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CHAPTER-6 RELIABILITY AND VALIDITY OF THE METACOGNITION INVENTORY 6.1 Introduction 6.2 Reliability 6.3 Validity
CHAPTER-6
RELIABILITY AND VALIDITY OF THE MET ACOGNITION INVENT ORY
6.1 Introduction
6.2 Reliability
6.3 Validity
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6.1 INTRODUCTION
In previous two chapters construction of the Metacognition Inventory
and Research Design were discussed.
The fundamental purpose of standardizing any psychological tool is to
establish its reliability and validity at as high a level as possible. In the present
chapter the statistical measurement for establishment of the reliability and validity
are discussed in detail.
6.2 RELIABILITY
The tendency towards consistency from one set of measurements to
another is called reliability. If a test is administered for frequent number of times
on the same group of subjects or individuals and each time the value of test
measurement or test score is almost the same then the test is said to be
reliable.
According to Anastasi & Urbina1 (2002),
"Reliability refers to the consistency of scores obtained bythe same persons when they are reexamined with the sametest on different occasions, or with different sets ofequivalent items, or under other variable examiningconditions."
In Classical Test Theory, reliability is defined mathematically as the ratio
of the variation of the true score and variation of the observed score. Or,
equivalently, one minus the ratio of the variation of the error score and the
variation of the observed score:
2 2
2 2' 1T E
X X
xxσ σσ σσ σσ σρρρρσ σσ σσ σσ σ
= = −= = −= = −= = −
Where rxx' is the symbol for the reliability of the observed score, X;
2Xσσσσ , 2
Tσσσσ , and 2Eσσσσ are the variances on the measured, true and error scores
respectively. Unfortunately, there is no way to directly observe or calculate the
true score, so a variety of methods are used to estimate the reliability of a test.
146
6.2.1 Types of Reliability
There are four general classes of reliability estimates, each of which
estimates reliability in a different way. According to Trochim, W. M. (2006)
they are:
• Inter-Rater or Inter-Observer Reliability
Used to assess the degree to which different raters/observers give
consistent estimates of the same phenomenon.
• Test-Retest Reliability
Used to assess the consistency of a measure from one time to another.
• Parallel-Forms Reliability
Used to assess the consistency of the results of two tests constructed in
the same way from the same content domain.
• Internal Consistency Reliability
Used to assess the consistency of results across items within a test.
There are a wide variety of internal consistency measures that can be used.
(A) Split Half Reliability
• Spearman and Brown Formula
• Rulon/Guttman's Formula
• Flanagan Formula
(B) Cronbach's Alpha (a)
(C) Method of rational equivalence
• Kuder Richardson - KR20
• Kuder Richardson - KR21
6.2.2 Reliability of the Metacognition Inventory
In the present study the reliability of the Metacognition Inventory was
calculated by
(A) Test-Retest Reliability
(B) Parallel-Forms Reliability
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(C) Internal Consistency Reliability
(C1) Split Half Reliability
• Spearman and Brown Formula
• Rulon/Guttman's Formula
• Flanagan Formula
(C2) Cronbach's Alpha (a)
(A) Test-Retest Reliability : In the present study there were two parallel
forms of the metacognition inventory. For both the forms test-retest
reliability was estimated. Details about the sample for Metacognition
Inventory Form A and Form B are shown in below tables. Schools
selected for the data collection were:
• Rural area : Chandramauli Vidyalaya, Vejalpur
• Urban area : Diwan Ballubhai Madhyamik Shlala, Paladi, Ahmedabad
Table 6.1
Sample for Reliability estimation for Form A
Std 8 Std 9 Std 10 Total
Rural 15 15 15 45
Urban 16 14 14 44
Total 31 29 29 89
Table 6.2
Sample for Reliability estimation for Form B
Std 8 Std 9 Std 10 Total
Rural 15 15 15 45
Urban 15 15 15 45
Total 30 30 30 90
Thus, Metacognition inventory form A was administered on total 89
students and Metacognition Inventory form B was administered on total 90
students to establish the estimate of reliability of the Inventory.
