Exploratory Factor Analysis
Suitable for FA? Based on what?
 Stages of making a decision on the factors to
be extracted
 What is the convergent validity? discriminant
validity?
 Reliability. Overall reliability? Extracted
factors’ reliability?
 Interpretation of the factor structure label
these extracted factors
 Conclusion

Suitable for FA?
 At
the initial stage of preliminary checking:
 Correlation R-Matrix
 These items are eyesores.
Q6 (r = .271), Q7(r = .225), Q10 (r =.254),
Q12 (r =.079), Q19 (r = - .095), Q20 (r =
.171), Q23 (r = .281), Q25 (r =.176), Q26 (r
= .151), and Q27 (r = .259)
 Why? The standard that the extent of
association among items should be within
0.3~0.8 is not met.
Suitable for FA?
 Communalities
table
singularity  Q12 (factor loading value is
0.297)
Determinant value : 0.00000124 < 0.00001
 multicollinearity problem

Suitable for FA?
At the initial stage of preliminary checking:
 KMO value (= .894) > 0.5
 Barlett’s test of sphericity: statistical sig.
 Anti-image Correlation Matrix shows that
values along diagonal line is larger than 0.5,
and values off the diagonal line are
dominantly smaller, which meet the Measure
of sampling adequacy (MSA) criteria with 0.5
set as the minimum requirement.

Suitable for FA?
 Bland’s
theory of research methods lecturers
predicted that good research methods
lecturers should have four characteristics
(i.e., a profound love of statistics, an
enthusiasm for experimental design, a love of
teaching, and a complete absence of normal
interpersonal skills).  supported or refuted?
 These four characteristics are correlated to
some degree.  Multicollinearity is
understandable .
Suitable for FA?
In terms of
KMO with statistical significance, an
indicator of sampling adequacy,
 Anti-image Correlation Matrix, meeting
the Measure of sampling adequacy (MSA)
 Communalities: most items have reached the
minimum criterion 0.5, indicating that most
items have reached the degree of being
explained by common factors


 Suitable for FA, but some items had better be
crossed out.
Stages of making a decision on the
factors to be extracted
At the preliminary stage :
 an action taken: Q12 (singularity problem)
and Q10 (comparatively low factor loading
value =0.417< 0.5) deleted.
 At the second stage:
an action taken : the remaining items (26
items) are under EFA by resorting to ablimin
rotation approach. ( because of expected
correlated underlying factors)

Stages of making a decision on the
factors to be extracted


At the second stage:
Pattern Matrix table
 Q21 and Q27 crossing-load on two
components
 the loading values of Q1, Q9, and
Q11 are suppressed due to their
coefficient values below the
threshold set as 0.4.
Stages of making a decision on the
factors to be extracted
 At
the second stage:
Q21, Q27, Q1, Q9, and Q11 deleted.
21 items are left for EFA again.
 At the third stage:
 determinant value (=0.000),slightly larger
than the benchmark 0.00001.
 Pattern Matrix : no crossing-loading
variables.
Stages of making a decision on the
factors to be extracted
At the third stage:
 KMO value is .868 with statistical
significance
 total variance of being explained : these
extracted five components after rotation
account for nearly 62 percent of variance
 eigenvalue of each component >1
 communalities: only one variable value, Q7
(= 0.478), is below the threshold value 0.5.

Stages of making a decision on the
factors to be extracted
Pattern Matrix : two items ---Q7 (.483),
Q26(.438) --- factor loadings are not as high
as other items loaded onto factors.
 But in terms of convergent validity criteria
flexibly varying with various sample sizes,
these variables Q7,Q26 still with sufficient
factor loading values (minimum benchmark
0.35~0.4 for sample size ranging from
250~200), if retained, can be justified.

Stages of making a decision on the
factors to be extracted
Kaiser’s criterion is not met
communalities values after extraction > 0.7
( if the # of variables is less than 30 )
sample size > 250
average communality > 0.6
 retain all factors with eigenvalues above 1
 Scree plot is the last resort to turn to if
sample size is large (i.e., around 300 or more)
 21 items decided  five factors extracted

Convergent Validity
refer to to what extent variables loaded within a
factor are correlated  the higher loading, the better.
 Factor structure :
 check Pattern Matrix to know about the
convergent validity
(no crossing-loadings between factors )
 variables precisely loading on factors


check convergent validity in terms of sample size.
In this case, the sample size is 239; the convergent
validity is acceptable, for most variables are above the
range of 0.35 to 0.4. in terms of loadings within
factors.
Discriminant Validity
2 ways to check discriminant validity
 Check Pattern Matrix to see no crossingloadings


