ArticlePDF Available

Commonality Analysis: Understanding Variance Contributions to Overall Canonical Correlation Effects of Attitude Toward Mathematics on Geometry Achievement



Content may be subject to copyright.
Capraro & Capraro
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
Commonality Analysis: Understanding Variance Contributions
to Overall Canonical Correlation Effects of Attitude Toward
Mathematics on Geometry Achievement
Robert M. Capraro Mary Margaret Capraro
Texas A & M University
Canonical correlation analysis is the most general linear model subsuming all other univariate and multivariate cases
(Kerlinger & Pedhazur, 1973; Thompson, 1985, 1991). Because “reality” is a complex place, a multivariate analysis
such as canonical correlation analysis is demanded to match the research design. It is the purpose of this paper to
increase the awareness and use of canonical correlation analysis and, specifically to demonstrate the value of the
related procedure of commonality analysis. Commonality analysis provides the researcher with information
regarding the variance explained by each of the measured variables and the common contribution from one or more
of the other variables in a canonical analysis (Beaton, 1973; Frederick, 1999). This paper identifies confidence as
contributing the most unique variance to the model, being more important than either intrinsic value or worry to
geometry content knowledge and spatial visualization.
n developing the concept of commonality analysis (CA) one must be familiar with canonical
correlation analysis (CCA), a multivariate technique. Most educational research settings demand an
analysis that accounts for reality so a multivariate analysis should be used to match the research
design as closely as possible. Canonical correlation analysis (CCA) is the most general case of the
general liner model (GLM) (Baggaley, 1981). All univariate and multivariate cases can be treated as
special cases of CCA (Thompson, 1984, 1991). As Henson (2000) noted, “CCA is superior to ANOVA
and MANOVA when the independent variables are intervally scaled, thus eliminating the need to discard
variance” otherwise one should refrain from using canonical correlation for these purposes.
There are several rational reasons for selecting CCA. Regarding OVA methods, the first is that CCA
honors the relationship among variables because CCA does not require the variables to be converted from
their original scale into arbitrary predictor categories (Frederick, 1999). Second, the method honors the
reality to which the researcher is often trying to generalize (Henson, 2000; Tatsuoka, 1971; Thompson,
1984,1991). Third, reality has multiple outcomes with multiple causes; thus, it follows that most causes
have multiple effects necessitating a multivariate approach (Thompson, 1991). Therefore, any analytic
model that does not account for reality in which research is conducted distorts interpretations and
potentially provides unreliable results (Tatsuoka, 1971). Historicalyr, research studies rarely used CCA.
Prohibitive calculations, difficulty in trying to interpret canonical results and general unfamiliarity with
the method contributed to CCA's absence from the literature (Baggaley, 1981; DeVito, 1976; Fan, 1996;
Thompson, 1984).
Using CCA in real-life research situations increases the reliability of the results by limiting the
inflation of Type I "experimentwise" error rates by reducing the number of analyses in a given study
(Shavelson, 1988; Thompson, 1991). As Thompson (1991) stated CCA's limitation of "experimentwise"
error, reduces the probability of making a Type I error anywhere within the investigation. Commonly,
Type I error refers to "testwise" error rates, the probability of making an error in regards to a specified
hypothesis test.
Thompson (1984) stated that some research almost demands CCA in which “ . . . it is the simplest
model that can do justice to the difficult problem of scientific generalization” (p. 8). Furthermore, the use
of CCA leads to the use of commonality analysis (Thompson, 1984). Although the voluminous output
from CCA can be difficult to interpret (Tatsuoka, 1971; Thompson, 1984, 1990), however, once complete
and noteworthy results emerge, one is obliged to consider the use of commonality analysis.
Commonality Analysis
Commonality analysis, also known as elements analysis and components analysis was developed for
multiple regression analysis in the late 1960's (Newton & Spurell, 1967; Thompson, Miller, & James,
1985). Commonality analysis provides the researcher with information regarding the variance explained
Commonality Analysis
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
by each of the measured variables and the common contribution from one or more of the other variables
(Beaton, 1973; Frederick, 1999). Partitioning of the variables takes two distinct forms. The first is in the
form of explanatory ability that is in common with other variable(s). The second explanatory power can
be attributed to unique contributions of a variable. This information should not be confused with
interaction effects of regression. Interaction effects cannot be considered as indicating a unique
contribution to the criterion set. Each variable in the predictor set simply adds predictive ability or
increased variance to the first one (variable) entered. Commonality analysis, however, determines the
variance explained that two or more predictor variables share that is useful in predicting relationships
with the criterion variable set. Essentially, Beaton (1973) stated that CA partitions the common and
unique variance of the several possible predictor variables on the set of criterion variables.