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The most obvious method for finding the reliability of the test scores is
by repeating the identical test on a second occasion. The reliability coefficient in
this case is simply the correlation between the scores obtained by the same
persons on the two administrations of the test. This is done using the Pearson
product-moment correlation coefficient (r). The value of "r" will always fall
within the range –1 to +1. Guilford (1956) offers an informal interpretation of
the value r, as shown in table 6.3.
Table 6.3
Interpretation of Pearson Product-moment correlation Coefficient (r)
Value of r Informal interpretation
Less than 0.2 Slight, almost no relationship
0.2-0.4 Low, correlation; definite but small relationship
0.4-0.7 Moderate correlation; substantial relationship
0.7-0.9 High correlation; strong relationship
0.9-1.0 Very High correlation; very dependable relationship
Another way of establishing a relationship between two sets of scores is
by examining a scatter plot drawn from the data.
To estimate the test-retest reliability of the inventory first Metacognition
Inventory form A and Form B were administered on the sample as shown in
table 6.2 and table 6.3. After two weeks again these forms were administered
on the same sample. For these two sets of data the Pearson product-moment
correlation coefficients were calculated with the help of MS-Office Excel
software application.
The formula for the Pearson product moment correlation coefficient, r, is:
(((( )))) (((( ))))(((( )))) (((( ))))2 2
x x y yr
x x y y
Σ − −Σ − −Σ − −Σ − −====
Σ − −Σ − −Σ − −Σ − −
Where x and y are the sample means Average (array1 (test)) and Average
(array2 (retest)).
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Results obtained for the reliability coefficient were as follows;
• Metacognition Inventory Form A Test-Retest Reliability Coefficient r = 0.75
• Metacognition Inventory Form B Test-Retest Reliability Coefficient r = 0.83
Considering Guilford's values in Table 6.3, the correlation between test
and retest for MCI-A and MCI-B were 0.75 and 0.83 can be considered as
high, indicating a strong relationship. Hence, both the forms of Metacognition
Inventory are reliable.
Results obtained from the scatter plot graph
A scatter plot is also needed when evaluating the correlation between
two sets of data. The purpose of the scatter plot is to show whether there is a
linear relationship amongst the two sets of data. The scatter plot graph in
Graph 6.1 was generated with the SPSS statistical analysis programme for the
scores obtained from the test and retest.
Scatter plot of test versus re-test for MCI-A
Graph: 6.1
An analysis of the scatter plot shows a definite tendency towards
linearity, as most of the scores are fairly close to the regression line. Thus, from
the correlation value of 0.75 and the scatter plot it can be concluded that the
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MCI-A was stable over the time span for which it was administered. Hence,
the Metacognition Inventory Form A is reliable.
Scatter plot of test versus re-test for MCI-B
Graph: 6.2
An analysis of the scatter plot shows a definite tendency towards
linearity, as most of the scores are fairly close to the regression line. Thus, from
the correlation value of 0.83 and the scatter plot it can be concluded that the
MCI-B is reliable.
Reliability Coefficient using scatter diagram method
The reliability coefficient was also calculated with scatter diagram
method. Scatter diagram scores on test and retest for MCI-Form A are shown
in Table 6.4.
151
86-95 96-105 106-115 116-125 126-135 136-145 146-155 156-165 166-175Total X’ fx’ x’y’ fx’x’
96-105 25 1 25 1 -4 -4 25 16
106-115 12 1 12 16 2 8 3 -3 -9 28 27
116-125 12 1 12 9 1 9 18 3 6 0 1 0 6 -2 -12 39 24
126-135 12 2 6 8 2 4 14 7 2 0 3 0 -2 1 -2 15 -1 -15 32 15
136-145 2 1 2 4 4 1 0 11 0 -3 3 -1 -4 2 -2 21 0 0 -1 0
146-155 0 4 0 0 8 0 0 9 0 0 6 0 0 1 0 28 1 28 0 28
156-165 -2 1 -2 0 1 0 8 8 1 2 1 2 9 3 3 14 2 28 17 56
166-175 4 1 4 1 3 3 4 9
Total 1 1 4 9 15 24 21 10 4 89 19 144 175
y’ -5 -4 -3 -2 -1 0 1 2 3
fy’ -5 -4 -12 -18 -15 0 21 20 12 -1
x’y’ 25 12 33 42 18 0 3 2 9 144
fy’y’ 25 16 36 36 15 0 21 40 36 225
Table 6.4
Scatter diagram of Scores on Test -Retest for MCI-A
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cx' = 0.2135 Sx'y'/N = 1.618
cy'= -0.11 N= 89
Sx' = 1.38 Sy' = 1.59
r = 0.74
From Table 6.4 the value of Correlation coefficient r = 0.74. Thus, the
value of reliability coefficient is high which indicates that the MCI-A is reliable.
