research Articles (https://lc.gcumedia.com/mediaElements/�nding-

empirical-research-articles/v1.1/)" (Grand Canyon University, n.d.) or read "Evaluating Sources: What Is a

Scholarly Source (http://libguides.gcu.edu/EvaluatingSources)" (Grand Canyon University, n.d.).

When was it published? While a seminal work is relevant to a proposed study no matter when it was

published, the problem space must be substantiated on current research in the �eld. This means that

when trying to establish a problem space, articles published within the last 3–5 years are the most

relevant. If looking for articles to provide contextual relevance for the review of literature, the

publication date may not be as relevant as understanding the historical importance of an article in

developing the �eld of literature. Not all articles are going to be published this year; however, the

references used in the dissertation literature review should be mostly current.

Where was it published? Not everything published meets the highest standards of rigor. What is the

journal’s impact factor? Is this a reputable journal or a predatory journal? For more information, read

"Citation Analysis (https://libguides.gcu.edu/publishing/citationanalysis) "(Grand Canyon University,

n.d.) or "Journal Impact Factors (https://libguides.gcu.edu/publishing/impact)" (Grand Canyon

University, n.d.).

Use the Cabell’s Directory of Publishing Opportunities to �nd out more about the journal title. Cabell’s

has a list of predatory publishers and journals. Make sure the publication is not on that list. Cabell's

Predatory Reports (http://www2.cabells.com.lopes.idm.oclc.org/predatory) identi�es predatory journals

and can be accessed through the GCU Library website. Learners can search by title and �nd out about

peer review, acceptance rates, and other guidelines/policies.

Title: The title of an article is important because it brie�y summarizes the study.

Abstract: Although there are multiple types of abstracts based upon journal guidelines, typically an abstract

brie�y summarizes the key features of a research study.

Keywords: Depending on the journal, there should be three to ten keywords for an article. These keywords are

important because they are used in research database searches and should be related to the major concepts of

the study.

The following questions can be used after reading the title, abstract, and keywords to evaluate the relevance of

an article for inclusion on a reading list.

Does the title suggest variables that are relevant to the reading list for the study?

Does the summary provided by the abstract and keywords indicate that the research relates in some

way to the proposed study? Information in the abstract and keywords generally speaks to what the

authors wanted to know and the short version of their �ndings. After reading the abstracts and

keywords, a reader should be able to quickly determine how relevant an article is to the proposed

dissertation research.

One key to ef�cient reading is knowing when to stop reading an article because it is not relevant. A keyword

search may result in hundreds or thousands of sources, which can lead a researcher down the proverbial

“rabbit hole.” Critically reading the �rst page of an article can save time by allowing the reader to discard

articles that are not relevant to the study and should not be placed on a reading list.

Reading Strategically to Evaluate Findings

Most learners read articles from start to �nish; however, researchers generally take a nonlinear approach to

reading an article. In the early stages of research project development, researchers invest a substantial amount

of time surveying the literature of the �eld of study, quickly evaluating sources that are pertinent. This

nonlinear approach helps to further re�ne the reading list, culling out articles that are less relevant to the

project. Later, when a key article is discovered, researchers may read that article multiple times to understand

how the article contributes to the �eld of literature and how the article can be used in their work. The strategy

used to read the article will differ based on the goals of the reader.

It is also important to practice reading strategically to improve ef�ciency. After the title, abstract, and

keywords, readers should move to the sections at the end of the article such as the discussion and conclusion.

Keep in mind that the sections of an article may vary depending on the journal and on the type of research;

these sections focus on questions that are important for quantitative studies. Here, readers will �nd it more

useful to �rst review the discussion of the �ndings rather than the results section because, in quantitative

studies, the results section is �lled with charts, �gures, tables, and statistics. Learners will �nd it easier to start

with the narrative description found in the discussion of �ndings rather than the data analysis.

Discussion: In the discussion section, the authors interpret the meaning of the study results and explain how

the �ndings answer the research questions. This section also presents how the �ndings of the current study

relate to other research in the �eld. Implications of the �ndings for future research as well as limitations of the

study will be included.

Conclusion: If a conclusion section is included, authors will tell the readers why the study matters. This

section will summarize the study, the results, and how those results can be used in real-world applications.

After reading the discussion and conclusion sections of an article, the reader has another opportunity to

decide whether to stop reading and remove the article from the reading list. The following questions can assist

a reader in determining if the reader should keep an article and continue reading.

Is the sample relevant? One way to evaluate the relevance of a study is to look at the overall sample of

the study. If a study is about the classroom motivation factors for undergraduate college students and

the article is about the classroom motivation factors of elementary school students, the information may

be tangentially relevant because of the variables, but ultimately, it is not relevant enough for inclusion in

a study of undergraduate college students. Similarly, there is always a discussion of when and how to

include studies that have been completed on international samples. Context will always drive the

evaluation of the source as relevant. For instance, a study investigating the leadership practices of

Australian CEOs may be relevant to include as context for a study being completed in the United States

because leadership practices may be similar in these organizations based on the size and multinational

context. Educational systems, on the other hand, do change based on location and culture, so a study

about Nicaraguan school children may not be useful to include in a dissertation that examines the

American school system. When considering international studies, it is important to evaluate whether

the study should be included based on where the data is being collected. In other words, how similar are

the participants in this completed study to those that are going to be used in the proposed study?

Are the �ndings important? Along with the discussion above about the sample, the �ndings may not be

important to the dissertation project. In discussion and conclusion sections, the author(s) will explain

what the key �ndings are, why they are important, and any practical implications for their use.

Looking Deeper into Quantitative Methods

As a learner continues to evaluate a source, the next sections to consider are the methods and results. By the

time a reader is looking at the methods section, an article should be deemed relevant to the proposed study

and be saved to the reading list. Reading these sections in a quantitative study may be the most dif�cult for

learners to comprehend let alone critique. This is because most doctoral learners are still novices in

developing their research skills. Understanding these sections will become easier with more exposure and

experience with the quantitative research framework. These two sections are the mechanics of how the

author(s) conducted the study, speci�cally how they collected and analyzed the data.

