allerup_multivariate

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International Journal of

Educational Research 39 (2003) 551563

Chapter 3

Multivariate analyses of student response

profilesacross countries and gender

Peter Allerup

Danish University of Education, Emdrupvej 101, DK 2400, Copenhagen NV, Denmark

Abstract

Phase one of the IEA Civic Study was designed for fourteen-year-old students. In Denmark

this included students from the eighth and ninth grades although civics is not part of the

required curriculum until grade nine. Students answers to questions concerning civic

knowledge were collected together with information related to student attitudes, whichprovided information on their perceptions of democratic values. This article analyses and

compares the structure of responses to the attitude questions across countries participating in

the Civic Study and investigates the relationship between knowledge (knowledge of content,

Type 1) and attitudes in terms of a gender perspective.

r 2004 Elsevier Ltd. All rights reserved.

1. Introduction

Many IEA Studies, such as the Reading Literacy Study (Elley, 1992) and theTIMSS Mathematics and Science Study (Beaton&Albert, 1996), include a number

of questions or items that constitute a set of dependent object variables, whose

variation will subsequently be explained by a set of independent variables,

predictors, or so-called controlling variables. Generally, the initial statistical analyses

investigate the relationship between the dependent and the independent variables to

identify whether there are any significant correlations among them. The traditional

perception of, e.g., reading ability being controlled, or predicted from a series of

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0883-0355/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijer.2004.07.004

E-mail address: [email protected] (P. Allerup).
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student and teacher background variables, lead the analyst to regress dependent

variables on the independent variables to determine those variables most responsible

for the variation of a dependent variable. It is, furthermore part of the same thinking

to believe, that, after having established a well-fitting statistical model describing therelationship, those independent variables that are malleable can be used to introduce

changes in the student environment with positive effects on the level of reading

ability.

In large part, this reasoning is not valid for the Civic Education Study. Although

knowledge and skills questions are organised together in one booklet, and

democratic values are caught by a series of attitude questions in a separate

booklet, the role of dependent and independent variables is not clearly assigned to

either set of questions. Knowledge and skills can be derived from student attitudes

and their composition of democratic values or, equally, democratic values may

presume the existence of knowledge and skills and can therefore be derived from this

knowledge.

Statistical analyses of Civic Study data, however, can determine, which set of

variables are the genuine independent and dependent variables at a later stage,

since most regression analyses are, in fact conditional analyses, where mainly for

technical convenience, one set of variables is kept as the conditioning, independent

variables. With this background in mind, we have selected knowledge as the

dependent variable and the attitude questions as independent variables. Thus, this

article will explore the relationship between civic knowledge and student democratic

values in a regression design using the attitude questions as the independentvariables.

In contrast to many other IEA Studies, the Civic Education Study emerged as a

study where initial statistical analyses of question-by-question information led to

scales information. In fact, statistical analyses and modelling by means of Rasch

Models (Rasch, 1960; Fischer et al., 1995; Allerup, 1994) aimed at evaluating

whether student attitudes could be assessed by calculating a one-dimensional student

score across a number of questions, rather than keeping track of the complete

student response pattern across the set of individual questions. The first international

cross country report (Torney-Purta, Lehman, Oswald, & Schulz, 2001) and the

Danish National Civic Report (Bruun, 2001) take advantage of these analyses, andthen present the results in terms of analyses of Rasch Scores as outcome scores from

two scales of knowledge and skills and from 11 student attitude scales. This strategy

will also be employed in this article.

2. Data collection

The sampling procedures for the Civic Study in Denmark were defined according

to the international sampling plan; thus,N= 3100 students in grade eight and N=

2600 students in grade nine were sampled. In addition to the international Civicquestions, students were also given a number of specific Danish questions as a

national option.

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P. Allerup / Int. J. Educ. Res. 39 (2003) 551563552


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3. Instruments

The knowledge scale and the 11 attitude scales are listed in Table 1 with

abbreviations for the scale names, as these will be the terms used in our discussion.

The international knowledge scale reports student Rasch scores as measures of

knowledge; these values are on an international basis constrained to mean value =100 and standard deviation=20. The attitude scales are also constrained

internationally, but these scales have been anchored to mean value = 10 and

standard deviation = 2.