Commonalities can be either positive or negative. Beaton (1973) explained that negative
commonalities are rare in educational research but more common in physical science research. While both
positive and negative commonalities are useful, negative commonalities indicate that one variable
confounds the variance explained by another. When referring to the power of CA, power is synonymous
with variance explained. Negative commonalities may actually indicate improved power when both
variables are used to make predictions (Beaton, 1973). The following example illustrates the relationship:
An Olympic track athlete must be fast and strong, therefore, a strong-fast athlete would be correlated with
success at running track. However, one would believe the two variables (fast and strong) would be
moderately negatively correlated, that is as muscle strength and mass increase, speed would decrease. The
negative commonality between speed and strength would indicate a confounded variable. In this case, by
knowing both the speed and strength one would expect to make better predictions of successful track
running. Imagine just knowing the speed or strength of the athlete. A fast athlete may perform well in a
short sprint but be severely impaired in a distance event. Conversely, a strong athlete may excel in
endurance and persevere for distance, but lack the speed to win. The negative commonality in this case
indicates that the power of both variables is greater when the other variable is also used.
Conducting a Commonality Analysis
The complexity of conducting a CA ranges from the unsophisticated to the sublime. Frederick (1999)
suggested the use of no more than four (predictor) measured variables because as the number of
predictors increases so does the difficulty of interpretation. Frederick continued, explaining that the
commonality calculations increase in difficulty exponentially as the number of predictors increases.
Pedhazur (1982) and Frederick (1999) recommend that to avoid some of the complexities one should
group similar variables or do some preliminary analyses to distinguish the most powerful predictors
before conducting the CA such as a canonical correlation analysis.
The full model CCA is run with the following SPSS syntax:
spacerel gcksum with int.val worry confid
/print=signif (multiv eigen dimenr)
/discrim=(stan estim cor alpha(.999))/design.
The criterion variables are space relations (spacerel) and geometry content knowledge
(gcksum). The predictor variables are confidence solving mathematics problems (confid), worry
(worry), and finally mathematics intrinsic value (int.val). Possible relationships among variables
are illustrated by Figure 1.
The Venn diagram illustrating commonality analysis in Figure 1 serves as a model for the comparison
of data examined in the present paper. The data was collected in a southeastern state and represents 287
sixth grade students' scores on three measures, the Space Relations portion of the Differential Aptitude
Test (Bennett, Seashore, & Wesman, 1973), the Geometry Content Knowledge test (Carroll, 1998), and
the Mathematics Attitude Scale (Gierl & Bisanz, 1997).
The first step in running a CA begins with the findings of the CCA (the syntax provided earlier; also
see the Appendix for the complete SPSS syntax). The next step involves running a descriptive analysis for
the purposes of obtaining the standard deviation and means of each variable in order to calculate z-scores.
The z-scores are computed for the observed variables by the following SPSS syntax:
Capraro & Capraro
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
COMPUTE zspace = (spacerel- mean)/standard deviation.
COMPUTE zgck = (gcksum- mean)/standard deviation.
To create the synthetic canonical variate scores, multiply the z-scores by the standardized canonical
function coefficients (found in the original CCA), and then sum the scores for the function. The following
SPSS syntax will yield the two sets of criterion variable composite scores (called crit1 and crit2) for both
canonical functions.
COMPUTE crit1=(standardized canonical function coefficient I*zspace)
+(standardized canonical function coefficient I*zgck).
COMPUTE crit2=(standardized canonical function coefficient II*zspace)
+(standardized canonical function coefficient II*zgck).
Next, the CA requires running several multiple regression analyses for each criterion composite i.e.,
crit1 and crit2 using all possible combinations of predictor variables. Refer to Table 1 for the
combinations for 2 or 3 predictor variables.
Figure 1. Illustrating Commonality Analysis.
Common to ALL
Variable 1 Variable 2 Variable 2
Unique to
variable 1
Unique to
variable 2
Common to
variable 1&2
Variable 3
Unique to
variable 3
Common to
Common to
1 & 3
Commonality Analysis
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
Table 1. Methods of Computing Unique and Common Variance.
Two Predictor Variables
2, U(2)=R2
1, C(12)=R2
1 -R2
Three Predictor Variables
23, U(2)=R2
13, U(3)=R2
12, C(12)= R2
23 -R2
123, C(13)= R2
2 +
123, C(23)= R2
1 + R2
123, C(123)= R2
2 + R2
3 -R2
Note: U= unique variance, C= common variance, C13 = Common to variables 1 & 3
R2=squared multiple correlation from the respective regression analysis.
Table 2. Commonality Table.