Methods: The methods section of an article is where the authors of a study discuss how they conducted the

study. Information about how data were collected and analyzed will be presented, including what instruments

were used. The information about any instrument, survey, scale, or checklist is provided along with associated

information on the reliability and validity of these measures. In qualitative research, the variables and how

they are measured must be clearly de�ned. In this section the independent, dependent, and other variables

will be discussed along with the parameters of measurement.

Results: This section tells readers the �ndings from the study, including demographic information and key

�ndings that pertain to the research questions. Figures, charts, and tables will likely be presented, and the

information there will also be discussed within the text. In quantitative studies, this is where the speci�c

statistical tests performed will be addressed.

The following questions should be explored for the methods and results section.

Is the selected research design appropriate? The methods section should include information on

research design and justi�cation for the choice.

Is the sample representative? Sampling methods should be appropriate for the speci�c design. In

quantitative study, random selection is better than convenience sampling but not always available to

researchers. The researchers should explain their sampling strategies and discuss the demographics of

their participants. The sample should be representative of the population so that generalization can

occur. If these conditions have not been met, the authors should address the issues as limitations in the

discussion section.

Is the sample large enough? In the methods section, a power analysis should appear to verify that the

researchers sampled enough participants to achieve statistical signi�cance. Additionally, inferential

statistical analysis requires enough participants so that the variables being tested can be normally

distributed.

Is there a control group? Not all quantitative designs require a control group, and, in some cases, it is not

possible to use one. However, the decision should be described in detail. If there is not a control group,

what steps have been taken to limit confounding factors?

The mean age of a sample of

on-campus students may be 20,

while the mean age of a sample

of online students may be 43.

What were the inclusion and exclusion criteria for the sample? Because quantitative studies focus on

generalization from a representative sample to a larger population, understanding sampling strategy is

of key import. The authors should be able to detail who was included and who was excluded from the

study and why these criteria were used.

Have the statistical analyses been appropriately chosen? Most studies provide descriptive statistics to

describe the sample. These are relevant factors about the participants such as age, gender, marital status,

class year, etc. To ensure that a sample is representative, it

would be crucial that the research give basic descriptive

statistics such as the mean and standard deviation on the

key demographics. For instance, the mean age of a sample

of on-campus students may be 20, while the mean age of a

sample of online students may be 43. Inferential statistics

are used to show correlations or make predictions about a

population based on a sample. While descriptive statistics are to be expected, they are not enough to test

most hypotheses. If a variable is not normally distributed or the variables are ranked or grouped, then

nonparametric tests must be used.

Have the variables been clearly de�ned?

Is reliability presented? Any surveys, scales, or instruments presented should be psychometrically

validated. Several types of reliability exist and describe the consistency of results. Reliability should be

presented in at least one manner, and internal consistency reported as Cronbach’s Alpha is the most

common. Included in the write up should be a description of the effect size from a seminal source.

Is validity presented? Validity is the degree to which the instrument accurately measures what it

intends to measure. The manuscript should include information about the validity of the measurement

and ideally address more than one type of validity, such as content, construct, and criterion validity.

Analyzing the Need for the Study

Learners are often advised to improve their writing skills by emulating the academic tone of the research

articles that they read. Experienced learners will realize that every research article is like a mini dissertation,

and as such, other skills, such as organizing an argument and providing context for a study can be garnered

from the reading of an article. Looking at the introduction is a great way to study how a researcher identi�es a

problem space, situates the current study within the relevant research of the �eld, and concisely builds a case

for the need for the study. More will be presented on argumentation later in this book, but for now, this will

help learners to understand the importance of the introduction.

Introduction: The purpose of an introduction is for authors to relate why they did the study. The introduction

sets up the problem space that they identi�ed and contextualizes the current study within the �eld of literature

on a topic. This is where the problem statement, purpose statement, and hypotheses are found. Generally

speaking, the review of literature will often be found in the introduction, occasionally the review of literature

is presented as a separate section depending on journal guidelines. When reading the introduction, consider

the following:

Is the problem clearly stated?

Is the purpose clearly stated, and is it aligned to the problem statement?

Is there a compelling need for the study? The introduction section for any article should provide a

compelling argument for the need for a study. This textbook includes a chapter on problem spaces and a

chapter on argumentation. The author must include context to situate the study within the framework

and demonstrate a gap in the literature (or problem space) that needed to be �lled with the current work.

How closely is the literature reviewed in the study related to previous literature?

Are the purpose and research questions clearly stated? In the introduction, the purpose of the research

and the associated research questions and hypotheses should be stated clearly so that the statistical

choices can be evaluated.

Sourcing References

When researchers read academic literature, they have "a thumb on the back page." That is, they keep the

reference section readily accessible while reading the article. This technique allows them to investigate the

reference page of the study while reading the article. This is one way of gathering additional resources that

could be used for their own research projects. Using a form of citation analysis, the reader can evaluate the

contribution of the study and the reference list.

References: The references are a list of sources the authors cited in the article but is also an important place

for learners to �nd additional sources to add to their own literature searches. Consider the following when

sourcing from references:

Is the literature review recent? Are there any outstanding references (those of vital conceptual

signi�cance) left out?

Does the reference list include seminal works from the �eld of literature?

Across several articles on the topic, which studies or researchers are repeatedly mentioned? Citation

analysis may be helpful in determining seminal works or key authors on a topic.

Authorship

Finally, the author information is an item that will be found in all research studies. There are guidelines

governing authorship. Who conducted the research is an important consideration when reading an article.

Speci�cally, is the author well known in the �eld as a proli�c contributor or an expert on a topic? Is this the

only study by this author in this line of research, or is the author established in this domain?

Author Information: This is a list of people who contributed to either conducting the study, writing the

manuscript, or both. The sequence of authorship is important because it denotes the contribution of work that

each author provided. The �rst author did the most work in developing, conducting, or writing the research,

while the last author contributed the least. In citations, the sequence of authors cannot be changed. For

instance, Smith and Hatmaker (2011) should never be cited as Hatmaker and Smith due to scholarly

conventions governing providing authorship credit. Often, one author will be listed as the contributing author,

or the author to contact for questions or permissions regarding the study. McGregor (2008) offered additional

information regarding evaluating author information.