4. Data analysisstructure of responses to attitude scales

Before analysing the relationship between civic knowledge and democratic values

derived from the 11 attitude scales, the internal structure of student responses to all

11 scales should be investigated. How do responses to the scales correlate? Does thespace spanned by the 11 scales enjoy a simpler structure? How can general

differences among student responses for all scales be investigated simultaneously?

And, finally, are any gender differences revealed by the scales?

5. Classical correlation analysis

One way of addressing the problem of correlation structure is to test whether the

content of the 11 scales can be caught by fewer latent dimensions. By means of

simple product moment correlations between the scales,Table 2displays the result ofapplying a classical unrestricted Factor Analysis to the Danish data set. As shown in

Table 2, the factor structure is not consistent across the two grades. For grade eight

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Table 1

One scale for assessing civic knowledge and 11 scales used for measuring student attitudes

Name Content

KNOWLMLE Knowledge Scale

CTCONMLE 1 Conventional Citizenship

CTSOCMLE 2 Social Movement Citizenship

GOVECMLE 3 Government Responsibility, Society Economy

GOVSOMLE 4 Government Responsibility, Society General

TRUSTMLE 5 Trust in Institutions

PATRIMLE 6 Patriotism

WOMRTMLE 7 Womens Rights

IMMIGMLE 8 Immigrants

CONFSMLE 9 School Participation

POLATMLE 10 Political Activities

CCLIMMLE 11 Classroom Climate

P. Allerup / Int. J. Educ. Res. 39 (2003) 551563 553


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there is a tendency towards one-dimensionality (first factor takes account of 42% of

the total variance), with PATRI outside the structure. A restricted two-factor

solution, however, still leaves approximately 45% to be explained by a second factor,

which seems to comprise CTCON, TRUST, POLAT and CCLIM. Grade nine offers

a clearer interpretation of the factor structure with approximately 32% of the

variance explained by the first factor and an even distribution of around 20% for

each of the other factors. Again, PATRI seems to constitute a single dimension(factor 4), while WOMR and IMMIG constitute the most loaded factor 1; the

government related issues GOVVEC and GOVSOM dominate factor 2 and, finally,

the general concept of conventional citizenship CTCON constitutes factor 3.

Factor analyses carried out for all 28 participating countries would produce

similar results. There would be a varying number of factors necessary to explain the

total variance, and country-specific factor patterns would emerge as latent

dimensions. Conclusions based on this kind of analysis of cross-country differences

are conclusions which start from a multi-faceted list of factors, their loadings and

interpretations. Only further local within-country analyses can offer valid and

reasonable interpretations to the factor structure found in a particular country. Thisprocedure cannot be undertaken as means of analysis and interpretation across all 28

countries, and other means of analysis are, therefore necessary.

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Table 2

Factor loadings (rotated solution, values exceeding 0.50 are marked) for Danish Data set grade eight and

grade nine. Eigenvalues exceeding 1 are listed

Variable Factors

F1 F2 F3 F4 F5

CTCONMLE 0.51* 0.32 0.42 0.33 grade 8

CTSOCMLE 0.57* 0.05 0.12 0.38 Eigen values

GOVECMLE 0.47 0.51* 0.07 0.23 2.6 1.3 1.2 1.1

GOVSOMLE 0.52* 0.43 0.21 0.15

TRUSTMLE 0.41 0.42 0.10 0.38

PATRIMLE 0.28 0.09 0.59* 0.54*

WOMRTMLE 0.59* 0.15 0.40 0.22

IMMIGMLE 0.53* 0.09 0.57* 0.09

CONFSMLE 0.57* 0.16 0.05 0.23

POLATMLE 0.25 0.63* 0.08 0.33

CCLIMMLE 0.50* 0.31 0.18 0.27

CTCONMLE 0.00 0.31 0.73* 0.18 grade 9

CTSOCMLE 0.15 0.54* 0.40 0.04 Eigen Values

GOVECMLE 0.10 0.73* 0.04 0.02 2.8 1.3 1.2 1.1

GOVSOMLE 0.09 0.71* 0.02 0.14

TRUSTMLE 0.40 0.16 0.31 0.46

PATRIMLE 0.01 0.16 0.03 0.84*

WOMRTMLE 0.71* 0.27 0.11 0.02

IMMIGMLE 0.70* 0.14 0.14

0.31CONFSMLE 0.47 0.34 0.03 0.26



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6. Measures of distance

As the international report (Torney-Purta et al., 2001) displays the mean values by