Variance Function I Function II
Partition Intrinsic Worry Confidence Composite Intrinsic Worry Confidence Composite
U Intrinsic 0.001 0.001 0.019 0.019
U Worry 0.009 0.009 0 0
U Confidence 0.188 0.188 .003 .003
C IW 0.002 0.002 0.002 0.002
C IC 0.049 0.049 0.049 0.049 -0.003 -0.003
C WC 0.004 0.004 0.004 0
C IWC -0.011 -0.011 -0.011 -0.011 0 0 0 0
R2 with Crit 0.041 0.004 0.230 0.242 0.018 0.002 0 0.021
Table 3. Comparisons of Multivariate CCA and Univariate Multiple Regression with All Predictors.
Statistic I II
Multiple Regression (R2) .242 .021
Canonical Correlation (Rc2) .242 .021
Finally, add or subtract relevant effects to calculate the unique and common variance components for
each predictor variable on each composite. Do this either by hand or by spreadsheet. The number of
components in an analysis will equal (2k-1), where k= number of predictor variables in the set. So, four
predictors produce, 15 components, four-first order (unique), six-second order (common to two
variables), four-third order (common to three variables), and one- fourth order (common to all).
The analysis of the present data consisted of two criterion variables, space relations and geometry
content knowledge, and three predictor variables from the subscales of the Mathematics Attitude Scales,
confidence, worry, and intrinsic value. One would expect, that through the application of (2k-1), to have
seven composites, three-first order (unique), three-second order (common to two) and one-third order
(common to all). Results are displayed in Table 2.
Recall that both a full CCA and multiple linear regression with all predictors were conducted. The
results displayed in Table 3 confirm that both procedures yielded the same results. Note that the R2 and
Rc2 for Functions I and II are the same for both the multiple regression and CCA. The R2 from the
multiple linear regression reflect the additive effects of all the predictor combinations. These numbers will
be confirmed again when summing all of the separate composites for each function (Table 2).
Analyzing Results
One must return to the Venn diagram (Figure 1) and then reconstruct it using the actual data from
Table 2. This graphic helps one to visualize the relationships of the partitioned variance. If one only
requires the variance explained from the entire CCA then there is no need to conduct a CA. However, the
Capraro & Capraro
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
Figure 2. Venn Diagram Showing Commonalities for Function I.
power to partition the variance and observe which variable contributes what variance is invaluable when
determining parsimony. In analyzing the data from Function I, one notices that confidence explains
18.8% of the variance alone while intrinsic value and confidence contribute 4.9 % in common. The three
predictors when taken together explained 24.2% of the first function. Worry and intrinsic value explain
very little of the variance from Function I, either uniquely (0.9% or 0.1%) or in common (0.1% to 0.4%)
with other measured predictor variables.
Frederick (1999) stated that negative commonalities should be interpreted as zero. While Beaton
(1973) believed that negative commonalities were actually confounding, increasing the predictive ability.
Caution needs to be taken when interpreting the negative commonality in the common to all variables
(Figure 2). As stated before in the analogy to the athlete, a negative commonality on one variable may
improve the overall prediction power. However, in this case it is more appropriate to interpret the
negative commonality as zero. Think of the situation this way, the variance explained by all three
variables inversely predicts the variance explained when all the variables are taken separately. This
scenario makes little sense and implies that the variables as a whole indicate an inverse relationship to the
criterion variables where they imply a direct relationship when considered individually.
In Function I, summing the variance explained from each of the unique variables and each of the
common contributions yields 0.242. The 0.242 is the variance explained in the multiple regression (R2)
and the canonical correlation Rc2. Because CA yields the partitioned values, one would expect that the
sum of the values would equal the total variance explained by either the univariate or the multivariate
approach. This also illustrates that CCA subsumes the univariate case.
Common to
Unique to Worry
Unique to
Unique to
Common to
Confidence &
Common to
Intrinsic &
Common to
Intrinsic &
0.001 or
0.1% 0.188 or
0.009 or
0.049 or
0.004 or
0.002 or
-0.011 or
Sum Total of all Commonalities
0.242 or 24.2%
Commonality Analysis
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
Figure 3. Venn Diagram Showing Commonalities for Function II.
In Function II the total variance explained is a paltry 2.1% This is hardly worthy of discussion except
for the relatively large sample size to variable ratio and effect size originally indicated in the CCA. The
effect size of 0.38, considered large in regards to educational research stands out in this case as well. The
practical importance can not be neglected either. In review of other research on this topic, the effect size
of 0.38 is large by comparison. The variance explained was partitioned into unique and common
contributions and a few interesting observations are noticed.
On Function II (Figure 3) the results appear a little more interesting. Intrinsic value contributes the
most variance explained 1.9% alone and confidence contributes 0.3% alone. When considering the
common variance between confidence and intrinsic a -0.3% variance explained exists. This confounding
seems to indicate that as the scores on confidence decreases (indicating less confidence) success on the
criterion variables increase. In this case scale may influence the negative commonality. This interpretation
defies logic and again implores the interpretation offered by Frederick (1999) that it should be interpreted
as zero. Again, in Function II (Figure 3) worry, traditionally attributed as a major cause of poor
performance in mathematics, was found to have virtually no influence.