De�nition of Quantitative Research Quantitative research could be de�ned using an etymological approach and simply discussing it as the use of

statistics to explore a phenomenon. Another approach would be to think about the different branches of

quantitative research, which include descriptive and inferential statistics. This approach is useful because it

provides an outline of the kinds of data generated from statistical analysis. Similarly, characteristics can help

to de�ne the �eld of quantitative research (Gelo, Braakmann, & Benetka, 2008). Lastly, one could simply

describe the different types of inquiry within this �eld of research, such as nonexperimental and

experimental. To combine the explanatory bene�t of characteristics and types of inquiry, this review will

explore both methodological characteristics and predominant approaches. The scienti�c method is the

foundation of quantitative research, which includes both a desire to describe and explain phenomena.

Quantitative research, as it is today, has several enduring characteristics that help to de�ne its approach,

including observing and de�ning objects of inquiry thoughtfully, making predictions about the phenomena of

interest, checking these predictions using hypothesis testing and statistical analysis, and generalizing the

results to a target population.

In quantitative research, the creation of variables by attributing characteristics to phenomena is a �rst step in

the de�ning process. Researchers often use abstract or hypothetical ideas, known as constructs, to label

phenomena (Dew, 2008; Freedman et al., 2007; Cronbach & Meehl, 1955). For example, intelligence is a construct

that can vary by person. The variation in human behavior, both observed and hypothetical, makes assigning

variables a useful way to organize numerical data.

Freedman et al. (2007) provided a useful way of understanding types of variables. In their taxonomy, there are

two top-level types of variables: quantitative and qualitative. Both quantitative and qualitative variables have

two subtypes: discrete and continuous (quantitative), and nominal and ordinal (qualitative). Discrete

characteristics have a limited number of values. An example of a discrete variable is the number of birthdays

celebrated by a study participant. Here a participant could not have celebrated a half or three-quarters of a

birthday. Conversely, the participant's age is a continuous variable because age can be calculated to in�nitely

small fractions of a second. A person's age can be 36 years, 3 months, 6 days, 2 hours, 19 minutes, ad in�nitum.

Qualitative variables, also known as categorical variables, have categories, and, by de�nition, all categorical

variables are discrete because their categories can be well de�ned (Freedman et al., 2007). For example, hair

color is a categorical variable (blonde, brown, black, or other). Categorical variables can either be nominal or

ordinal. Hair color is nominal in that there is no inherent order of hair color. An ordinal categorical variable

requires some sort of ranking system such as military rank. The categories have order. In order to know which

combination of variables to establish for research, it is necessary both to identify such variables and to predict

likely relationships between those variables.

In doctoral research, predictions come from research questions, which arise from gathering and reviewing

previous scienti�c literature on a topic. In most cases, a literature review will include both exploring relevant

theories and a systematic assessment of empirical studies on a topic. Most empirical research articles and

dissertations provide recommended questions for future research. Answering these recommended questions

may address a problem space in the literature for which the propositions and resulting hypotheses will

provide answers (Boote & Beile, 2005). Testing these hypotheses results in accepting or rejecting predictions.

Hypotheses are predictions that have the requirement of being tested. In quantitative research, hypothesis

testing involves using a statistical procedure to determine whether predictions are correct (Burdess, 2010).

This is done by creating both an alternative (experimental) hypothesis and a null hypothesis for each research

question and deductively testing them using probability—either accepting or rejecting the null hypotheses

(Wilkinson, 2013). Formulation of hypotheses will be discussed in more detail in later chapters.

The terms population and target population are important to consider when putting forth hypotheses. In

social science, population is a term that describes some group of people. The target population is some subset

of the entire population of people. For example, suppose the researcher were exploring a relationship between

teaching method in freshman university science courses and learner academic achievement (Wiersma, 2000).

The total population would be all freshman university science classes. The target population would be

freshman science teachers (and their learners), teaching at a particular kind of university (large public), and in

a speci�c region (Midwestern United States). The sample would be the actual teachers participating in the

study, which would be a subset of the target population. Here, a null hypothesis might predict that there is no

relationship between teaching method and learner academic achievement while the alternative hypothesis is

what the researcher expects to �nd a relationship between teaching method and learner academic

achievement for the speci�c target population. The goal is either to accept or reject the null hypothesis. If the

null is rejected, the alternative hypothesis would be accepted, and vice versa.

Predictions in quantitative research seek to determine to what degree the sample is representative of the

entire target population. Generalization is the term used to refer to this goal. As Reichhardt (2011) stated, "an

effect is generalizable to the extent it varies relatively little across a given range of treatments, recipients,

settings, times, or outcome variables" (p. 51). Generalizability is important in quantitative research because, if

the sample is representative of the target population, researchers can then make predictions about the target

population.

Research Problems Suited for Quantitative Research

Doctoral researchers �rst identify a broad �eld of interest that they may want to study in the dissertation.

Sources used to identify research problems can include literary articles, social, political, or religious issues,

practical workplace situations, topics of personal interest and experience, or extensions of prior research

studies. The most important aspect of identifying the research problem is to thoroughly read the available

research and literature in the �eld of interest to �nd out what has not been studied. This leads to the elusive

problem space that the doctoral study can �ll. A topic of interest does not always make a feasible research

study. Some problems suited for quantitative research may include:

Determining whether the climate of an organization is impacted by the level of emotional intelligence

displayed by the leader.

Determining whether high stakes test scores were improved by learner participation in an accelerated

math curriculum over a 3-year period.

Determining whether the level of moral reasoning of employees is related to or correlates with the

number of years they have spent with a company.

The steps for conducting a quantitative study closely resemble the steps of the scienti�c method:

Identify a problem or problem space based on prior research that is appropriate for a dissertation study.

1. Establish research objectives.

2. Identify the appropriate methodology and design.

3. Plan for and collect data.

4. Process and analyze data.

5. Report and interpret data.

Overview of Quantitative Core Designs While there are a number of designs that are appropriate for quantitative studies, GCU has endorsed speci�c

designs that facilitate a smooth dissertation journey for learners. As shown in Table 4.1, these fall into three

broad categories: experimental research, quasi-experimental research, and nonexperimental research.

Nonexperimental studies can be further classi�ed as descriptive, correlational, and causal-comparative.