Scatter diagram scores on test and retest for MCI-Form B are shown
in Table 6.5.
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86-95 96-105 106-115 116-125 126-135 136-145 146-155 156-165 166-175Total X’ fx’ x’y’ fx’x’
96-105 20 1 20 32 2 16 3 -4 -12 52 48
106-115 9 1 9 3 1 3 2 -3 -6 12 18
116-125 12 3 4 6 3 2 0 1 0 7 -2 -14 18 28
126-135 3 1 3 2 1 2 6 6 1 0 2 0 -1 1 -1 11 -1 -11 10 11
136-145 0 4 0 0 2 0 0 5 0 0 3 0 0 1 0 15 0 0 0 0
146-155 -4 2 -2 0 9 0 12 12 1 23 1 23 8 23
156-165 22 11 2 24 6 4 6 1 6 18 2 36 52 72
166-175 42 7 6 36 4 9 11 3 33 78 99
Total 1 2 2 10 12 17 27 14 5 90 49 230 299
y’ -5 -4 -3 -2 -1 0 1 2 3
fy’ -5 -8 -6 -20 -12 0 27 28 15 19
x’y’ 20 32 12 10 15 0 33 66 42 230
fy’y’ 25 32 18 40 12 0 27 56 45 255
Table 6.5
Scatter diagram of Scores on Test -Retest for MCI-B
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cx' = 0.54 cy'= 0.21
Sx' = 1.74 Sy' = 1.67
Sx'y'/N = 2.556 N= 90
r = 0.84
From Table 6.5 the value of Correlation coefficient r = 0.84. Thus, the
value of reliability coefficient is high which indicates that the MCI-B is reliable.
(B) Parallel-Forms Reliability
In parallel forms reliability first, the researcher should have to create
two parallel forms. And then administer both tools to the same sample of
students. The correlation between the two parallel forms is the estimate of
reliability.
The researcher had constructed the two parallel forms namely
Metacognition Inventory form A and Metacognition Inventory form B. Both the
forms were prepared in such a way that they can be used as independent
instrument to meet the same specifications. Both the forms contained the same
number of items and they covered the same type of content. The t-values of
the items on both the forms were near to equal. Instructions, time limits,
illustrative examples, format, and all other aspects of the inventory were
equivalent.
Both the forms namely MCI-A and MCI-B were administered on the
sample as mentioned above in table 6.1. The reliability coefficient for the
parallel forms A and B was, r = 0.815. It indicated the high correlation; strong
relationship between both the forms. Hence, Parallel forms reliability coefficient
indicated that the both the forms are reliable.
Results obtained from the scatter plot graph
The scatter plot graph in Graph 6.3 was generated with the SPSS
statistical analysis programme for the scores obtained from the MCI-A and
MCI-B.
155
Scatter Plot of scores obtained from Form B versus Form A
Graph-6.3
An analysis of the scatter plot shows a definite tendency towards
linearity, as most of the scores are fairly close to the regression line. Thus, from
the correlation value of 0.815 and the scatter plot it can be concluded that the
MCI-A and MCI- B are reliable.
(C) Internal Consistency Reliability
Test-retest method and parallel form reliability methods have the
disadvantage that they are time consuming. In most cases the researcher wants
to estimate the reliability from a single administration of a test. This requirement
has led to the measuring of internal consistency, or homogeneity. Internal
consistency measures consistency within the tool. Several internal consistency
methods exist. All internal consistency measurements have one thing in common,
namely that the measurement is based on the results of a single measurement.