After performing the CCA, sufficient evidence existed (i.e., an interpretable Rc2) to continue and
determine the unique and common contributions of the predictor variables. Particularly, the full model
effect size of 0.38 aided the researcher in deciding to continue with further analysis. The CA yielded
results on two functions. On Function I, the unique variance accounted for largely resides with the
confidence variable (18.8%). This represents the overwhelming portion of the total variance 24.2%
accounted for by all three of the variables - confidence, worry, and intrinsic value. This leads to an
Common to
Unique to Worry
Unique to
Unique to
Common to
Confidence &
Common to
Intrinsic &
to Intrinsic &
0.019 or
1.9% 0.003 or
0.0 or
-0.003 or
0.000 or
0.002 or
0.000 or
Sum Total of all Commonalities
0.021 or 2.1%
Capraro & Capraro
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
interesting supposition. First, contrary to contemporary findings this study seems to indicate that worry,
contributing less than 1% of the variance, also referred to as math anxiety, is not a powerful predictor of
mathematics achievement. Perhaps more time spent working on confidence and building "mathematics
self-esteem" will improve mathematics achievement. Second, the results of Function II indicate that all
three variables account for slightly more than 2.0% of the variance in the criterion set. This result is not
very promising. However, of the variance accounted for intrinsic value accounts for 1.9 %, confidence
accounts for 0.3%, and worry accounts for 0.0% of the total variance. On function II intrinsic value
appears to be more helpful in predicting geometry achievement than either of the other two subscales. A
list of all the SPSS syntax used in this analysis is listed in the Appendix.
The value of CA resides in the fact that the procedure yields unique and common variance explained
from each of the predictor variables. The variance explained is not summative nor is it a result of
interaction effects. The variance explained from the full model can be understood and the contributions of
each separate variable can be interpreted in relation to the full model for the results of the unique effects.
This helps to determine the most parsimonious model and relevant data sources, particularly when using a
test containing subscales.
Baggaley, A.R. (1981). Multivariate analysis: an introduction for consumers of behavioral research.
Evaluation Review, 5, 123-131.
Beaton, A. E. (March, 1973). Commonality. (ERIC Document Reproduction Service No. ED 111 829)
Bennett, G. K., Seashore, H. G., & Wesman, A. G. (1973). Differential aptitude tests: Administrator’s
handbook. New York: Psychological Corporation
Carroll, W. M. (1998). Geometric knowledge of middle school students in a reform based mathematics
curriculum. School Science and Mathematics, 98 (4), 188-198.
DeVito, P. J. (May, 1976). The use of commonality analysis in educational research. Paper presented at
the annual meeting of the New England Educational Research Association, Provincetown, MA. (ERIC
Document Reproduction Service No. ED 146 210)
Fan, X. (1996). Canonical correlation analysis as a general analytic model. In B. Thompson (Ed.),
Advances in social sciences methodology (Vol. 4, pp. 71-94). Greenwich, CT: JAI Press.
Fan, X. (1997). Canonical correlation analysis and structural equation modeling: What do they have in
common? Structural Equation Modeling 4, 65-79.
Frederick, B. N. (1999). Partitioning variance in the multivariate case: A step-by-step guide to canonical
commonality analysis. In B. Thompson (Ed.), Advances in social sciences methodology (Vol. 5, pp.
305-318). Stamford, CT: JAI Press.
Gierl, M., & Bisanz, J. (1997). Anxieties and attitudes related to mathematics in grades 3 and 6. Journal
of Experimental Education, 63 (2), 139-158.
Henson, R. (2000). Demystifying parametric analyses: Illustrating canonical correlation analysis as the
multivariate general linear model. Multiple Linear Regression Viewpoints, 26 (1), 11-19.
Kerlinger, F. N. & Pedhazur, E. J., (1973). Multiple regression in behavioral research. New York, NY:
Holt Rinehart & Winston.
Newton, R. G., & Spurell, D. J. (1967). Examples of the use of elements for classifying regression
analysis. Applied Statistics, 16,165-172.
Pedhazur, E. (1982). Multiple regression in behavior research: Explanation and prediction. (2nd ed.).
New York, NY: Holt Rinehart, and Winston.
Pedhazur, E. (1997). Canonical and discriminant analysis, and multivariate analysis of variance. In
Multiple Regression in Behavior Research. (3rd ed., pp. 924-979). Fort Worth, TX: Harcourt Brace.
Shavelson, R. J. (1988). Statistical reasoning for the behavioral sciences. Boston: Allyn & Bacon.
Stevens, J. (1999). Canonical correlations. In Applied Multivariate Statistics for the Social Sciences (3rd
ed., pp.429-449). Mahwah, NJ: Lawrence Earlbaum Associates.