GCU Core Quantitative Designs

Experimental

Quasi-Experimental

Descriptive (Survey)

Correlational

Causal-Comparative

Table 4.1

Quantitative Designs, Descriptions, and Examples

Design Description Example

Experimental Used to test an idea, treatment, or program to see if it makes a difference.

The effect of a new discipline plan on student incidences of misbehavior.

Determines if there is an effect/outcome of some form of treatment(s) using random assignment of subjects to treatment and control groups.

A comparison of the effect of direct instruction vs. cooperative groups on students’ ability to compute multistep math equations.There is a control group and a test group.

Individuals are assigned randomly to the two groups.

One group gets the treatment (test group) and the other group (control group) does not get the treatment.

There is a pretest and posttest for both groups in a traditional experimental design.

Standardization of all aspects of research procedures employed to ensure conditions are the same for all participants.

Designed to demonstrate unambiguous cause-and-effect relationship between variables.

Quasi-Experimental Designed to demonstrate cause-and-effect relationship between variables.

Determines if there is an effect/outcome of some form of treatment(s) using preexisting groups of subjects assigned to treatment and control groups.

Does not meet all requirements of an experimental design, thus cannot produce an unambiguous cause-and-effect explanation.

It is the same as experiment in that there is a control and test group; however, current groups are used as is rather than randomly assigning people to the two groups.

Both groups receive the pretest and posttest in a traditional design. Typically no random assignment—participants are in preexisting groups or groups that are formed naturally.

Inclusion of participants in the control or treatment group is determined by conditions beyond the control of the researcher.

Conducted with similar rigor and control as experimental studies with clearly defined treatments.

Design contains a confounding variable or factor that prevents the research from obtaining an absolute cause-and-effect answer.

Nonexperimental Descriptive (Survey)

Describes the opinions, attitudes, or trends of a population numerically.

A description of how parents participate in school activities.

Provides a description of individual variables but is not concerned with the relationship between variables.

A description of the extent to which high school teachers integrate technology into math instruction.

Uses a process of surveying a sample to generalize to the population.

Correlational Determines if there is a relationship between two or more variables on a single group of participants with the intent of predicting or defining a relationship.

The relationship between employee perceptions of servant leadership and job satisfaction.

Observes relationships between variables in a naturally occurring setting.

The relationship between teacher collaboration and student achievement.

Valid approaches to data collection such as validated surveys or databases.

Process for Selecting a Quantitative Design Selecting a method and design for a research study depends on what one wants to accomplish. The focus of

the research must be considered as well as the desired outcomes. Quantitative research is sometimes based on

worldviews of realism or positivism, attempting to disclose an existing reality in a world that functions based

on predictable patterns of cause and effect. The researcher knows a certain truth exists and attempts to

There is a theoretical or logical explanation that can be used to predict a correlation.

Variables should not or cannot be manipulated.

The intent is to determine if and to what degree the variables are related.

It does not imply one causes the other.

Causal Comparative

Compare two groups with the intent of understanding the reasons or causes for the two groups being different.

The effect of preschool attendance on reading ability at the end of the third grade.

Determines the causes of differences that already exist between or within two or more groups on two or more variables.

The effect of gender on math achievement.

Identify one or more groups that serve as the independent variable.

The effect of single- gender schools and student achievement.

Define the dependent variable on which the groups will be compared.

Select sample groups that are as homogeneous as possible.

Note. Adapted from "Nonexperimental quantitative research designs," by J. H. McMillan, 2012, Educational Research: Fundamentals for the Consumer, Chapter 7. Copyright 2012 by Pearson.

uncover facts in a systematic, objective manner (Balnaves & Caputi, 2001). Thus, quantitative research is not in

opposition to the Christian worldview, which asserts that truth can be known. Ultimately, the researcher will

select a method and design based on the problem of the study and the stated research questions.

If the goal of the researcher is to address research questions with a quantitative answer, to be able to

generalize the results of a study to a larger population, or to test a theory numerically, the researcher will select

a quantitative method and design. Suppose a GCU doctoral learner works in a hospital and wants to determine

whether there is a relationship between registered nurses' (RN) perceptions of their nursing manager's

leadership style and RN job satisfaction. This study is an attempt to determine whether a relationship exists

between variables; therefore, a quantitative method and correlational design can be used. The researcher

would include hypotheses that serve as a possible explanation for a factual situation that merits investigation

Thus, quantitative research is appropriate for research questions that need to be answered quantitatively,

when numerical changes are studied or a hypothesis is tested or when one wants to describe the current state

of a situation or explain a phenomenon (Balnaves & Caputi, 2001).

Variables and Subvariables

Variables are the building blocks or foundation of quantitative research. Variables represent the

characteristics of an individual, an event, a group, or an organization that can assume different values or

amounts and can be numerically measured through instruments, surveys, or observations. Variables can vary

in degree or amount (e.g., income level, temperature) or by type or kind (e.g., gender, marital status). Some

variables differ by degree, amount, or level of measurement. Other variables take on a speci�c role, such as

explaining how the world functions, or are used in the implementation of speci�c research designs.

Variables That Differ by Degree, Amount, or Level of Measurement

Nominal variables are considered the most rudimentary level of measurement, and are categorical in nature,

meaning that they are made up of different categories. They cannot be ordered in any speci�c manner; they

are just different. Nominal variables simply name the characteristic being measured, with no ranking. Gender,

religion, marital status, and political party are other types of nominal variables. The attribute is simply named,

but one is not ranked over the other (Trochim, 2006).

Ordinal measures represent variables that can be rank ordered, such as socioeconomic status, education

levels, or grades received in classes; however, the distance between the groups or levels has no meaning. For

example, there is no speci�c or de�ned difference between levels of education. If a researcher were to ask

customers how satis�ed they were with their service, they could offer a survey in which the customers

selected answers on a scale of 1 to 5 with 1 being very satis�ed to 5 being very dissatis�ed. The researcher

could not say that the difference between satis�ed to somewhat satis�ed is the same as being very

dissatis�ed. All he or she could say is that some customers were more satis�ed than others (Trochim, 2006).

Interval variables can be rank ordered, but the distance between the levels or categories has a speci�c

meaning. For instance, temperature has speci�c distance between degrees, or numbers on the Richter scale

that measure the intensity of an earthquake can be interpreted, as they are a speci�ed distance apart (Trochim,

2006).