In the present study to estimate the internal Consistency Reliability the
Metacognition Inventory Form A and Form B was administered on the sample
as mentioned in table-6.6 and 6.7.
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Table 6.6
Sample for Internal Consistency reliability for Form A
Standard 8 Standard 9 Standard 10 Total
AREA Girls Boys Total Girls Boys Total Girls Boys Total Girls Boys Total
Rural 221 416 637 234 342 576 192 341 533 6471099 1746
Urban 271 273 544 306 190 496 209 207 416 786 6701456
Total 492 689 1181 540 532 1072 401 548 949 1433 1769 3202
Table 6.7
Sample for Internal Consistency Reliability for Form B
Standard 8 Standard 9 Standard 10 Total
AREA Girls Boys Total Girls Boys Total Girls Boys Total Girls Boys Total
Rural 173 277 450 196 289 485 168 279 447 537 8451382
Urban 231 420 651 199 421 620 213 390 603 6431231 1874
Total 404 697 1101 395 710 1105 381 669 1050 1180 2076 3256
In the present study Split-Half technique and Cronbach's Alpha method
were used to estimate the internal consistency reliability. The statistical analysis
for Split half reliability (Spearman and Brown formula and Guttmann's formula)
and Cronbach's Alpha reliability, SPSS 17 Statistical Software was used. The
calculation for the Split half reliability by Flanagan's formula MS-Excel software
was used.
(C1) Split Half Reliability
In the Split-Half reliability method, the inventory was first divided into
two equivalent halves and the correlation coefficient between scores of these
half-test was found. This correlation coefficient denotes the reliability of the half
test. The self correlation coefficient of the whole test is estimated by different
formulas. The measuring instrument can be divided into two halves in a number
of ways. But the best way to divide the measuring instrument into two halves is
to find the correlation coefficient between scores of odd numbered and even
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numbered items. In the present study the correlation coefficient was calculated
by using following formulas :
• Spearman and Brown Formula
• Rulon/Guttmann's Formula
• Flanagan Formula
Spearman and Brown Formula
The spearman and Brown formula was designed to estimate the
reliability of a test n times as long as the one for which we know a self-
correlation. From the reliability of the half test, the self-correlation coefficient of
the whole test is estimated by the following Spearman and Brown formula:
(((( ))))2
1hh
tthh
rr
r====
++++
Where, rtt = Reliability of a total test estimated from reliability of one of its
halves (Reliability coefficient of the whole test)
rhh = Self correlation of a half test (Reliability coefficient of the half
test)
With help of SPSS software the calculation was done and the for MCI
form A the reliability coefficient was 0.86 and for form B it was 0.89.
1. MCI-Form A : rtt = 0.86 (N = 3202)
2. MCI-Form B : rtt = 0.89 (N = 3256)
The reliability of both the forms was quite high. Hence, it can be said
that the Metacognition inventory Form A and Form B are reliable.
Rulon /Guttmann's formula
An alternate method for finding split-half reliability was developed by
Rulon. It requires only the variance of the differences between each person's
scores on the two half-tests (SDd2) and the variance of total scores (SDx2);
these two values are substituted in the following formula, which yields the
reliability of the whole test directly:
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2
21 dtt
x
SDr
SD= −= −= −= −
Where, rtt = Reliability of the test
SDd = SD of difference of the scores
SDx = SD of the scores of whole test
With help of SPSS software the calculation was done and the for MCI
form A the reliability coefficient was 0.86 and for form B it was 0.89.
1. MCI-Form A : rtt = 0.86 ( N = 3202)
2. MCI-Form B : rtt = 0.89 (N = 3256)
The reliability of both forms was quite high. Hence, it can be said that
the Metacognition inventory Form A and Form B are reliable.
