Factor Analysis Paper

This paper discusses the methodology, results, and analysis of a factor analysis study on the big five personality traits in Inuit children aged between 9 and 12 years. The study used a 25-item questionnaire that is IPIP scale sensitive to capture the responses of the children. The objective of the study was to ensure that each set of five questions measure the same personality.

Running head: FACTOR ANALYSIS 1
Factor Analysis Paper
Student’s Name
Professor’s Name
Affiliation
Date

FACTOR ANALYSIS 2
Factor Analysis
Methodology
A 25-item questionnaire that is IPIP scale sensitive was used to capture the responses of Inuit children
aged between 9 and 12 years; A set of five questions was used to represent each of the big five personality
traits i.e. OCEAN. The term OCEAN refers to openness, conscientiousness, extraversion, agreeableness, and
neuroticism. The questions are randomly placed to ensure that the respondents do not offer biased answers that
distort the truthfulness of the information gathered. A 5-point Likert-scale is used to measure the responses
provided by the Inuit children. The response options are given on a scale of 1 (strongly disagree) to 5 (strongly
agree). The hypothesis being evaluated is that the questions given through the IPIP-25 questionnaire effectively
measure each of the big five personality traits in Inuit children aged 9 to 12 years. Therefore, factor analysis is
facet of data reduction that seeks to establish correlation between a set of variables in a data set. The correlation
between the variables can be explained by an overall outcome. For example, if there is correlation between five
questions in the same category, then it is expected that the association between the variables can be explained
by a given personality trait. And as a result, we are able to report that those five correlated questions are can be
used in a research situation to gather information about the underlying personality trait. Hence, the objective of
performing a factor analysis in this study is to ensure that each set of five questions measure the same
personality (Williams, et. al., 2010).
According to provisions in the IPIP scales the 25 question are categorized as followed with regard to the
specific personality trait they are hypothesized to measure: extraversion (4,6,14,20,25); neuroticism
(5,8,11,15,24); openness (3,9,10,21,23), agreeableness (1,7,12, 16,18) and conscientiousness (2,13, 17, 19,22).
The 25-IPIP questionnaire then used to gather data from 1,006 respondents (Inuit children aged between 9 years
and 12 years). The questionnaires were issued randomly to potential respondents to eliminate biasness and
thereby increase the reliability of the information collected. The data will be assessed in SPSS with regard to
principal component analysis, parallel analysis, and finally the factor analysis will be performed. The principal

FACTOR ANALYSIS 3
component analysis is meant to aid with segmentation of large datasets into small groups that provide sensible
information. With regard to the parallel analysis the “rawpar.sps” syntax will be used given 95% confidence
interval, 1006 individuals, and 500random matrices. The results will be presented in the result section of this
assessment. The discussion segment will discuss the various implications made by the findings with regard to
exhibition of the big five personality traits in Inuit children. Finally, the research conclusion will
document/summary the overall insight gathered through the assessment of previous studies, data analysis, and
discussion of results (Lopez & Whitehead, 2013).
Results
Principal Component Analysis using Scree Plot
With regard to principal component analysis we can look at the solution below and conclude that we are
expected to retain only 6 components out of the 25 given. It is clear when the cut off is or where the plot starts
to form a scree this takes place below an Eigen value of 1. In this unrotated factor analysis we see that the basis
for the selection of components was based on an Eigen value of 1 as well. We see that the remaining 19 values
cannot be considered because they are below the cutoff of greater than or equal to 1 Eigen value (Mishra, et al.,
2017).

FACTOR ANALYSIS 4
Parallel Analysis
From the table of raw data Eigen values, means, and percentiles, we are able to compare the rawa data to
the 95% confidence level values. If the raw data Eigen values are larger than the values given for 95%
confidence level then we will retain that root. From the tables we can see that the express Raw data≥ Perctil e
holds for the first five roots after which the express becomes Raw data< Perctil e. We can therefore state that the
number of relevant component will be 5. (Watkins, 2005) Looking at the scree plot presented below we can see
that the means and percentiles values are also include with the raw data Eigen values for a visual presentation of
the findings. The green line is the 50th percentile (mean) and the brownish-yellow line above it is the 95th
percentile (95% confidence level). Both lines intersect with the blue line of raw data Eigen values and we are
only to consider the components above the 50th and 95th percentiles. But more stress on values that are actually

FACTOR ANALYSIS 5
above the 95th percentile; looking at the roots (on the x-axis) we see that there are points above and below the
point of intersection for the blue and brownish-yellow line. We get that only 5 roots are above (significant) and
20 roots are below (no significant at 95% confidence level) the aforementioned intersection point. If we
compare the results obtained in principal component analysis with those gotten here; the best decision would be
to utilize the parallel analysis results because they are more robust. Hence, for our factor analysis we will
employ five components for each personality trait assessment (Weng & Cheng, 2005).
Raw Data Eigenvalues, & Mean & Percentile Random Data Eigenvalues
Root Raw Data Means Prcntyle
1.000000 2.160310 1.295865 1.336507
2.000000 2.114087 1.251654 1.285520
3.000000 1.892693 1.218679 1.243876
4.000000 1.702515 1.190089 1.214297
5.000000 1.642168 1.163547 1.186615
6.000000 1.064408 1.139139 1.161055
7.000000 .932449 1.115932 1.136062
8.000000 .906597 1.093426 1.113389
9.000000 .881236 1.072733 1.091421
10.000000 .865622 1.052225 1.071099
11.000000 .849637 1.031594 1.049763
12.000000 .828118 1.012243 1.029279
13.000000 .817099 .992610 1.010130
14.000000 .805146 .973117 .990972
15.000000 .768596 .954227 .971641
16.000000 .756220 .935851 .952927
17.000000 .740031 .917260 .934336
18.000000 .726630 .897628 .915169
19.000000 .706204 .878232 .896913
20.000000 .683508 .858631 .877524
21.000000 .678491 .838397 .856061
22.000000 .668181 .816751 .836903
23.000000 .633149 .794527 .816868
24.000000 .595849 .769288 .791525
25.000000 .581056 .736356 .763021