Finally, ratio variables are similar to interval data, but the ratio data has an absolute zero or has no numbers

below zero. Height and weight are examples of ratio data. If one wants to measure an individual's weight in

pounds, there are speci�c quantities that can be measured in equal units and that measurement cannot go

below zero (Trochim, 2006).

Table 4.2

Nature of Numerical Data Variables

Variables That Take on a Speci�c Role

There are two main types of variables that describe the way phenomena work or that researchers use when

conducting quantitative studies: independent and dependent. Independent variables can stand alone, but they

can also cause changes in other variables. On the other hand, a dependent variable depends on, relates to, or is

caused by other factors. It changes as the independent variable changes. Therefore, independent variables are

the cause of other variables, whereas dependent variables represent the outcome or effect. The dependent

variable is a phenomenon one is attempting to explain or predict. In experimental studies, the independent

variable is the treatment, intervention, or the manipulated variable. In nonexperimental studies, no variables

are manipulated, so the independent variable explains or predicts the dependent variable.

In some quantitative studies, there are extra variables that are not a primary focus but may be related to the

independent or dependent variables. These are called extraneous variables. For example, a researcher wants

to study the relationship between pay and job satisfaction; however, he or she also believes that the workers'

motivation may impact their job satisfaction. The extraneous variable would be motivation. In other studies,

moderator variables may impact the strength of relationship between the independent and dependent

variable. An example of a moderator variable in the above example may be organizational climate.

Sometimes a researcher wants to investigate how one variable affects or impacts the other. An intervening,

mediating, or mediator variable is a causal link between two variables. For example, excessive food

consumption may cause obesity, but another effect can be that the individual becomes diabetic, which is an

intervening variable (Frankfort-Nachmias & Leon-Guerrero, 2006; Trochim, 2006).

Nature Table

Binary Variable Variables that often are listed as zero and one. These are variables that exist in two different states—yes/no, completed/not completed, effective/not effective, exists/doesn’t exist.

Categorical Variable Categorical data. Examples—gender (male/female), married status (married/single/divorced/widowed), employment status (employed/self-employed/not employed), etc. Variables are assigned numerical values, e.g. male=0, female=1. AKA: Nominal Variable.

Continuous Variable A variable that demonstrates continuous movement of time, range and space (e.g. age range, time, size intervals, IQ ranges). AKA: Interval Variable

Dichotomous Variable See Binary Variable

Discrete Variable Variables that can take on a finite number of values (e.g. responses on a five-point rating scale, specific number of integers, finite values). All qualitative variables are discrete.

Interval Variable See Continuous Variable

Nominal Variable See Categorical Variable

Ordinal Variable A variable for which order matters (e.g. scales of measurements, Likert scales)

Table 4.3

Role of Relative Position Variables

Role Table

Confounding Variable An extraneous variable, the presence of which in the study could damage the validity of the research if the researcher fails to control or eliminate it.

Control Variable A variable that the researcher does not want to examine in the study. The variable is controlled.

Criterion Variable The predicted outcome variable in correlational research or a nonexperimental study.

Dependent Variable The predicted outcome variable (attribute or characteristic) of a study. The dependent variable is influenced by independent variables.

Dummy Variable A bucket of binary variables with more than two variables in two categories of variables. For example, marital status—married, single, divorced, widowed—can be bucketed into married or not married.

Endogenous Variable Used in a causal model. It is a variable that is changed by one of the functional relationships within the study or model. For example, changing the income demand curve using quantity and price (variables within the model).

Exogenous Variable A variable that is not within the study or model. The variable is either endogenous (from within the study/model) or exogenous (outside of the study/model).

Independent Variable A variable that affects the outcome of a dependent variable or an outcome. For example, in a study examining the effects of sleep on test scores, sleep is the independent variable.

Intervening Variable A variable that provides a link (causal) between other variables.

Latent Variable A variable that cannot be observed. They exist to define/explain other variables. For example, patterns that underlie specific behaviors related to voting for a president—Republican/Democratic.

Manifest Variable This variable is the opposite of a latent variable. Variables that can be directly observed.

Manipulated Variable An independent variable that is manipulated to determine a particular effect. For example, the amount of helium in a balloon would be the manipulated variable.

Mediating Variable A variable that creates a link between two variables that is causally associated.

Standardized Measurements and Instruments

After a researcher has de�ned the variables present in a situation, he or she must decide how to measure them;

therefore, measures and indicators must be considered. Measures are instruments that directly assess

quantities. For example, if one wanted to ask participants about their level of income, weight, or age, responses

to a survey would measure these variables. Other questions are considered indicators, as they are not direct

numeric measurements.

Selecting a valid and reliable instrument is required for a quantitative study, as one goal of the researcher is to

be able to generalize the results of the study to a larger population. First, the researcher needs to determine the

type of data to be collected by reviewing the stated research questions, determining the scope or parameters of

the study, reviewing the methods that were used in prior research on the topic, and the nature of the data to be

collected (qualitative, quantitative, or both).

At GCU, learners as researchers should become familiar with the instruments used in studies on their

dissertation topic through a thorough review of literature on the topic. This occurs as they develop Chapter 2 of

the dissertation, the literature review. As a doctoral learner considers the proper selection of instruments for

his or her dissertation study, he or she should consider how data on the topic was gathered in prior research

studies, whether the identi�ed instrument is appropriate for the nature or type of data needed, whether the

instrument will collect data to answer all research questions, and whether the instrument is valid and reliable.

Challenges arise when the learner or researcher does not conduct a robust review of prior studies on the topic

and is unaware of the existing critiques of instruments. At times, though better or more robust instruments

may exist, a researcher attempts to use an instrument that has not been tested for reliability and validity, or

the researcher uses an instrument for a population or sample for which the instrument is not intended. At

GCU, learners are discouraged from designing their own quantitative instruments as calibrating the

instrument, �eld testing the questions, and establishing validity and reliability is a study in and of itself, and

outside of the scope of the GCU program timeframe.

Moderating Variable A variable that increases or decreases the proven effect of the independent variable on the dependent variable.

