Factor Analysis Report: Personality Traits, Sampling, and Results

This report presents a factor analysis study that investigates personality traits based on the IPIP big personality model. The study employs a stratified random sampling approach with a sample size of 1006, collecting data through questionnaires distributed online and by post. The methodology includes principal component analysis and rotation methods, with data cleaning to ensure consistency. The results section analyzes extraversion, neuroticism, openness, agreeableness, and conscientiousness, presenting KMO and Bartlett's test values, communalities, total variance explained, and component matrices. The interpretations provide insights into the significant variables and their variance percentages for each personality trait, offering a comprehensive analysis of the data collected and the factors identified within the personality model.

FACTOR ANALYSIS

TABLE OF CONTENTS
Method.............................................................................................................................................1
Results..............................................................................................................................................2
Extraversion.....................................................................................................................................2
Non-rotation................................................................................................................................2
Neuroticism......................................................................................................................................5
Non-rotation................................................................................................................................5
Openness..........................................................................................................................................8
Non-rotation................................................................................................................................8
Rotation.....................................................................................................................................10
Agreeableness................................................................................................................................13
Non-rotation..............................................................................................................................13
Rotation.....................................................................................................................................15
Conscientiousness..........................................................................................................................19
Non-rotation..............................................................................................................................19
REFERENCE.................................................................................................................................22

Method
In the present research study factor analysis method is used. This method is used in social
science and market research. In the questionnaire multiple questions are covered and few of them
need to be select for proper analysis. Selection of variable out of available questions is done on
basis of factor analysis results (Mackey and Gass, 2015). Two approaches of factor analysis are
used to obtain results namely principle component analysis and rotation method. In few cases
rotation method does not generate any sort of result and due to this reason relevant tables are not
added in the file. Sometimes, the initial solution results in strong correlations of a variable with
several factors or in a variable that has no strong correlations with any of the factors (Rahn.,
2019). In order to make the location of the axes fit the actual data points better, the program can
rotate the axes. Ideally, the rotation will make the factors more easily interpretable. In the present
research study sample of 1006 is taken by following stratified random sampling approach. In this
approach from different groups sample units are taken. As in the research children and adults are
taken as sample units. Within children those are also taken that are well familiar with English
and not familiar with the mentioned language.
This, reflect that diverse groups of individuals are taken as sample units in the present
research study. This is done to ensure that data is taken from the reliable sources and to ensure
that it will represent entire population perfectly. There were also options in respect to sampling
methods like simple random sampling method. This method was not picked for research purpose
because under this approach randomly sample units are picked. In this approach there was
probability that specific group of people may not get selected in the sample. Thus, research may
go in wrong direction and it may show results that are far from reality. In order to avoid such
kind of situation stratified sampling method was used instead of simple random sampling
method. In order to collect data questionnaire was distributed among respondents. Through
internet medium and by post data was gathered from the sample units.
After data collection its cleaning was done and under this gathered data was analysed
in proper manner to identify reliability of obtained data (Flick., 2015). Many times, it
happened that respondents provide data but there is absence of consistency in answer. For
example, three questions are interrelated and when respondent’s response will be analysed
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then answer will be in different direction. If such error is identified then data cleaning is
used to ensure that there is consistency in the answers provided by the respondents. Hence,
data collection and cleaning were important part of the research work. Apart from this,
choice of stratified sampling method also assists in gathering data in better way. Thus, it can
be said that current research study is carried out in proper manner. IPIP big personality
model was selected to prepare entire questionnaire. In questionnaire varied questions are
taken which are based on 5 personality trait models. All questions in the questionnaire are
related to factors openness, conscientiousness, extraversion, agreeableness and neuroticism.
Questions related to these factors are asked to respondents and gathered data is analysed by
using factor analysis method. In this way, entire research work is carried out.
Results
Extraversion
Non-rotation
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling
Adequacy. .718
Bartlett's Test of
Sphericity
Approx. Chi-Square 359.533
df 10
Sig. .000
Communalities
Initial Extractio
n
4 1.000 .294
6 1.000 .429
14 1.000 .385
20 1.000 .322
2

25 1.000 .428
Extraction Method:
Principal Component
Analysis.
Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared Loadings
Total % of
Variance
Cumulative
%
Total % of
Variance
Cumulative
%
1 1.858 37.151 37.151 1.858 37.151 37.151
2 .870 17.399 54.550
3 .822 16.433 70.982
4 .735 14.691 85.673
5 .716 14.327 100.000
Extraction Method: Principal Component Analysis.
3

Component
Matrixa
Component
1
4 .542
6 -.655
14 .621
20 .568
25 .654
4

Extraction Method:
Principal
Component
Analysis.
a. 1 components
extracted.
Interpretation
Value of Kaiser-Mayer test is 0.718 in above given table as it can be seen that its value is nearby
to 1. It can be concluded on basis of statistic that adequate sample is taken into account. Level of
significance for Bertlett test is 0.00>0.05 which reflect indicate that matrix is not identity matrix.
Results clearly indicated that 6th and 25th variable extraction value is highly represented in
common factor space. Variable 1 contain 37.15% of overall variance and due to this reason, it is
selected as factor for Extraversion.
Neuroticism
Non-rotation
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling
Adequacy. .727
Bartlett's Test of
Sphericity
Approx. Chi-Square 355.790
df 10
Sig. .000
Communalities
Initial Extractio
n
5 1.000 .347
5