Check Factor Correlation Matrix :
correlations between factors do not
exceed 0.7.
Discriminant Validity
Correlations
between factors
do not exceed 0.7
Factor
1
Factor Correlation Matrix
1
2
3
4
5
1.000
.452
.585
.480
.322
2
.452
1.000
.506
.205
-.127
3
.585
.506
1.000
.351
.351
4
.480
.205
.351
1.000
.315
5
.322
-.127
.351
.315
1.000
Extraction Method: Principal Axis Factoring.
Rotation Method: Promax with Kaiser Normalization.
Overall Reliability of the 21 items in the
dataset (TOSSE.sav.)
Larger
than 0.7
Reliability Statistics
Cronbach's
Cronbach's
Alpha Based on
Alpha
N of Items
Standardized Items
.879
.881
21
Reliability Statistics
Reliability of
Comp 1> 0.7
Cronbach's Alpha
Based on
Standardized Items
Cronbach's Alpha
.880
N of Items
.886
6
Reliability Statistics
Reliability of
Comp 2
=. 0.7
Cronbach's Alpha
.679
Cronbach's Alpha
Based on
Standardized Items
.679
N of Items
3
Reliability Statistics
Reliability of
Comp 3
> 0.7
Cronbach's Alpha
Based on
Cronbach's Alpha
Standardized Items
.717
N of Items
.742
4
Reliability Statistics
Reliability of
Comp 4 =. 0.7
Cronbach's Alpha
Based on
Cronbach's Alpha
Standardized Items
.690
N of Items
.692
3
Reliability Statistics
Reliability of
Comp 5 > 0.7
Cronbach's Alpha
Based on
Cronbach's Alpha
Standardized Items
.
.736
737
N of Items
5
Interpretation of extracted 5 factors






labels of the five factors:
Component 1: ‘Passion for Applying
Statistics Knowledge’
Component 2 : ‘Apprehension for Teaching ’
Component 3: ‘Obsession with
Successfully Applying Statistics to
Experiment’
Component 4: ‘Preference for being alone’,
Component 5: ‘Passion for teaching
Statistics’
Component 1: ‘Passion for Applying Statistics
Knowledge’
Component
Thinking about whether to use repeated or
independent measures thrills me
1
.835
I'd rather think about appropriate dependent
variables than go to the pub
.824
I quiver with excitement when thinking about
designing my next experiment
.773
I enjoy sitting in the park contemplating whether to
use participant observation in my next experiment
.752
Designing experiments is fun
.597
I like control conditions
.582
2
3
4
5
Component 2 : ‘Apprehension for Teaching’
Teaching others makes me want to swallow a large
bottle of bleach because the pain of my burning
oesophagus would be light relief in comparison
.819
If I had a big gun I'd shoot all the students I have to
teach
.782
Standing in front of 300 people in no way makes
me lose control of my bowels
.526
Component 3: ‘Obsession with Successfully
Applying Statistics to Experiment’
I tried to build myself a time machine so that I
could go back to the 1930s and follow Fisher
around on my hands and knees licking the floor on
which he'd just trodden
.767
I memorize probability values for the Fdistribution
.742
I worship at the shrine of Pearson
.570
I soil my pants with excitement at the mere
mention of Factor Analysis
.530
Component 4: ‘Preference for being alone’
I often spend my spare time talking to the pigeons
... and even they die of boredom
.763
My cat is my only friend
.760
I still live with my mother and have little personal
hygiene
.734
Component 5: ‘Passion for teaching Statistics’
Passing on knowledge is the greatest gift you can
bestow an individual
.705
I like to help students
.686
I love teaching
.677
Helping others to understand Sums of Squares is a
great feeling
.483
I spend lots of time helping students
.438
Conclusion
The extracted five factors refute Bland’s
theory through the EFA, for
 we are asked to test the theory of four
personality traits
 the labeling of Component 2
(Apprehension for Teaching) contradicts the
labeling of Component 5 (Passion for
teaching Statistics)
 Individual Factor reliability ---Comp 2 /
Comp 4 at the margin of 0.7, not above 0.7

Why
don’t we first group the
question items into four
components in correspondence
with the four characteristics
proposed by Bland, and then run
FA? CFA?
Conclusion
 When
EFA is resorted to, very often an
extracted factor loaded with some variables
as a cluster is hard to be labeled. And thus
several trials seem unavoidable until the
labeling of a factor can comprehensively
interpret the variables loaded on that factor.
 As such, this dataset seems to be more like a
CFA case because of the already-existing
hypothesis about the underlying constructs
(i.e., four personality traits).