country for the attitude scales, a comprehensive picture of similarities and differencesacross countries is available for each scale. However, it is not possible with these

analyses to produce a composite student profile, i.e., how students simultaneously

respond to all 11 scales. Each response profile constitutes a point in an 11th

dimensional vector space. Groups of students go together in clusters of points. The

total set of students (approximately N 94000 students) form a sphere around the

international mean=(10,10,10,y,10) with a standard deviation on the distance to

this point of (2,2,y,2) ; these are the international mathematical constraints on the

Rasch scores for each of the 11 scales. Location and distance between points in

this multidimensional space will be evaluated using various multivariate statistical

techniques.

A widely used measure of distance among response vectors of higher dimensions is

the Mahalanobis Distance (Rao, 1965). This is a measure based on standardized

scale values and determined before measures of distance between any two

eleven-dimensional points will be calculated. It takes into account both the

actual site of a point (or a cluster of points) and the correlation structure of the

scales by attributing more length to the distance between two fixed points placed in

high correlating scales (co-ordinate axes) compared to independent scales. Points

with equal distances from the international mean=(10,10,10,y,10) form a rugby-

like football.

7. Between-country distances

The calculation of between-country distances results in an upper triangle of

bilateral distances, where each country can be fixed as an anchor. Taking Denmark

as one anchor for such distances, the results are presented inTable 3(Since Denmark

is the centre, the first distance measure is zero).

It must be emphasized thatTable 3does not report high or low scores on the 11

scales, and it is therefore not a ranking table of the countries in terms of levels forstudent responses to the 11 scales. Nor does it reveal anything about statistically

significant deviations between Denmark and the other countries. FromTable 3it can

be read, for example, that considering allattitude scales simultaneously, the average

response patterns of Danish grade 8 students very closely resemble averageresponse

profiles from Switzerland, Norway, Australia, Germany and Belgium, quite closely

resemble response profiles from England, Czech Republic, Sweden, Hungary and

Finland, while student profiles from Latvia, Portugal, Slovenia, Russia, Lithuania,

Chile, Bulgaria, Cyprus, Romania, Poland, Greece and Colombia seem to be rather

different.

Although it seems that the country means can be clearly distinguished inTable 3, there might be an overlap on the student level. This overlap can

to some extent be evaluated using linear discriminant functions. This

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technique generalizes the idea of drawing a simple straight line somewhere

between two groups of points. If the two groups can be separated completely bythe straight line, the percentage correct classified points in each of the groups, by

means of the line, is 100%. Often the best line leaves points from one group on the

wrong side of the line, where the other group points are placed; and a certain overlap

emerges.

Table 4 displays the result of applying 28 linear discriminant functions to the

28 country groups of response vectors xv = (x1v,y, x11v). It is seen that Denmark

as a group is most isolated in the sense of property to be separated from the

other countries (by a linear subspace). The degree of isolation is high, too, for

COL = Colombia, GRC = Greece and CYP = Cyprus, which fits well with the

fact that these countries are among the most distant countries from Denmark,(cf. Table 3, where distances between country means are shown). As another

example, Chile differs much from Denmark (3.74, cf. Table 3) but student

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Table 3

Between-country Mahalanobis distances measuring distances between country by means of eleven attitude

scales (no pooling of covariance matrices)

Abbreviation Distance Country

DNK 0.00 Denmark

CHE 0.70 Switzerland

NOR 0.73 Norway

AUS 1.01 Australia

DEU 1.25 Germany

BFR 1.40 Belgium

ENG 1.71 England

CZE 1.79 Czech Republic

SWE 1.79 Sweden

HUN 1.85 Hungary

FIN 1.87 Finland

USA 1.95 United States

EST 2.08 Estonia

ITA 2.19 Italy

SVK 2.21 Slovak Republic

HKG 2.67 Hong Kong

LVA 3.10 Latvia

PRT 3.25 Portugal

SVN 3.29 Slovenia

RUS 3.38 Russia

LTU 3.39 Lithuania

CHL 3.74 ChileBGR 3.85 Bulgaria

CYP 4.05 Cyprus

ROM 4.23 Romania

POL 4.28 Poland

GRC 4.50 Greece

COL 4.65 Colombia



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responses cannot clearly be separated from the other countries (2.48% correct

classification, cf.Table 4).