Tatsuoka, M. (1971). Discriminant analysis and canonical correlation. In Multivariate Analysis:
Techniques for Educational and Psychological Research (Chapter 6, pp. 157-194). New York: Wiley.
Thompson, B. (1984). Canonical correlation analysis uses and interpretations. Newbury Park, CA:
Commonality Analysis
Multiple Linear Regression Viewpoints, 2001, Vol. 27(2)
Thompson, B. (1991). Methods, plainly speaking: A primer on the logic and use of canonical correlation
analysis. Measurement and Evaluation in Counseling and Development, 24 (2), 80-93.
Thompson, B., & Miller, J. H. (February, 1985). A multivariate method of commonality analysis. Paper
presented at the annual meeting of the Southwest Educational Research Association, Austin, TX.
(ERIC Document Reproduction Service No. ED 263 151)
Send correspondence to: Robert M. Capraro, College of Education, Department of Teaching,
Learning, & Culture, Texas A & M University, 308 Harrington Tower, College Station, TX 77843-4232.
SPSS Syntax for Conducting CA
Opens the file containing the data for the analyis
"C:\WINDOWS\DESKTOP\Dissertation Data\Modified Dissertation Data File.sav"
Runs the descriptives that will be necessary for creating CRIT1 and CRIT2
VARIABLES=spacerel gcksum
The full CCA syntax supplies the Rc2 and the structure & function coefficients
spacerel gcksum with int.val worry confid
/print=signif(multiv eigen dimenr)
/discrim(stan estim cor)alpha(.999))/design.
The syntax to create CRIT1 and CRIT2
COMPUTE crit1 = (.482*zspace)+(.645*zgck) .
COMPUTE crit2 = (-1.113*zspace)+(1.027*zgck) .
All the syntax to run all possible combinations multiple regressions for the 3
predictor variables.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter int.val worry confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter int.val worry confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter int.val confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter int.val confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter int.val worry.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter int.val worry.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter confid worry.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter confid worry.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter int.val.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter int.val.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter confid.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit1/enter worry.
regression variables=crit1 crit2 int.val worry confid/
dependent=crit2/enter worry
... These coefficients are analogous to beta weights in multiple regression. Importantly, discrepancies between these indicators are informative of multicollinearity and suppressor effects (Capraro & Capraro, 2001;Kuylen & Verhallen, 1981;Nimon et al., 2010). Thus, variables with high loadings but low weights may be indicative of multicollinearity, i.e., variance in these variables has been explained by other variables in the function coefficients. ...
... Furthermore, high weights do not necessarily mean that there is a high contribution of that trait to the prediction of prosocial behaviour. Variables with high weights but low loadings have been suggested as suppressors in linear equations (Capraro & Capraro, 2001;Nimon et al., 2010), meaning that traits showing such a pattern would not be directly related to prosocial behaviour, but rather they would be subtracting irrelevant variance of other traits in the affective/psychiatric CV to increase their predictive power in relation to the prosocial behaviour CV. ...
Full-text available
Prosocial behaviours-actions that benefit others-fundamentally shape our interpersonal interactions. Psychiatric disorders have been suggested to be related to prosocial disturbances, which may underlie many of their social impairments. However, broader affective traits, present in different degrees in both psychiatric and healthy populations, have also been linked to variability in prosociality. Therefore, it is unclear to what extent prosocial variability is explained by specific psychiatric disorders relative to broad affective traits. Using a computational, transdiagnostic approach in two online studies, we found that participants who reported being more affectively reactive across a broad cluster of traits manifested greater frequencies of prosocial actions in two different contexts: they reported being more averse to harming others for profit, and they were more willing to exert effort to benefit others. These findings help illuminate the profile of prosociality across psychiatric conditions as well as the architecture of prosocial behaviour in healthy individuals.
... It generates variance explained by each set of the measured independent variables and the common contribution of two or more sets of the independent variables jointly. The difference between these two analyses is that RDA assumes linear relations between multiple dependent variables and multiple independent variables, while CCA is more suitable for the relationship between multiple dependent and multiple independent variables that is unimodal [49,50]. Multivariate analyses have been broadly used to calculate the percentages of freshwater indicator variances explained by environmental factors at different spatial scales [9,51,52]. ...