Outcome Variable A variable that is the result the researcher compares in a study or experiment. AKA: Dependent Variable, Response Variable

Polychotomous Variable Variables with more than two possible values. Includes binary variables and categorical variables with multiple categories.

Predictor Variable Predicted cause on a nonexperimental study. Typically used in correlational studies. For example, if studying whether GPA predicts intent to go to college, GPA is the predictor variable.

Treatment Variable See Independent Variable

Table 4.4

Types of Variables Categorized by Level of Measurement

Type of Variable Characteristics Example

Level of Measurement

Nominal/Categorical Most rudimentary level of measurement

Categorical in nature

Cannot be ordered in any specific manner

Gender

Religion

Marital status

Political party

Ordinal Can be rank ordered

Distance between the groups or levels has no meaning

Socioeconomic status

Education levels

Grades received in classes

Interval Can be rank ordered

Distance between the levels or categories has a specific meaning

Temperature

Richter scale

Ratio Can be rank ordered

Has an absolute zero or no numbers below zero

Height

Weight

Role Taken by Variable

Independent Can stand alone

Can cause changes in other variables

In experimental studies, the independent variable is the treatment or intervention, or the manipulated variable.

In nonexperimental studies, the independent variable explains or predicts the dependent variable.

Quantitative data can be gathered from a variety of sources; however, they must be collected systematically

from a prede�ned protocol. Additionally, the instrument used to gather data must be valid and reliable in order

to ensure the study can be replicated and that the results can be generalized to other populations or settings

(Golafshani, 2003). As shown in Table 4.5, data collection instruments can be categorized into two groups:

those the researcher completes, and those participants complete.

Dependent Depends on, relates to, or is caused by other factors

Changes as the independent variable changes

Represents the outcome or effect

The variable is a phenomenon one is attempting to explain or predict.

Mediating/Intervening Causal link between two variables

Moderator Impacts the strength of relationship between the independent and dependent variable

Table 4.5

Quantitative Data Collection Instruments

Sampling Approaches for Quantitative Research

When the researcher is ready to apply the selected data collection instruments, he or she needs to consider

who is going to participate in the study and who will complete those instruments. First, the researcher needs

to always consider the purpose of the study and the practicality as well as strengths and weaknesses of

different sampling methods.

Probability and Nonprobability Sampling

Probability sampling – in this strategy, the sample is speci�cally selected and directly

re�ects the characteristics of this population. Probability sampling provides the most

credible (valid) results because it directly represents the population. Examples of

probability sampling include simple random sampling, strati�ed sampling, and

multistage cluster sampling.

Nonprobability sampling – this strategy is less desirable than probability sampling, as

the sample may not represent the population. This strategy is used when the

researcher does not care about the direct representation, they are not able to obtain a

sample suf�cient for the research, or it is too expensive to obtain a random sample.

Examples of nonprobability sampling include convenience, purposive, quota, or

snowball sampling.

Researcher-Completed Instruments Subject-Completed Instruments

Rating scales, archival databases, media sources Questionnaires, tests, surveys

Interview or focus-group guides Self-checklists

Tally sheets Attitude scales

Flowcharts Personality inventories

Performance checklists Achievement or aptitude tests

Time-and-motion logs Projective devices

Observation forms Stoichiometric devices

Note. Adapted from Research Rundowns > Quantitative Methods > Instrumentation, Validity, Reliability by Research Rundowns, 2009. Retrieved from https://researchrundowns.�les.wordpress.com/2009/07/rrinstrumentvalidityreliability_72009.pdf

Every researcher has to select a sample or participants from a larger population. For the dissertation study, the

population includes the people or units that will be addressed by the research problem and research questions.

For example, the population of interest to the researcher may include teenage males in K-12 schools in the

United States, if the goal of a study is to determine whether a relationship exists between socioeconomic

status and academic achievement. In quantitative studies, the researcher should strive to select a

representative sample from the population, meaning that the group of individuals selected will produce results

that can be generalized to that larger population.

The sampling frame includes the group of people who can be realistically selected for the sample, or to be

recruited to participate in the study. For instance, in the previous example about teenage males in K-12

schools, the researcher may only have access to learners in one school district located in Georgia; therefore,

only learners in those schools will be recruited to participate in the study. This sample represents some bias as

the researcher wants to be able to generalize the results of the study but the demographics of the learner

sample from one district in Georgia may be different than other schools in the United States. The researcher

will, therefore, acknowledge the bias, which is relatively common in dissertation studies. Ultimately, the

sample includes the actual individuals who consent to participate in the study. Figure 4.1 includes a graphic of

the population, target population, sample, and data collection.

Questions to Consider When Selecting an Instrument

Consider the following questions as you make your decision:

Will you use an existing instrument?

What permissions do you need if you are using an existing instrument?

Are you considering creating your own instrument?

Will you access data from a database?

Do you have permission to use existing database information, or does the

database contain public information?

Are you using pretests and posttests (for experiment or quasi-experiment designs)?

Do you need permission to use the tests for research?

Are the tests valid?

Are the tests suitable for retesting at different time points?

Is there another source for data other than an instrument, database, or tests?

What is the source of data?

Sample Size

The sample size of a study is determined by the required or desired level of statistical signi�cance. Larger

samples reduce the risk of statistical errors and improve the statistical power and con�dence of the data. In

the most simplistic form, a sample should be equivalent to √N where N is the size of the population. For

example, if the population is the 150 �fth-grade learners at ABC Elementary School, a reasonable sample would

be 150≈12.24 learners. Because the measure of number of learners is a discrete measure, the minimum sample

size required is 13 learners. Advanced data analysis techniques require more advanced calculations of sample

size.

Sampling Strategies

There are two basic kinds of sampling: random and nonrandom. Random sampling means that every unit in

the established sampling frame has an equal chance of being selected. This should result in the sample

representing the larger population from which it is drawn. There are four types of random sampling: strati�ed,

systematic, cluster, and multistage. Strati�ed random samples occur when the population is divided into strata

or levels, and the sample is randomly selected from each level. In systematic sampling, the researcher

systematically selected every nth individual from a list of people. Cluster sampling occurs when the

population is divided into groups, and individuals are then randomly selected from each group. Multistage

sampling occurs when the researcher wants to combine different random sampling strategies hierarchically

from this group.