Flanagan Formula
Flanagan gave a parallel formula for finding reliability using split half
method. Flanagan's Formula for reliability is described below:
2 21 2
22 1ttt
SD SDr
SD
++++= × −= × −= × −= × −
Where, rtt = Reliability of the test
SD1 = SD of the scores on 1st half
SD2 = SD of scores on 2nd half
SDt = SD of scores of whole test
In the present study the value of rtt as per Flanagan's Formula was
calculated with MS-Office Excel package. And the value of rtt for MCI- form
A was 0.87 (N = 3202) and for MCI-Form B it was 0.88 (N = 3256).This
yielded a very good value for reliability.
(C2) Cronbach's Alpha (aaaaa)
Cronbach's Alpha is mathematically equivalent to the average of all
possible split-half estimates. A statistical analysis computer programme SPSSS
17 was used to calculate the Cronbach's Alpha (a). The value of rtt for Form
A and Form B were;
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1. MCI-Form A : rtt = 0.89 (N=3202)
2. MCI-Form B : rtt = 0.90 (N=3256)
Hence, as per the value of Cronbach's Alpha (a), both the forms are reliable.
6.2.3 Comprehensive view of the Reliability of the Metacognition
Inventory
In table 6.8, reliability coefficients for different methods, have been
shown.
Table 6.8
Reliability coefficients for MCI-A and MCI-B by different methods
Sr. Reliability MCI-A MCI-B
1 Test Retest Reliability 0.75 0.83
2 Parallel Form Reliability 0.81
3 Internal Consistency Reliability
3.1 Split Half Reliability MCI-A MCI-B
1. Spearmen and Brown Formula 0.86 0.89
2. Rulon /Guttmann's formula 0.86 0.89
3. Flanagan's formula 0.87 0.88
3.2 Cronbach's Alpha (a) 0.89 0.90
As shown in Table 6.8 above, the values of reliability coefficients for
Metacognition Inventory form A and Metacognition Inventory Form B by
different methods are moderately high. By this, it can be said that the reliability
of the MCI-A and MCI-B are moderately high.
6.3 VALIDITY
A test is said to be valid when it measures what it is supposed to
measure. Alternatively, a test whose performance closely resembles with an
objectively defined criterion is said to be valid.
160
According to Freeman4 (2006),
"An index of validity shows the degree to which a testmeasures what it purports to measure, when comparedwith accepted criteria."
The validity of the test concerns what the test measures and how well it
does so. It tells us what can be inferred from test scores. The first essential
quality of a valid test is that it should be highly reliable. Reliability of a test can
be estimated by repetition of measurements; while validity of a test can be
obtained by comparison with some standard criterion.
6.3.1 Types of Validity
According to Patel,5 (2011) following are some different types of
validity:
1. Operational or Content Validity
2. Functional or Concurrent Validity
3. Factorial Validity
4. Face Validity
5. Cross Validity
According to Anastasi & Urbina6 (2002) following are some ways of
estimating validity.
1. Content Description Procedures
• Representation of Content
• Face Validity
2. Criterion Prediction Procedures
• Concurrent Validity
• Predictive Validity
3. Construct Identification Procedures
• Factor Analysis
• Internal Consistency
• Convergent and Discriminant Validation
• Structural Equation Modeling
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6.3.2 Validity of the Metacognition Inventory
For estimating the validity of the present Metacognition Inventory Form
A and Form B, following methods were used,
1. Criterion Prediction Procedures :
a) Concurrent Validity
2. Construct Identification Procedures
b) Convergent Validity
c) Factorial Validity
1. Criterion Prediction Procedures :
a) Concurrent Validity : Concurrent Validity refers to the degree to
which the operationalization correlates with other measures of the same
construct that are measured at the same time. To determine the
concurrent validity, the correlation coefficient between Metacognition
Inventory prepared by the investigator and Metacognition Inventory
prepared by the Mahesh Narayan Dixit were administered on the
sample mentioned in below table. Both the Inventories were
administered with the gap of one period only.
Table 6.9
Sample for Validity estimation for Form A
Std 8 Std 9 Std 10 Total
Rural 15 15 15 45
Urban 16 14 14 44
Total 31 29 29 89
Table 6.10
Sample for Validity estimation for Form B
Std 8 Std 9 Std 10 Total
Rural 15 15 15 45
Urban 15 15 15 45
Total 30 30 30 90
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Thus, Metacognition inventory form A and Metacognition Inventory
prepared by Mahesh Dixit were administered on total 89 students and
Metacognition Inventory form B and Metacognition Inventory prepared by
Mahesh Dixit were administered on total 90 students to establish the Validity of
the Inventory.
