Introduction Part 1 Using the Shi et al. (2017) article from this weeks readings and a published study in which factor analysis

Running head: FACTOR ANALYSIS 1

Explore the Relationship Between Factor Analysis and Survey Design

Joshua Lane

Northcentral University

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FACTOR ANALYSIS 2

Explore the Relationship Between Factor Analysis and Survey Design

To explore the relationship between factor analysis and survey design requires a

conversation about confirmatory analysis. As a statistical tool used to interpret and evaluate data,

the analysis has been beneficial for surveys and questionnaires within research. These benefits

stem from the two types of factory analysis; confirmatory factor analysis (CFA) and analysis

exploratory factor analysis (EFA). This assignment was designed to discuss the relations of a

factor analysis and survey design. To achieve such objective, a comparison will be done between

two articles that uses the factor analysis tool. It will be used to gain a new perspective on how

researchers utilize the statistical tool.

Factor analysis is a functional tool that is used in statistics. It is useful for describing

factors within a questionnaire that can be associated with research or even tracking patterns

across multiple variables. Prudon (2015) defines the analysis as a research tool used to predict a

test’s factor structure and then compares the results with the structure’s item scores derived from

an empirically based analysis. This tool is a test of validity of the test items, justification of the

prediction, and validity of the test’s constructs altogether (Prudon, 2015). For the past 20 years,

confirmatory factor analysis has illustrated the variances between the empirical and predicted

factor structure simultaneously considering the model fit while the factor loadings and

modifications are providing feedback (Prudon, 2015).

For the validation of a construct’s questionnaire researchers utilizes the confirmatory

factor analysis when the test is multidimensional. Knowing this, Prudon (2015) calculates a

covariance matrix with the scores from a number of subjects and the confirmatory factor

analysis. Then an observation of whether a presumed factor structure or pattern has been

contradicted by the matrix occurs (Prudon, 2015). Because Confirmatory factor analysis is a

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FACTOR ANALYSIS 3

complex analysis it usually runs in conjunction with structural equation modeling (SEM).

Researcher Prudon (2015) defines SEM as a sophisticated statistical tool used for testing

complex theoretical models on data. Solely for the measurement parts of the models,

confirmatory factor analysis not only uses SEM, but LISREL, AMOS, which is included in

SPSS, EQS, and Mplus (Prudon, 2015). These computer programs have become extremely

popular and accessible to the personal computer which has heighten the use of the analysis.

Article Regarding Confirmatory Factor and Rasch Analyses

Confirmatory factor and Rasch analyses were used to accomplish the aim of this study

which was to evaluate the factor structure using in healthy firefighters. It developed a 14-item

organizational, policies, and practices scale by adding three additional items to an already

existing ergonomics subscale. This was accomplished by gathering enough data to produce a 261

sample of firefighters (Shi et al., 2017). The approach was to use the confirmatory factor and

Rasch analyses to assess the 14-item scale’s psychometric characteristics, internal consistency,

and factor structure. In conclusion, a solid factor structure and the firefighters’ internal

consistency was revealed. The CFA confirmed the consistency of the original structure with the

comparative fit index (CFI) being 0.97, Tucker Lewis Index (TLI) being 0.96, and the Root

Mean Square Error of Approximation (RMSEA) being 0.053 (Shi et al., 2017). There were five

items showing as misfits that were rescored and then four subscales satisfied Rasch’s

expectations with an acceptable reliability (Shi et al., 2017).

Article Regarding Dimensionality of the system usability scale among professionals using

internet-based interventions for depression: Confirmatory Factor Analysis

The aim of this study was to assess the factor structure of the System Usability Scale

(SUS), measuring usability of internet based Cognitive Behavioral Therapy for depression in a

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FACTOR ANALYSIS 4

sample of professionals. Their psychometric properties, convergent validity and reliability of the

SUS was tested. The SUS was made up of 242 professionals from six different European

countries. A confirmatory factor analysis was conducted to determine the best fit of a one-factor,

two-factor, tone-model or bi-direct model. Complementary statistical indices were used to assess

reliability and to assess convergent validity while the SUS total score was correlated with an

adapted Client Satisfaction Questionnaire (Mol et al., 2020). According to Mol et al. (2020) the

one-factor, two-factor and tone-model was supported by CFA, but the bi-factor model was the

best fitted. Reliability of the SUS was good, and the total SUS score correlated moderately

indicating the convergent validity (Mol et al., 2020).