Figure 4.1

Population, Target Population, and Sample

When a researcher employs nonprobability sampling, he or she does not use random techniques. This

sampling strategy is not as reliable or powerful as random sampling, as the results cannot always be

generalized to a larger population; therefore, the researcher relies on more haphazard methods of recruiting

people to participate in the study. There are several types of nonprobability sampling. At GCU these usually

include convenience, purposive, or snowball samples. When applying a convenience sampling strategy, the

researcher selects units or individuals from a group that is readily available. A purposive sample is comprised

of a prespeci�ed group of individuals that the researcher speci�cally seeks out to recruit for participation in a

study. Usually these individuals have speci�c characteristics, such as males age 18 and older attending

alternative schools in Georgia. Finally, snowball sampling is used when the researcher recruits initial

individuals who participate in a study, and then those individuals may provide names of other people who

could be contacted to complete data collection instruments. Table 6.6 contains the most common sampling

strategies used at GCU.

Reliability and Validity in Quantitative Studies

Reliability in quantitative research focuses on the degree to which the variable is consistently measured.

Because instruments such as surveys are used to measure variables, then a reliable instrument is one that will

gather reasonable and plausible data and produce similar results consistently over time. Test-retest reliability

and inter-rater reliability are two types of reliability that researchers address in quantitative studies. In order

Table 4.6

Quantitative Sampling Strategies

Type of Sampling Strategy De�nition

Random sample Every participant has an equal chance of being selected.

Accidental, haphazard, or convenience sampling Participants are sampled according to what is conveniently, accidentally, or haphazardly available.

Researcher selects participants who are readily available.

Purposive sample Participants from a prespecified group are purposively sought out and sampled

Researcher selects participants based on predefined criteria.

Snowball sample Initial participants are sampled, and then they identify more people to sample, and so on.

to establish test-retest reliability, the researcher administers the same instrument at two given times, and one

person scores the instrument. In order to establish inter-rater reliability, one version of the instrument is

administered at one time, and two people score it. Then, their scores are compared (Golafshani, 2003).

Validity refers to the degree the �ndings of the research can be applied or trusted. Whereas reliability is

concerned with the consistency of which a variable is measured, validity focuses on whether an instrument

measures what it is intended to measure. For instance, if a participant's height is measured three times, it is

likely that the measurements will be consistent or reliable. However, a researcher could not measure a

participant's height and claim that this is an accurate or valid measure of intelligence. Therefore, a valid

instrument allows the researcher to draw meaningful and useful inferences from the scores on the

instrument. If a participant took the SAT �ve times, the scores should be roughly consistent and, therefore,

reliable; the SAT should also be a valid measure of what a student learned in high school. In general,

quantitative researchers must consider three types of validity. Content validity refers to whether the questions

are representative of all questions on the topic. Criterion related validity refers to how well the scores on an

instrument relate to and predict an outcome. The criterion is the condition or standard by which people differ.

Construct validity refers to what the scores mean (Golafshani, 2003).

Validity assumes reliability. If a researcher has an unreliable or unstable variable, it is not valid. An unreliable

variable can change over time and cannot provide a true indication of what it is supposed to measure. If

variables are internally unreliable, then they measure more than one concept and then do not accurately

measure the concept under study (Golafshani, 2003).

Common Approaches to Quantitative Data Analysis

Researchers collect quantitative data and then analyze that data to discover and describe patterns.

Types of Variables

When determining what statistical tests to run on a variable, it will be important to know

both the nature of the numerical data provided by the variable and the speci�c variable type

identi�ed by your data source for the variable.

There are speci�c terms that describe variables used in research studies. There are two

different sets of terminology for variables. The �rst set of terminology describes the nature of

the numerical data that you collect and is de�ned by the data source you use. These

Table 4.7

Three Kinds of Analysis

Univariate Analysis Descriptive statistics describe the distribution of variables

Bivariate Analysis Analysis of the relationship between two variables

Multivariate Analysis Analysis of the relationship between more than two variables

variables include binary/dichotomous variables, categorical/nominal variables,

continuous/interval variables, discrete variables, or ordinal variables. For example, in a two-

way ANOVA analysis of learner test score, you may group the learners into two different

instructional methods and two gender groups within each instructional method, so

instructional method and gender are the categorical variables (or binary/dichotomous

variables if there are only two levels within each category) for the study, while test score is

the continuous/interval (or "scale" in SPSS language).

The second set of terminology describes the role of/or relative position of the variable(s) in

your study. These variables include confounding, control, criterion, dependent, dummy,

exogenous, independent, intervening, latent, manifest, manipulated, mediating, moderating,

outcome, polychotomous, predictor, and treatment variables. Depending on the research

design, you will use the relevant terms to describe the variables in your study. For example,

in a multiple regression analysis of learner test scores, you could use hours of study,

instructional method, gender as predictor variables and the test score as an outcome or

criterion variable.

Univariate Analysis

In Chapter 4 of the dissertation at GCU, the researcher will use descriptive statistics to describe the sample and

some of the data collected. Often, tables and graphs are used for this purpose. The sample, for example, may be

described in a table displaying the age, gender, job role, and years of experience of the sample. Other graphics,

such as histograms, are used to show the distribution of data along a continuum with no problem spaces. The

researcher may use a histogram to show the years of education for the sample. Frequency distributions are

often used to demonstrate how often a particular score or range of scores appears in the data set.

Measures of central tendency are used to summarize the mean, median, and mode of a data set. The mode is

the most frequently occurring value, the median is the middle value (i.e., divides the distribution in half), and

the mean represents the average value. Other summary statistics can include the range and distribution of

data. The range includes the entire possible set of data from the lowest to highest point. The standard

deviation, or distance, from the mean is often calculated.

Parametric vs. Nonparametric Tests

Based on the way data are distributed, the researcher will conduct parametric or nonparametric tests.

Parametric tests are used when the data assume a normal distribution, meaning that half the points fall

equally on either side of the mean. Nonparametric tests are used when the data are not normally distributed.

