Exploratory Factor Exploratory Factor AnalysisAnalysis

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? 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? Suitable for FA? Communalities table singularity Q12 (factor loading

value is 0.297)

Determinant value : 0.00000124 < 0.00001

multicollinearity problem

Suitable for FA? 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? 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? 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 Stages of making a decision on the factors to be extracted 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 Stages of making a decision on the factors to be extracted 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 Stages of making a decision on the factors to be on the factors to be extractedextractedAt 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 Stages of making a decision on the factors to be extractedthe 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 Stages of making a decision on the factors to be extractedthe 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 Stages of making a decision on the factors to be extractedthe 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 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 Discriminant Validity 2 ways to check discriminant

validity Check Pattern Matrix to see no

crossing-loadings

Check Factor Correlation Matrix : correlations between factors do not exceed 0.7.

Factor Correlation Matrix

Factor 1 2 3 4 51 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.

Discriminant Validity Correlations between factors do not exceed

0.7

Reliability Statistics

Cronbach's

Alpha

Cronbach's

Alpha Based on

Standardized Items

N of Items

.879 .881 21

Overall Reliability of the 21 items in the dataset (TOSSE.sav.)

Larger than 0.7

Reliability Statistics

Cronbach's Alpha

Cronbach's Alpha Based on

Standardized Items N of Items

.880 .886 6

Reliability of Comp 1> 0.7

Reliability Statistics

Cronbach's Alpha

Cronbach's Alpha Based on

Standardized Items N of Items

.679 .679 3

Reliability of Comp 2 =. 0.7

Reliability Statistics

Cronbach's AlphaCronbach's Alpha

Based on Standardized Items N of Items

.717 .742 4

Reliability of Comp 3

> 0.7

Reliability Statistics

Cronbach's AlphaCronbach's Alpha

Based on Standardized Items N of Items

.690 .692 3

Reliability of Comp 4 =. 0.7

Reliability Statistics

Cronbach's AlphaCronbach's Alpha

Based on Standardized Items N of Items

.736.

737 5

Reliability of Comp 5 > 0.7

Interpretation of extracted 5 Interpretation of extracted 5 factorsfactors 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 2 3 4 5Thinking about whether to use repeated or independent measures thrills me

.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

Component 1: ‘Passion for Applying Statistics Knowledge’

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 2 : ‘Apprehension for Teaching’

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 F-distribution

.742

I worship at the shrine of Pearson .570

I soil my pants with excitement at the mere mention of Factor Analysis

.530

Component 3: ‘Obsession with Successfully Applying Statistics to Experiment’

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 4: ‘Preference for being alone’

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

Component 5: ‘Passion for teaching Statistics’

ConclusionConclusion 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 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).