Full-text available
Disentangling the effects of natural factors and human disturbances on freshwater systems is essential for understanding the distributions and composition of biological communities and their relationship with physicochemical and biological factors. As the spatial extent of ecological investigations increases from local to global scales, efforts to account for the increasing influence of natural factors become more important. This article synthesizes the current knowledge and commonly used approaches for disentangling these effects on aquatic systems. New understanding has been facilitated by the availability of large-scale geospatial landscape databases that facilitate regional analyses and classifications in conjunction with novel approaches to identify reference conditions and statistical partitioning analyses. This synthesis begins with a summary of how natural factors and human disturbances interactively affect aquatic systems. It then provides an overview of why it is essential to separate the effects of natural factors and human disturbances and a description of examples of landscape databases that make the separation of natural and human factors feasible. It last synthesizes currently-used common approaches for separating the effects of natural factors from human disturbances. Our synthesis assembles representative approaches to disentangling human disturbances in one place to provide new insights that stimulate integrated uses of multiple approaches and the development of new approaches so that management actions can be taken to protect and restore aquatic ecosystem health.
... and the explained variance .10 [47,56]. Based on this criterion, despite being statistically significant (Wilk's λ = .928, ...
Background: While literature includes a number of studies about burnout in teaching, investigations on teaching field-specific perspective remain limited. Research is needed to improve practical implications based on structured theoretical models and methodological basis that focusses on the unique environment of PE teaching field and causal factors behind burnout. Objective: The present study aimed to examine burnout among physical education (PE) teachers based on the job demands-resources (J-DR) model. Methods: A sequential explanatory mixed design was conducted in the study. 173 teachers replied to questionnaires, of which 14 teachers thereafter participated in semi-structured interviews. Demographic information form, Maslach Burnout Inventory, and J-DR scale for PE teachers were used, as well as an interview form. 173 teachers were first asked to report demographic information, and score Maslach Burnout Inventory and J-DR scale. Then a subsample group (n = 14) was identified/sampled for a semi-structured interview. Canonical correlation and constant comparative analysis were used to unpack the data. Results: Teachers' states of burnout varied, and physical, organisational, and socio-cultural resources were closely related with burnout levels. Demands that cause pressure on burnout were determined as paperwork and bureaucracy, student-related factors, and pandemic-related experiences. In addition to supporting the general model, specific J-DR factors for PE teaching were observed that is linked with burnout. Conclusion: J-DR factors that might lead to negative conditions in the teaching environment should be considered, and field-specific factors should be focused on through arrangements to increase teaching efficiency and improve the quality of PE teachers' professional life.
... We found it creates more challenges than insight in commonality analysis, as the visualisations and interpretations become opaque when exploring that many predictors. For example, whereas a three-cue model produces seven variance components in the commonality analysis results, a four predictor model produces 15 components: four components representing unique variance, six representing common variance between two variable pairings, four representing common variance between three variable pairings and one that represents the variance common to all variables in the model (Capraro & Capraro, 2001). ...
Full-text available
Audiences, juries, and critics continually evaluate performers based on their interpretations of familiar classics. Yet formally assessing the perceptual consequences of interpretive decisions is challenging – particularly with respect to how they shape emotional messages. Here, we explore the issue through comparison of emotion ratings (using scales of arousal and valence) for excerpts of all 48 pieces from Bach’s Well-Tempered Clavier. In this series of studies, participants evaluated one of seven interpretations by highly regarded pianists. This work offers the novel ability to simultaneously explore (1) how different interpretations by expert pianists shape emotional messages, (2) the degree to which structural and interpretative elements shape the clarity of emotional messages, and (3) how interpretative differences affect the strength of specific features or cues to convey musical emotion.
... These results were visualized with EulerAPE (Micallef and Rodgers, 2014), which can be used to plot overlapping ellipses proportional to the variance partition of the total explained variance (Groen et al., 2018). Although in principle, negative variance can reflect informative relationships among predictors (Capraro and Capraro, 2001), in the present context these values were typically so small they are negligible (e.g., À0.1% of the total explained variance). They were therefore excluded from the visualization. ...
Some of the most impressive functional specialization in the human brain is found in occipitotemporal cortex (OTC), where several areas exhibit selectivity for a small number of visual categories, such as faces and bodies, and spatially cluster based on stimulus animacy. Previous studies suggest this animacy organization reflects the representation of an intuitive taxonomic hierarchy, distinct from the presence of face- and body-selective areas in OTC. Using human fMRI, we investigated the independent contribution of these two factors - the face-body division and taxonomic hierarchy - in accounting for the animacy organization of OTC, and whether they might also be reflected in the architecture of several deep neural networks that have not been explicitly trained to differentiate taxonomic relations. We found that graded visual selectivity, based on animal resemblance to human faces and bodies, masquerades as an apparent animacy continuum, which suggests that taxonomy is not a separate factor underlying the organization of the ventral visual pathway.Significance StatementPortions of visual cortex are specialized to represent whether types of objects are animate in the sense of being capable of self-movement. Two factors have been proposed as accounting for this animacy organization: representations of faces and bodies or an intuitive taxonomic continuum of humans and animals. We performed an experiment to assess the independent contribution of both of these factors. We found that graded visual representations, based on animal resemblance to human faces and bodies, masquerade as an apparent animacy continuum, suggesting that taxonomy is not a separate factor underlying the organization of areas in visual cortex.