Therefore, no assumptions can be made about the form or boundaries of the population distribution from

which the study sample was recruited. When data are normally distributed and parametric tests are used,

then tests of assumptions must be calculated including normality tests to see if the data is normally

distributed, (approximating a normal or "bell-shaped" curve) and possibly homoscedasticity tests (required for

some statistical analyses such as ANOVA) to see if the data values are spread out to about the same degree. If

the assumptions are not met, the researcher may need nonparametric tests instead of typical inferential

statistical tests. The researcher may need to normalize the data if using different tests to allow for the

comparison of the raw scores on different tests. In this case, the researcher would calculate the z-scores to

normalize or standardize the data from the two tests.

Bivariate and Multivariate Analysis

Bivariate and multivariate analyses are used to determine if a relationship exists between two or more

variables, respectively. Inferential statistics estimate the degree of con�dence that can be placed in

generalizations from a sample to the population from which the sample was selected.

Steps for Conducting Quantitative Data Analysis The following steps are followed for conducting quantitative analysis of data:

1. Clean and prepare data.

2. Compute descriptive statistics.

3. Conduct assumptions testing (not used with descriptive/survey design).

a. Normality

b. Homoscedasticity

c. Nonparametric tests

4. Calculate z- or t-scores.

5. Perform inferential statistics if assumptions are met.

6. Use nonparametric techniques if assumptions are not met.

Table 4.8

Parametric and Nonparametric Tests

Table 4.9 shows the inferential statistical tests most commonly performed. For example, the t-test is used to

see whether there is a signi�cant difference for the means between two samples or groups.

Bivariate, Multivariate

Type Example Parametric test

Nonparametric test

Bivariate Compare the difference between two distinctively different groups.

Is there a difference in the mean math scores of students who participate in a technology-rich math class versus those who do not?

Two sample t- test

Wilcoxon rank-sum test

Bivariate Compare two quantitative measures completed or taken from the same person.

Is there a significant change in the mean math scores of students who participate in a technology-rich math class for a 16-week semester?

Paired t-test Wilcoxon signed- rank test

Multivariate Compare means between three or more distinctively different groups.

If the math class has three groups (those who experience traditional instruction, those who have access to technology in the classroom on a daily basis, and those who go to the computer lab once a week), how will their mean scores differ over time?

Analysis of variance

Kruskal-Wallis test

Bivariate Estimate the degree of association between two variables.

Is student math achievement associated with gender?

Pearson coefficient of correlation

Spearman’s rank correlation

Table 4.9

Parametric vs. Nonparametric Tests

There are resources and information doctoral learners can use to determine the best approach for their

dissertation study. These include:

1. Books from methodology, design, and statistical analysis classes,

2. SAGE research resources (i.e., books and articles) in the GCU Library databases, and

3. Resources such as YouTube.

In all cases, the credibility of the resource must be considered.

Designs Using Quantitative Data Analysis in Quantitative Studies

Sometimes researchers will use quantitative data in qualitative studies. As noted earlier, the researcher often

uses descriptive statistics to provide a summary of the sample in terms of demographics such as age, gender,

and number in each category. In qualitative studies, such as case studies and grounded theory studies, the

researcher will often use descriptive statistics to provide counts of words in interview transcripts to establish

patterns and codes. Inferential statistics and causal statistics can also be used in qualitative case studies.

Conclusion Quantitative research offers a systematic and structured process for answering research questions.

Quantitative studies are often used in the social sciences, as they are quick, considered to be scienti�cally

valid, and establish important �ndings for the researcher. Quantitative studies require the use of statistical

techniques and a structured data collection plan to ensure that the study can be replicated. Additionally,

quantitative studies require the use of valid and reliable instruments, surveys, or databases to quantify

variables.

There are several quantitative designs GCU suggests researchers use. These include experimental,

nonexperimental, and quasi-experimental studies. Under the quasi-experimental umbrella, researchers can

select descriptive, correlational, or causal-comparative designs. Ultimately, the method and design will be

determined by the goals of the research and research questions. Quantitative researchers must carefully

Parametric Tests Nonparametric Tests

t-test (independent means) Mann-Whitney U test

t-test (correlated means) Kruskal-Wallis one-way analysis of variance Sign tests

ANOVA (ANalysis Of VAriance) Friedman two-way analysis of variance

ANCOVA (Analysis Of COVAriance) Chi square (for categorical data)

MANOVA (Multivariate Analysis Of Variance)

t-test for r

t-test for difference in proportions (for categorical data)

construct a data collection plan, use valid and reliable instruments, consider appropriate sampling strategies,

and understand the nature of the variables used in the study. These factors will dictate the statistical analysis

conducted in efforts to glean results that can be generalized to a larger population.

Checks for Understanding 1. What are the GCU core designs for quantitative research?

2. How does a researcher know which quantitative design is right for the research project, if one is right at

all?

3. Why is instrument selection important in quantitative research?

4. How are sample size and sampling approach determined in quantitative research?

5. How are quantitative data analysis methods selected?

References American Psychological Association. (2020). Types of articles and papers. In American Psychological

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Balnaves, M., & Caputi, P. (2001). Introduction to quantitative research methods: An investigative approach.

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research. British Journal of Nursing, 16(11), 658–663. https://doi.org/10.12968/bjon.2007.16.11.23681

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281–302.

Dew, D. (2008). Construct. In P. J. Lavrakas (Ed.), Encyclopedia of survey research method (pp. 134–135). SAGE.

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Answers

1. They are experimental, quasi-experimental, descriptive (survey), correlational, and

causal-comparative.

2. If the goal of the researcher is to address research questions with a quantitative answer,

to be able to generalize the results of a study to a larger population, or to test a theory

numerically, the researcher will select a quantitative method and design.

3. This is signi�cant because one goal of the researcher is to be able to generalize the

results of the study to a larger population.

4. The sample size of a study is determined by the required or desired level of statistical

signi�cance. Sampling strategy is largely determined by the availability of sample

populations related to the study.

5. The researcher must know both the nature of the numerical data provided by the

variable and the speci�c variable type identi�ed by the data source for the variable.

Freedman, D., Pisani, R., & Purves, R. (2007). Statistics (4th ed.). W. W. Norton & Company.

Gelo, O., Braakmann, D., & Benetka, G. (2008). Quantitative and qualitative research: Beyond the debate.

Integrative Psychological and Behavioral Science, 42(3), 266–290. https://doi.org/10.1007/s12124-008-9078-

3

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