Correlation coefficient between the scores of both the Metacognition
Inventory was calculated.
Correlation coefficient between the scores of MCI-A and Metacognition
Inventory prepared by Mahesh Dixit was 0.74
Correlation coefficient between the scores of MCI-B and Metacognition
Inventory prepared by Mahesh Dixit was 0.73
Results obtained from the scatter plot graph for MCI-A
The scatter plot graph in Graph 6.4 was generated with the SPSS
statistical analysis programme for the scores obtained from the MCI-form A and
Metacognition Inventory prepared by Mahesh Dixit.
Scatter Plot of scores obtained from Form A versus Scores of Metacognition
Inventory prepared by Mahesh Dixit
Graph-6.4
163
An analysis of the scatter plot shows a definite tendency towards
linearity, as most of the scores are fairly close to the regression line. Thus, from
the correlation value of 0.74 and the scatter plot it can be concluded that the
MCI-A is valid.
Results obtained form the scatter plot graph for MCI-B
The scatter plot graph in Graph 6.5 was also generated with the SPSS
statistical analysis programme for the scores obtained from the MCI-form B
and Metacognition Inventory prepared by Mahesh Dixit.
Scatter Plot of scores obtained from Form B versus Scores of Metacognition
Inventory prepared by Mahesh Dixit
Graph: 6.5
An analysis of the scatter plot shows a definite tendency towards
linearity, as most of the scores are fairly close to the regression line. Thus, from
the correlation value of 0.73 and the scatter plot it can be concluded that the
MCI-B is valid.
The Values of correlation coefficient shows moderate high correlation
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between both the inventories. And result of the scattered plot graph also
supports linear correlation. Thus, the metacognition inventory Form A and Form
B are moderately valid.
2. Construct Identification Procedures
b) Convergent Validity : To estimate the Convergent Validity of the
Metacognition Inventory the correlation coefficient between the scores of
Metacognition Inventory and Verbal and Non verbal Intelligence test
published by Akash Manomapan Kendra, Ahmedabad was calculated.
The values of correlation coefficient between the scores of both the
forms of Metacognition Inventory and Intelligence test were calculated. That is
as mentioned below.
• Correlation coefficient between MCI-A and Verbal Non Verbal
Intelligence Test published by Akash Manomapan Kendra, Ahmedabad
was 0.78
• Correlation coefficient between MCI- B and Verbal Non Verbal
Intelligence Test published by Akash Manomapan Kendra, Ahmedabad
was 0.73
The values of correlation coefficient are moderately high so that it can
be said that the present inventories; form A and form B are valid.
c) Factorial Validity : Factor analysis is a statistical method used to
describe variability among observed variables in terms of a potentially
lower number of unobserved variables called factors.
Type of factor analysis
• Exploratory Factor Analysis (EFA) is used to uncover the underlying
structure of a relatively large set of variables. The researcher's a priori
assumption is that any indicator may be associated with any factor. This
is the most common form of factor analysis. There is no prior theory
and one uses factor loadings to intuit the factor structure of the data.
• Confirmatory Factor Analysis (CFA) seeks to determine if the number of
165
factors and the loadings of measured (indicator) variables on them
conform to what is expected on the basis of pre-established theory.
Indicator variables are selected on the basis of prior theory and factor
analysis is used to see if they load as predicted on the expected number
of factors.
Types of factoring
• Principal Component Analysis (PCA) : The most common form of factor
analysis, PCA seeks a linear combination of variables such that the
maximum variance is extracted from the variables. It then removes this
variance and seeks a second linear combination which explains the
maximum proportion of the remaining variance, and so on. This is called
the principal axis method and results in orthogonal (uncorrelated)
factors.
• Canonical Factor Analysis, also called Rao's canonical factoring, is a
different method of computing the same model as PCA, which uses the
principal axis method. CFA seeks factors which have the highest
canonical correlation with the observed variables. CFA is unaffected by
arbitrary rescaling of the data.