... For example, even a variable without any association may receive a large weight if it explains error variance in other variables completely independent of maltreatment (cf. Suppression Effect in Capraro and Capraro [4]). Thus, considering importance maps cannot remedy the problem outlined above. ...
... Also, canonical correlation values less than .30 are not interpreted as the variance explained by variable pairs is below 10% (Capraro & Capraro, 2001). Therefore, the findings of the first canonical variable pair were interpreted, and the findings of the second canonical variable pair were not interpreted. ...
Full-text available
The current study aims to determine whether there is a relationship between transformational leadership and teachers' motivation and whether this relationship if any, differs significantly based on various demographic variables. Within the framework of this aim, two scales were applied to 418 teachers working at primary, middle, and high schools in Istanbul. The data collection tools used in the study are the "Multidimensional Work Motivational Scale" developed by Gagné et al. (2010), and the "Transformational Leadership Scale" developed by Brestrich (2000). During the analysis of the data collected through scales, mean, frequency, and descriptive values such as standard deviation were used as well as independent groups t-test, multivariate variance analysis (MANOVA), and canonical correlation analysis. The results showed that as teachers perceive their principals as transformational leaders, their motivation including their inner motivation decreases. Besides, teachers' perceptions of the transformational leadership skills of the principals change according to time of working in their current school, education levels and gender. It was also explored that the motivation status of female teachers was higher than male teachers.
... The effects of L1 and L2 phonological awareness on English word reading Commonality analyses were used to calculate commonality coefficients to examine the unique and common contributions of Arabic and English phonological awareness to English word reading (Capraro & Capraro, 2001;Ray-Mukherjee et al., 2014). The commonality coefficients for the unique variance explained by phonological awareness in each language as well as the shared variance for phonological awareness across languages is calculated (see Table 6). ...
Word reading is a fundamental skill in reading and one of the building blocks of reading comprehension. Theories have posited that for second language (L2) learners, word reading skills are related if the children have sufficient experience in the L2 and are literate in the first language (L1). The L1 and L2 reading, phonological awareness skills, and morphological awareness skills of Syrian refugee children who speak Arabic and English were measured. These children were recent immigrants with limited L2 skills and varying levels of L1 education that was often not commensurate with their ages. Within- and across-language skills were examined in 96 children, ages 6 to 13 years. Results showed that phonological awareness and morphological awareness were strong within-language variables related to reading. Additionally, Arabic phonological awareness and morphological processing were strongly related to English word reading. Commonality analyses for variables within constructs (e.g., phonological awareness, morphological awareness) but across languages (Arabic and English) in relation to English word reading showed that in addition to unique variance contributed by the variables, there was a high degree of overlapping variance.
Full-text available
Karar verme stilleri ile ilgili literatürde farklı kategorilendirmeler bulunmaktadır. Bu durum karar verme stillerinin diğer değişkenlerle ilişkilerinde karmaşık sonuçlara yol açmaktadır. Özellikle karar verme stillerinin şekillendiği aile ortamında bu stillerin anne baba tutumları ile ilişkileri yeterince açığa çıkarılmamıştır. Mevcut çalışmada bu iki değişken arasındaki karmaşık ilişkileri açığa çıkarmak için çok değişkenli ilişkileri açığa çıkarmada kullanılan Kanonik Korelasyon Analizi kullanılmıştır. Bu doğrultuda çeşitli üniversitelerden uygun örnekleme yöntemi ile 378 (302 kadın ve 76 erkek) katılımcıdan veri toplanmıştır. Toplanan veriler, Kanonik Korelasyon Analizi ile analiz edilmiştir. Kanonik Korelasyon analizi sonucunda, algılanan anne baba tutumu ve karar verme stilleri veri setlerinin % 8.1’lik bir varyansı paylaştıkları belirlenmiştir. Araştırmada ayrıca karar verme stilleri veri setinin % 40’ının kendi alt boyutları, %3’ünün ise anne baba tutumları alt boyutları tarafından açıklandığı; anne baba tutumları veri setinin ise % 67’sinin kendi alt boyutları, % 6’sının da karar verme stilleri alt boyutları tarafından açıklandığı bulgulanmıştır. Bu bulgular neticesinde anne baba tutumları ile karar verme stilleri arasında çok değişkenli yaklaşımın, basit korelasyondan daha fazla açıklayıcı bir güce sahip olduğu, bu iki değişken kümesi arasındaki doğrudan ilişkilerin zayıf olduğu ve dolaylı ilişkilerin araştırılması gerektiği sonuçlarına ulaşılmıştır.