Comparison of the Articles

Both articles utilized the confirmatory factor analysis. The statistical tool helped render

conclusions the researchers eagerly worked to see. Questionnaires were included in both articles

along with four models to be analyzed. Samples exceeded 200 for both studies as well. Bandalos

(2014) and Forero et al. (2009) collectively agree on the recommended sample size is between

200-500 to gain sufficient estimations. In both articles, the best fitted constructs, had a high

comparative index fit, greater than or equal to 0.95, and a high Tucker-Lewis Index, also

exceeding 0.95. These are interpreted as incremental fit indices that compared the both the

hypothesized and original model. While the most popular measure of model fit is the RMSEA,

authors MacCallum et al. (1996) would consider the two studies results of 0.05 but less than

0.08 as a good fit.

Difference Within the Articles

The article regarding confirmatory factor analysis used the Rasch model to assess the

psychometric properties of its constructs. The researchers employed the Rasch approach to

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FACTOR ANALYSIS 5

evaluate the structures unidimensional four subscales. On the other hand, the article regarding

the dimensionality of the system usability scale, applied further analysis towards psychometric

properties of their factor structure. As their two-factor model, usability and learnability were

viewed as two different factors worthy of a statistical approach.

Organizational Leadership

As a graduate student pursuing a degree in the organizational leadership program, the use

of conformity factor analysis has been used to further interpret data collected for statistical

purposes. For instance, researchers Alias et al. (2015) engaged in a study that observed a

measurement model for leadership skills. According to the authors of the research, a major

criterion for employers in recruiting employees is leadership (Alias et al., 2015). The aim was to

measure the validity and reliability of the instrument in relation to leadership (Alias et al., 2015).

The confirmatory factor analysis, the comparative fit index value, Tucker Lewis Index and

RMSEA was used to verify factors. The findings from this research demonstrated that a

leadership model for employers and Higher Education Institutions in the nation could be

developed. The confirmatory factory analysis helped the researchers inform leaders and

confirmed their significant influence on the behavior and performance of those underneath.

Conclusion

This assignment was designed to explore the relationship between factor analysis and

survey design. It brought awareness to confirmatory factor analysis and how it can be performed

in research. Two articles were reviewed and compared to one another with the intentions to see

how different researchers’ perspective and uses of the statistical tool. Organizational leadership

was later discussed in reference to a research interest and how the analysis has already been

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FACTOR ANALYSIS 6

used. The confirmatory analysis has helped support hypotheses of a relationship between

observed variables and their underlying latent constructs.

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FACTOR ANALYSIS 7

References

Alias, R., Ismail, M., & Nurhanis, S. (2015). A Measurement Model for Leadership Skills Using

Confirmatory Factor Analysis (CFA). Procedia – Social and Behavioral Sciences. 172.

717-724.

Bandalos, D. (2014). Relative performance of categorical diagonally weighted least squares and

robust maximum likelihood estimation. Structure Equality Model Multidiscipline.

Forero, C., Maydeu-Olivares, A. & Gallardo-Pujol, D. (2009). Factor analysis with ordinal

indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structure

Equality Model.

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and

determination of sample size for covariance structure modeling. Psychological

Methods, 1, 130-149.

Mol, M., van Schaik, A., Dozeman, E., Ruwaard, J., Vis, C., Ebert, D. D., Etzelmueller, A.,

Mathiasen, K., Moles, B., Mora, T., Pedersen, C. D., Skjøth, M. M., Pensado, L. P., Piera-

Jimenez, J., Gokcay, D., Ince, B. Ü., Russi, A., Sacco, Y., Zanalda, E., & Zabala, A. F.

(2020). Dimensionality of the system usability scale among professionals using internet-

based interventions for depression: a confirmatory factor analysis. BMC

Psychiatry, 20(1), 1–10.

Prudon, P. (2015). Confirmatory Factor Analysis as a Tool in Research Using Questionnaires: A

Critique,. Comprehensive Psychology.

Shi, Q., MacDermid, J., Tang, K., Sinden, K., Walton, D., & Grewal, R. (2017). Confirmatory

Factor and Rasch Analyses Support a Revised 14-Item Version of the Organizational,

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FACTOR ANALYSIS 8

Policies, and Practices (OPP) Scale. Journal of Occupational Rehabilitation, 27(2), 258–

267.

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1 Running Head: EXPLORE

Explore the Relationship between Factor Analysis and Survey Design

Nikki Owens

BUS-7106: Statistics II

Northcentral University

Dr. Fred Rispoli

June 6, 2021

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2 EXPLORE

Explore the Relationship between Factor Analysis and Survey Design

Introduction

“Factor analysis is a way to take a mass of data and shrink it to a smaller data set that is

more manageable and more understandable. It’s a way to find hidden patterns, show how those

patterns overlap and show what characteristics are seen in multiple patterns. Also used to create a

set of variables for similar items in a set” (Glen, 2021).