• Common Factor Analysis, also called Principal Factor Analysis (PFA) or
Principal Axis Factoring (PAF), seeks the least number of factors which
can account for the common variance (correlation) of a set of variables.
• Image factoring: based on the correlation matrix of predicted variables
rather than actual variables, where each variable is predicted from the
others using multiple regressions.
• Alpha factoring based on maximizing the reliability of factors, assuming
variables are randomly sampled from a universe of variables. All other
methods assume cases to be sampled and variables fixed.
• Factor regression model : A combinatorial model of factor model and
regression model; or alternatively, it can be viewed as the hybrid factor
model, whose factors are partially known.
166
Factor Analysis of the Metacognition Inventory
In the present study the exploratory factor analysis was done with the
help of SPSS17 statistical analysis software. The analysis was done on the data
collected from the entire sample as shown before in table 6.6 and 6.7. KMO
and Bartlett's Test of sphericity was done to check the sampling adequacy.
Principal Component analysis was done. Varimax orthogonal rotation was
selected for the analysis.
• Kaiser-Meyer-Olkin Measure of Sampling Adequacy for MCI-A is
0.925 and for MCI-B it is 0.922 which indicated that the data were
appropriate for the factor analysis. It also shows the reliability of the
inventory.
• Bartlett's Test of Sphericity for MCI-A is 9795 and for MCI-B it is
11240. Both the values are significant at 0.000 levels which indicated
that the data were appropriate for the factor analysis.
Table 6.11 shows the correlation matrix of the scores of Metacognition
Inventory form A. It shows the Pearson correlation coefficient between all pairs
of components. Majority of the values are greater than 0.05. So that there is
no need to eliminate any item from factor analysis.
Table 6.12 shows the communalities and table 6.13 shows the total
variance explained. According to the table 6.13 only one factor is extracted
with eigen value greater than one (Eigen value = 4.14). Which indicates that all
the components measures the only one constyruct that is metacognition. Thus,
the results indicates the high validity of the Metacognition Inverntory form-A.
167
Table 6.11
Correlation Matrix of the Scores of MCI-A
1 2 3 4 5 6 7
1 1.000 .492 .503 .541 .516 .518 .480
2 .492 1.000 .497 .519 .530 .535 .538
3 .503 .497 1.000 .501 .493 .511 .530
4 .541 .519 .501 1.000 .554 .556 .535
5 .516 .530 .493 .554 1.000 .528 .568
6 .518 .535 .511 .556 .528 1.000 .556
7 .480 .538 .530 .535 .568 .556 1.000
1 .000 .000 .000 .000 .000 .000
2 .000 .000 .000 .000 .000 .000
3 .000 .000 .000 .000 .000 .000
4 .000 .000 .000 .000 .000 .000
5 .000 .000 .000 .000 .000 .000
6 .000 .000 .000 .000 .000 .000
7 .000 .000 .000 .000 .000 .000
Table 6.12
Communalities for MCI-A
Initial Extraction
1 1.000 .562
2 1.000 .582
3 1.000 .557
4 1.000 .612
5 1.000 .607
6 1.000 .612
7 1.000 .613
Cor
rela
tion
Sig
. (1-
taile
d)
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Table 6.13
Total Variance Explained for MCI-A
Component Initial Eigenvalues Extraction Sums of
Squared Loadings
Total % of VarianceCumulative % Total % of VarianceCumulative %
1 4.145 59.214 59.214 4.145 59.214 59.214
2 .541 7.723 66.937
3 .523 7.475 74.412
4 .481 6.871 81.284
5 .469 6.701 87.985
6 .434 6.200 94.185
7 .407 5.815 100.000
Scree plot of the Metacognition Inventory form A
Graph 6.6
Graph 6.6 show the scree plot obtained with SPSS software. The
X-axes shows the component number and the Y-axes shows the Eigen values.
The Eigen Value for the first factor is 4.14 and for the second factor it is 0.54.
169
The difference between the Eigen value of the first and second factor is 3.60
which is greater than 2. The difference between the first and second factor is
high. afterwards the diffrence decreases. So that the graph shows an elbo
shape. As per the scree plot only one factor can be extracted.