Full-text available
Although studies of musical emotion often focus on the role of the composer and performer, the communicative process is also influenced by the listener’s musical background or experience. Given the equivocal nature of evidence regarding the effects of musical training, the role of listener expertise in conveyed musical emotion remains opaque. Here we examine emotional responses of musically trained listeners across two experiments using (1) eight measure excerpts, (2) musically resolved excerpts and compare them to responses collected from untrained listeners in Battcock and Schutz (2019). In each experiment 30 participants with six or more years of music training rated perceived emotion for 48 excerpts from Bach’s Well-Tempered Clavier ( WTC) using scales of valence and arousal. Models of listener ratings predict more variance in trained vs. untrained listeners across both experiments. More importantly however, we observe a shift in cue weights related to training. Using commonality analysis and Fischer Z score comparisons as well as margin of error calculations, we show that timing and mode affect untrained listeners equally, whereas mode plays a significantly stronger role than timing for trained listeners. This is not to say the emotional messages are less well recognized by untrained listeners—simply that training appears to shift the relative weight of cues used in making evaluations. These results clarify music training’s potential impact on the specific effects of cues in conveying musical emotion.
Full-text available
A review of the research literature suggests that teachers need to provide students with engaging problems, facilitate their discovery of analysis methods, and encourage classroom discussion and presentation of their approaches to solving problems. The present article illustrates how canonical correlation analysis can be employed to implement all the parametric tests that canonical methods subsume as special cases, including multiple regression. The point is heuristic: all analyses are correlational, all apply weights to measured variables to create synthetic variables, and all yield effect sizes analogous to r 2. Knowledge of such relationships helps inform researcher judgement of analysis selection and use.
This paper describes the use of elements in regression analysis (Newton and Spurrell, 1967) to clarify the problems which arose in two industrial studies. The use of elements contributed significantly to a better understanding of the processes under investigation.
Little is known about the development of mathematics anxiety in elementary school students. To address this gap in knowledge, the authors evaluated students in Grades 3 and 6 on measures of mathematics anxiety, school test anxiety, and attitudes toward mathematics to determine (a) whether different forms of mathematics anxiety exist, (b) whether mathematics test anxiety differs from school test anxiety, and (c) whether mathematics anxiety is related to different attitudes toward mathematics. Evidence was found for two distinct forms of mathematics anxiety: test and problem-solving anxiety. Mathematics test anxiety increased with age relative to mathematics problem-solving anxiety; this result demonstrated that children become more anxious about mathematics testing situations as they progress through school. Mathematics test anxiety was related, but not identical, to school test anxiety, and students in both grades were less anxious about math tests than about academic testing generally. Finally, older students tended to show more positive attitudes toward mathematics than did younger students, and relations between these attitudes and the two forms of mathematics anxiety also changed between Grades 3 and 6.
This article illustrates the relation between structural equation modeling (SEM) and canonical correlation analysis (CCA). The representation of CCA in SEM may provide some important interpretive information that is not available from conventional CCA, that is, statistical tests for the canonical function and index coefficients, and statistical tests for individual canonical functions. Hierarchically, the relation between the two analytic approaches suggests that SEM stands to be a more general analytic approach. For researchers interested in these techniques, an understanding of the interrelation among them can be helpful to our choice of analytic method.
A diagram is used to aid discussion of how several of the frequently used multivariate statistical techniques are interrelated. All of those discussed can be regarded as special cases of canonical correlation.
This paper focuses on three aspects related to the conceptualization and application of canonical correlation analysis as a dominant statistical model: (1) partial canonical correlation analysis and its application in statistical testing; (2) the relation between canonical correlation analysis and discriminant analysis; and (3) the relation between canonical correlation analysis and chi-square contingency table analysis. The paper shows that canonical correlation analysis can be conceptualized as the statistical model that brings together many other statistical techniques in a unified manner, and the power of this overarching model is significantly increased by applying the concept of partial correlation to the canonical case. Two data sets (one with two Y variables, three X variables, and two classification variables; and the other with two mixed variables with three levels for each) are used to illustrate the points covered. Computer program results are presented to augment the discussion. Appendix A presents the SAS program for some tabulated data. Six tables present analysis results, and there is a 29-item list of references. (Author/SLD)
Canonical correlation analysis and the closely related method J. Cohen (1982) calls set correlation can be viewed as the most general of the traditional least-squares methods for the analysis of data structures. In the opening section of this chapter I describe set and canonical correlation analysis as a widely applicable taxonomy for data analysis (presented here in a general social science context), show how they are related, and explain how all other least-squares procedures can be derived as conceptual special cases. Then I develop the traditional canonical analysis model, show its relations to principal components analysis, and review significance tests and other interpretive aids such as redundancy and the rotation of canonical components. I conclude with a discussion of methodological issues in the use of canonical analysis, including stepwise procedures and the need for cross-validation. I provide an example, using one of the commercially available statistics packages, to illustrate the elements of a canonical analysis. (PsycINFO Database Record (c) 2012 APA, all rights reserved)