This assignment is about exploring the relationship between factor analysis and survey

design. To compare the relationship between factor analysis and survey design requires the

researcher to talk about confirmatory analysis. Confirmatory analysis has been used as a

statistical tool in the form of surveys and questionnaires for many research papers and articles

and is very beneficial to the researcher when analyzing results. Confirmatory analysis benefits

are formed from the two types of factor analysis. These two types of factor analysis are

confirmatory factor analysis (CFA) and exploratory factor analysis (EFA).

Confirmatory factor analysis (CFA) “is used for verification as long as the researcher has

a specific idea about the pattern or structure the data is or how many dimensions are in the set of

variables” (Glen, 2021). Exploratory factor analysis (EFA) “is when the researcher has no idea

what pattern or structure the data is or how many dimensions are in the set of variables” (Glen,

2021). Thus, this paper will summarize and compare two articles that use factor analysis. These

two articles will help understand how researchers use these types of statistical tools in their

research. The paper will end with a conclusion of the assignment followed by reference list.

Article 1: Confirmatory Factor and Rasch Analyses

This article is about confirmatory factor and Rasch analyses being used to develop the

14-item organizational, policies and practices (OPP) which led to the aim of the study. The aim

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3 EXPLORE

of the study is to evaluate the factor structure for healthy firefighters. The 14-item OPP was

developed from an existing 11-item ergonomic scale by adding 3 additional items. The 14-item

OPP was accomplished by collecting data from a sample size of 261 healthy firefighters. The

goal was to use the confirmatory factor and Rasch analyses to “assess the internal consistency,

factor structure and psychometric characteristics of the OPP 14-item ergonomic scale” (Shi et al.,

2017). Based on the results of the analyses, a factor structure and internal consistency in the

healthy firefighters was determined. “The confirmatory factor analysis determined that the fit

index was 0.97, the Tucker Lewis index was 0.96 and the root mean square error of

approximation was 0.053 based on the consistency of the structure. The analysis showed 5 items

with misfits that were rescored and 4 subscales that satisfied the Rasch test analysis with a well

target and acceptable reliability” (Shi et al., 2017).

Article 2: Confirmatory Factor and Rasch Analyses to examine the dimensionality of The

Patient Assessment of Care for Chronic Illness Care (PACIC)

This article is about confirmatory factor and Rasch analyses being used to examine the

dimensionality and psychometric properties of the Patient Assessment of Care for Chronic Illness

Care (PACIC) (Lambert et al., 2021). Data was collected from a sample size of 221 Canadian

adults in the form of an online survey. These adults who participated in the online survey had one

or more physical and/or mental chronic diseases they were living with daily. The goal was to use

the confirmatory factor and Rasch analyses to examine the properties of the PACIC. The

properties that the Rasch analyses wanted to study was item/person misfit, reliability, response

format, targeting, unidimensionality of subscales, and differential item functioning (DIF). The

properties that the confirmatory factor analysis wanted to study was the factor structures

(Lambert et al., 2021). Based on the results of the analyses, patient activation, delivery system,

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4 EXPLORE

and problem-solving subscales all satisfied the Rasch test analysis. It was found that item 10 had

a disorder and was recoded to correct the disorder. Out of the 5 follow-up subscale items, 4 had a

disorder and was recoded also. All the subscales were found to be unidimensional and no

dependency were located. The DIF was only found in some of the items in the subscale. As for

the confirmatory factor analysis, it was found that none of the factor structures were right for the

data. In the end, it was found that with some modifications, some of the items in the subscale

became psychometric (Lambert et al., 2021).

Comparison of Articles

In comparison, both articles used the confirmatory factor analysis. The confirmatory

factor analysis helped the researchers solve the results they were wanting to determine. Surveys

were used to collect the data in both articles. The sample size for both studies were over 200

participants and the participants were from Canada for both studies. After running the analysis

for both articles, the findings were similar and the results the researcher was working towards

were determined. Both articles also used the Rasch analysis in addition to the confirmatory factor

analysis.

Contrast of Articles

In contrast, one article used healthy firefighters and the other article used adults with one

or more physical and/or mental chronic illnesses for the study. In the first article, the factor

structure was found to be promising but in the second article, the factor structure was not a fit for

the data after analyzing the information for both studies.

Advanced Accounting

As a graduate student pursuing a PhD in Business Administration with Advanced

Accounting program, factor analysis is used to help business owners maximize profit by helping

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5 EXPLORE

with production output to increase revenue. For example, a study was found that is related to

advanced accounting. This study used exploratory factor analysis to identify dimensions for non-

banking financial institutions due to the dimensions causing non-performing assets (Rajeev &

Subramoniam, 2017). The purpose of the study is to verify the factors that are causing the non-

performing assets to happen. The exploratory factor analysis and a questionnaire was used to find

the causing factors. Based on the analysis findings, 3 components were found to be the factor.