FACTOR ANALYSIS 6
Factor Analysis
After performing the factors analysis taking into account 5 factors, we see that the correlation matrix for
all 25 variables is dominated by weak positive correlations, with a considerable number of weak negative
correlations. It is also important to observe that there are two variables with no correlation; one measures
extraversion and the other measures conscientiousness. Similarly there are numerous variables that have
correlations that are considerably close to a value of zero both from the positive and negative sides (Liu, et. al.,
2014). The presence of numerous weak correlations maybe an indication that factor analysis is not valid and
should not have been performed on the dataset provided in the 25 variables. Moreover, this could be an
indication that the variables are not appropriate measures for the various personality traits in Inuit children.
However, looking at the KMO measure of Sampling adequacy we see that the value is greater than 0.5; meaning
that it was appropriate to perform factor analysis on the given variables. This result disproves the previously
held notion of inadequacy due to poor correlation figure. In addition, Bartlett’s test of sphericity evaluates the
presence of at least one correlation in the entire correlation matrix that is statistically significant. Form the

FACTOR ANALYSIS 7
significant level less than 0.05 it is accurate to conclude that there is at least one correlation that is statistically
significant in the correlation matrix (Liu, et. al., 2014).
Looking at the table of communalities we can see that almost all the variables have good extraction
percentages of above 20% with two or three variables having less than that. There is one variable that is
employed as a measure of openness in the children that has very low extraction percentage of 0.3% based on
multiple-regression. This means that this variable should not have been included in the factor analysis. Looking
at the table variance explained, we can see that the 5 factors used in our assessment can effectively explain 22.
96% of the total variance, this is an acceptable level and furthermore, we can see that even if we would have
employed the Eigen value of 1 basis to our analysis all of our five factors would have still been included. (Liu,
et. al., 2014). The five factors account for almost the same percentage in the total variance with only minimal
difference as you more down from factor 1 to factor 5. Lastly, on this table of variance explained, we can
effectively conclude that the variance is shared evenly by the factors based on their respective rotated sum of
squares values. The rotated sum of square values for all five range between 0.8 and 1.4 (a significantly short
interval). The scree plot represents the same finding as those indicated in parallel analysis. The goodness of fit
test is not significant; therefore, we can conclude that no additional factors beyond the 5 already in use can be
extracted from the given data. Nevertheless it is important to indicate that this test is highly sensitive to sample
size and specifity (Liu, et. al., 2014).
Goodness-of-fit Test

FACTOR ANALYSIS 8
Chi-Square df Sig.
166.221 185 .836
The Pattern matrix has to be the most important with regard to factor analysis looking at the table below. We
can see that the grouping of the variables has been done collectively for majority of the variables. However, one
variable that is supposed to measure agreeableness has been categorized with the five variables meant to
measure neuroticism. Overall we can conclude, that there is considerable consistent in the factor analysis
developed for this assessment of big five personality traits in Inuit children aged between 9 and 12 years. It is
important to note that none of the variables load on more than one factor. Lastly, from the factor correlation

FACTOR ANALYSIS 9
matrix we see that all five personality traits are correlated with each other; although the correlation are
considerably weak positive and negative correlations.
Pattern Matrixa
Factor
1 2 3 4 5
Conscientiousness 4 .543 .023 -.019 .081 -.049
Conscientiousness 1 .525 -.016 -.003 .002 .038
Conscientiousness 5 .518 -.009 .005 -.030 -.019
Conscientiousness 3 .506 -.003 .020 -.004 -.025
Conscientiousness 2 -.506 .012 .013 -.001 -.019
Neuroticism 2 -.045 .520 .020 -.018 -.053
Agreeableness 4 .002 .508 -.028 .037 -.039
Neuroticism 3 -.016 .491 .033 .033 .063
Neuroticism 5 .082 .477 -.039 -.010 .003
Neuroticism 1 -.025 .430 -.007 -.028 -.010
Neuroticism 4 .009 -.407 -.001 -.012 -.016
Extraversion 5 -.029 -.048 .526 .011 -.008
Extraversion 2 -.021 .009 -.520 -.010 -.004
Extraversion 3 -.033 -.018 .478 .040 -.011
Extraversion 4 .016 -.008 .400 .020 -.020
Extraversion 1 -.041 .003 .383 .026 -.035
Openness 2 .015 .012 .049 -.019 .013
Openness 3 .049 -.051 -.014 .554 -.046
Openness 1 -.022 .048 -.014 .536 .050
Openness 5 .055 .000 .018 .507 .044
Openness 4 -.027 .019 .038 .422 -.015
Agreeableness 5 -.014 -.013 .000 -.017 .536
Agreeableness 1 -.032 -.010 .027 .052 .447

FACTOR ANALYSIS 10
Agreeableness 2 .051 -.008 -.011 .010 .446
Agreeableness 3 -.032 .010 -.036 -.018 .410

FACTOR ANALYSIS 11
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