Thus, Communalities, number of factor extracted, and scree plot shows
the construct validity of the Metacognition Inventory form A.
Factor Analysis for Metacognition Inventory Form B
Table 6.14 shows the correlation matrix of the scores of Metacognition
Inventory form B. It shows the Pearson correlation coefficient between all pairs
of components. Majority of the values are greater than 0.05. So that there is
no need to eliminate any item from factor analysis.
Table 6.15 shows the communalities and table 6.16 shows the total
variance explained. According to the table 6.16 only one factor is extracted
with eigen value greater than one (Eigen value = 4.324). Which indicates that
all the components measures the only one constyruct that is metacognition.
Thus, the results indicates the high validity of the Metacognition Inverntory
form-B.
170
Table 6.14
Correlation Matrix of the Scores of MCI-B
1 2 3 4 5 6 7
1 1.000 .529 .609 .590 .557 .554 .519
2 .529 1.000 .511 .621 .545 .558 .559
3 .609 .511 1.000 .527 .574 .555 .527
4 .590 .621 .527 1.000 .542 .558 .587
5 .557 .545 .574 .542 1.000 .516 .562
6 .554 .558 .555 .558 .516 1.000 .531
7 .519 .559 .527 .587 .562 .531 1.000
1 .000 .000 .000 .000 .000 .000
2 .000 .000 .000 .000 .000 .000
3 .000 .000 .000 .000 .000 .000
4 .000 .000 .000 .000 .000 .000
5 .000 .000 .000 .000 .000 .000
6 .000 .000 .000 .000 .000 .000
7 .000 .000 .000 .000 .000 .000
Table 6.15
Communalities for MCI-B
Initial Extraction
1 1.000 .629
2 1.000 .618
3 1.000 .611
4 1.000 .650
5 1.000 .609
6 1.000 .601
7 1.000 .605
Cor
rela
tion
Sig
. (1-
taile
d)
171
Table 6.16
Total Variance Explained for MCI-B
Component Initial Eigenvalues Extraction Sums of
Squared Loadings
Total % of VarianceCumulative % Total % of VarianceCumulative %
1 4.324 61.767 61.767 4.324 61.767 61.767
2 .565 8.074 69.841
3 .498 7.119 76.960
4 .451 6.448 83.408
5 .429 6.122 89.530
6 .387 5.525 95.054
7 .346 4.946 100.000
Scree plot of the Metacognition Inventory form B
Graph 6.7
172
Graph 6.7 shows the scree plot obtained with SPSS software. The
X-axes shows the component number and the Y-axes shows the Eigen values.
The Eigen Value for the first factor is 4.32 and for the second factor it is 0.56.
The difference between the Eigen value of the first and second factor is 3.76
which is greater than 2. The difference between the first and second factor is
high. afterwards the difference decreases. So that the graph shows an elbo
shape. As per the scree plot maximum One factor can be extracted.
Thus, Communalities, number of factor extracted, and scree plot show
the construct validity of the Metacognition Inventory form B.
173
REFERENCES
1 A., Anastasi, & A., Urbina, (2002). Psychological Testing (7th Edition). New
Delhi: Pearson Education (Singapore) Pvt. Ltd., Indian Branch,
p. 84.
2 William, M. Trochim, The Research Methods Knowledge Base, 2nd Edition.
Internet WWW page, at
URL: <http://www.socialresearchmethods.net/kb/> (version
current as of October 20, 2006).
3 J. P, Guilford, (1956). Fundamental Statistics in Psychology and
Education (3rd Edition). Tokyo, Japan: Asian Students Edition,
McGraw-Hill Book Company, Inc., p: 145.
4 S. F., Freeman, (2006). Theory and Practice of Psychological Testing, (3rd
Edition), India : Surjeet Publication, p:88.
5 R. S., Patel, (2011). Statistical Methods for Educational Research,
Ahmedabad: Jay Publication, p. 445.
6 A., Anastasi, & A., Urbina, (2002). Op.Cit., pp. 114-135.