8 1.000 .414
11 1.000 .410
15 1.000 .319
24 1.000 .374
Extraction Method:
Principal Component
Analysis.
Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared Loadings
Total % of
Variance
Cumulative
%
Total % of
Variance
Cumulative
%
1 1.864 37.275 37.275 1.864 37.275 37.275
2 .832 16.637 53.912
3 .808 16.159 70.071
4 .752 15.047 85.118
5 .744 14.882 100.000
Extraction Method: Principal Component Analysis.
6

Component
Matrixa
Component
1
5 .589
8 .643
11 .640
15 -.565
24 .612
7

Extraction Method:
Principal
Component
Analysis.
a. 1 components
extracted.
Interpretation
Results reflect that value of Kaiser-Mayer test is 0.727 which is nearby to 1. It can be deduced
from statistic that adequate sample is taken into account. Level of significance for Bertlett test is
0.00>0.05 as can be seen in the table given above. This means that matrix is not identity matrix.
8th and 24th variable extraction value is highly represented in common factor space. Variable 1
contain 37.27% of overall variance and due to this reason, it is selected as factor for Neuroticism.
Openness
Non-rotation
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling
Adequacy. .686
Bartlett's Test of
Sphericity
Approx. Chi-Square 320.629
df 10
Sig. .000
Communalities
Initial Extractio
n
3 1.000 .478
9 1.000 .959
8

10 1.000 .491
21 1.000 .394
23 1.000 .451
Extraction Method:
Principal Component
Analysis.
Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared Loadings
Total % of
Variance
Cumulative
%
Total % of
Variance
Cumulative
%
1 1.760 35.204 35.204 1.760 35.204 35.204
2 1.013 20.261 55.465 1.013 20.261 55.465
3 .796 15.927 71.392
4 .723 14.460 85.852
5 .707 14.148 100.000
Extraction Method: Principal Component Analysis.
Component Matrixa
9

Component
1 2
3 .680 .128
9 -.029 .979
10 .694 .094
21 .605 -.167
23 .671 -.034
Extraction Method:
Principal Component
Analysis.
a. 2 components extracted.
Rotation
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling
Adequacy. .686
Bartlett's Test of
Sphericity
Approx. Chi-Square 320.629
df 10
Sig. .000
Communalities
Initial Extractio
n
3 1.000 .478
9 1.000 .959
10 1.000 .491
21 1.000 .394
10

23 1.000 .451
Extraction Method:
Principal Component
Analysis.
11

Component Matrix
Component
1 2
3 .680 .128
9 -.029 .979
10 .694 .094
21 .605 -.167
23 .671 -.034
12

Extraction Method:
Principal Component
Analysis.
a. 2 components extracted.
Interpretation
In present case in the table given above it can be seen that value of Kaiser-Mayer test is 0.686
which is nearby to 1. Statistic indicate that adequate sample is taken into account. Level of
significance for Bertlett test is 0.00>0.05 which reflect that matrix is not identity matrix. 3rd and
9th variable extraction value is highly represented in common factor space. Variable 1 contain
35.20% of overall variance and due to this reason, it is selected as factor for Openness.
13

Agreeableness
Non-rotation
14

15

Rotation
16

Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared
Loadings
Rotation
Sums of
Squared
Loadingsa
Total % of
Variance
Cumulative
%
Total % of
Variance
Cumulative
%
Total
1 1.629 32.581 32.581 1.629 32.581 32.581 1.629
2 1.003 20.053 52.633 1.003 20.053 52.633 1.003
3 .854 17.082 69.715
4 .779 15.577 85.292
5 .735 14.708 100.000
Extraction Method: Principal Component Analysis.
a. When components are correlated, sums of squared loadings cannot be added to obtain a total
variance.
17

Component Matrixa
Component
1 2
1 .630 .080
7 .630 .013
12 .602 .012
16 -.018 .995
18 .688 -.071
18

Extraction Method:
Principal Component
Analysis.
a. 2 components extracted.
Interpretation
Results reflect that value of Kaiser-Mayer test is 0.658 nearby to 1 which reflect that adequate
sample is taken into account. Matrix is not identity matrix and this is evident from the statistic of
Bertlett test whose value is 0.00>0.05. 16th and 18th variable extraction value is highly
represented in common factor space. Variable 1 contain 32.358% of overall variance and due to
this reason, it is selected as factor for Openness.
19

Conscientiousness
Non-rotation
20

21

Value of Kaiser-Mayer test is 0.751 nearby to 1 which reflect that adequate sample is taken
into account. Level of significance for Bertlett test is 0.00>0.05 which reflect that matrix is not
identity matrix. 2nd and 19th variable extraction value is highly represented in common factor
space. Variable 1 contain 41.53% of overall variance and due to this reason, it is selected as
factor for Openness.
22

REFERENCE
Online
Rahn., M., 2019. Factor analysis short introduction part 2 rotations. Available through:<
https://www.theanalysisfactor.com/rotations-factor-analysis/>.
Mackey, A. and Gass, S.M., 2015. Second language research: Methodology and design.
Routledge.
Flick, U., 2015. Introducing research methodology: A beginner's guide to doing a research
project. Sage.
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