These 3 components were “professional incapability of the borrower in running the firm,

borrower nature in wilful default and his/her influential nature on financial institution and

government, and weak internal policy of the firm or external environment which aid non-

repayment of loan” (Rajeev & Subramoniam, 2017). The exploratory factor analysis helped the

researcher come up with a solution that will help non-banking financial institutions control non-

performing assets and become profitable going forward.

Conclusion

In conclusion, this paper was about exploring the relationship between factor analysis and

survey design. The two factor analyses were explained. Two articles were summarized and

compared/contrasted. Advanced accounting was explained by stating how factor analysis is

employed within the field followed by a study used as an example to advanced accounting. This

assignment has helped me understand how factor analysis is used as a statistical tool for research.

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6 EXPLORE

References

Glen, S. (2021). Factor Analysis: Easy Definition. Retrieved from

Lambert, S., McCusker, J., Belzile, E., Yaffe, M., Ihejirika, C., Richardson, J., & Bartlett, S.

(2021). Using confirmatory factor analysis and Rasch analysis to examine the

dimensionality of The Patient Assessment of Care for Chronic Illness Care

(PACIC). Quality of Life Research: An International Journal of Quality-of-Life Aspects

of Treatment, Care and Rehabilitation – An Official Journal of the International Society

of Quality-of-Life Research, 30(5), 1503. https://doi-org.proxy1.ncu.edu/10.1007/s11136-

020-02750-9

Rajeev, K. S., & Subramoniam, S. (2017). Exploratory Factor Analysis for the Identification of

Dimensions Which Cause Non-Performing Assets in Non-Banking Financial

Institutions. International Journal of Financial Management, 7(2/3), 60–74.

Shi, Q., MacDermid, J., Tang, K., Sinden, K., Walton, D., & Grewal, R. (2017). Confirmatory

Factor and Rasch Analyses Support a Revised 14-Item Version of the Organizational,

Policies, and Practices (OPP) Scale. Journal of Occupational Rehabilitation, 27(2), 258–

267.

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BUS-7106-6

Explore the Relationship between Factor Analysis and Survey Design

Professor:

Course ID: BUS-7106 V1

1

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BUS-7106-6

Introduction

Article I: Using Factor Analysis to Investigate the Impact of Accommodations on the Scores

of Students with Disabilities on a Reading Comprehension Assessment.

Linda C., Eignor J., Steinberg Y. (2017). Journal of Educational Testing Service. Vol. 13, P.276

The Act of No Child Left Behind in 2001 mentions that the states, schools and districts, are

responsible for all the students’ academic successes, which includes the students who have

disability. However, this matter is very important for the school districts and the states for

implementation, and would be challenging the time is applied for disabled students.

In this research study, the tests are done without and with a read-aloud test subjects which

was administered by utilizing the CD (compact disc) player using headphones. Confirmatory and

exploratory factor analyses have been utilized for evaluating the GMRT Comprehension subtest

that if is calculating the same underlying construct while administering by considering a read-

aloud testing change. Different research studies about the impact of audio presentation were

analyzed by researchers shows no development for students with or without disabilities or the

same impact for the both groups. Sample sizes might have explained the different outcome

between different studies show the interaction model testing for differential boosting. All students

in the standard situations had the assessment with instructions about how to do the test and the

passages loudly with their pace choices. The research purpose was to study about the effect of a

read-aloud test change administered by the Gates-MacGinitie Reading Test (GMRT) by

considering the measurement of underlying constructs by the subset comprehension. The study

research evaluating the factor structures for the Comprehension subtest of level four

which was given to the fourth-grade students as a sample in the New Jersey. Some of the students

were disable and some other students had not any disability regarding to reading-based learning

2

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BUS-7106-6

disabilities. Both factor analyses, confirmatory and exploratory, have been used to show if the

measurement of GMRT Comprehension subtest the same underlying constructs when

administered for the read-aloud test change. The analyze results showing the factorial invariance

which is held the time that Comprehension subtest was applied to the students’ group that have not

disabilities and took the test in the standard a read-aloud test change conditions.

However, for evaluating the test’s structure, the authors supposedly, should take out the

components analyze principal on the correlations matrix from the six subtests making up the

test for the examinees’ group which is indicated that a single factor was enough in order to

summarizing data. The authors clearly included the results of the research which is indicated

that a one-factor model might be utilized for explaining the data of students with disabilities and

the normal form for the students without disabilities. The study is focused to analyses, compare

and determine the number of factors for the students without or with disabilities taking the S

factor for GMRT.

Method

Summary of

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