8. Within-country distances

When dealing with within-country distances, calculations are then restricted to a

group of students within a fixed country and must be seen in relation to a fixed

reference point, e.g., the international mean value (10,10,10,y,10). Fig. 1displays

averagewithin-country distances, grouped according to gender. The interpretation of

Fig. 1 is simple: The greater the distance, the greater is the deviation from the

neutral attitude point (10,10,10,y,10), which by definition is a neutral Rasch

score point. However, this does not necessarily mean in the middle betweenstrongly disagree and strongly agree on the underlying Likert response scale! In

fact, most students did not select the Strongly disagree answer, and a 10 does not

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Table 4

Summary of linear discriminant analyses of 28 countries. Pct is the percentage correct classified number of

observations in the country by means of linear separators

Abbreviation Pct Country

DNK 39.61 Denmark

COL 31.15 Colombia

GRC 31.07 Greece

CYP 24.43 Cyprus

FIN 22.2 Finland

DEU 21.22 Germany

HKG 19.74 Hong Kong

ENG 19.48 England

LTU 19.31 Lithuania

SWE 18.96 Sweden

POL 18.71 Poland

ROM 17.74 Romania

SVN 16.02 Slovenia

PRT 15.49 Portugal

RUS 14.81 Russia

NOR 14.69 Norway

BFR 14.28 Belgium

LVA 11.18 Latvia

CHE 11.04 Switzerland

USA 9.28 United States

HUN 8.22 Hungary

EST 7.69 EstoniaBGR 6.48 Bulgaria

ITA 6.20 Italy

CZE 4.82 Czech Republic

SVK 3.51 Slovak Republic

AUS 3.31 Australia

CHL 2.48 Chile



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mean the same thing when you compare results from one scale to another. A great

distance indicates that the response is very heterogeneous, greatly deviating from the

neutral point.

In Fig. 1 we note several distinct patterns. First, it can be observed that girls

systematically respond closer to the neutral point (10,10,10y,10) compared to

their male schoolmates, because the curve in Fig. 1 for girls is placed consistently

below the curve for boys. In other words girls tend to use the underlying scale ofagreement by selecting response categories with less variation across the eleven scales

than boys.

Another characteristic of Fig. 1 is the rather large general differences

across countries. One explanation for this difference in the underlying scale of

agreement is based on cultural background. Or perhaps some students may be

hesitant to select the scale extremes. The countries with the lowest average

student distances are CZE = Czech Republic, EST = Estonia , HKG = Hong

Kong, LVA = Latvia, PRT = Portugal, RUS = Russia, and SVK = Slovak

Republic. Hong Kong, however, also shows the greatest gender difference. Countries

with the greatest distances are BFR = Belgium, BGR = Bulgaria, GRC = Grece,ROM = Romania, SWE = Sweden and USA. Danish students are placed in the

middle.

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15

14

13

12

11

10

9

mahala

A B B C C C C C

C

D D E E F G

GG

H H I

I

L L

L

N

NN N

P P R

RR

R S

S

S S U

UU F G H H O Y Z E N N S KK

U TT

TT

V V VO OO RS R R E L L P U U A AAU M K E

W S

ALPHA NUMERIC COUNTRY CODE

GIRL OR BOY 1 2

Fig. 1. Within-country Mahalanobis Distances calculated for all students in the international data set(pooled covariance matrix) by gender: Girls (1 3 * ) Boys (23K).



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9. The general level of correlation among eleven Civic scales

Usually, correlation is defined and calculated as a measure of co-variation between

two variables. This would lead to 55 pair-wise correlation coefficients for the elevenscales. The resulting matrix containing these values could be calculated for each

country and then be compared using various statistical techniques. Overall, this

would involve approximately 1500 correlations. Quite often, however, the matrices

of correlation are used for factor analysis. A concept of general correlation is still

missing.

The following calculations are based on the prior analysis with the Mahalanobis

Distance. In fact, one way to assess general correlation is to compare average student

Mahalanobis Distances under an assumption of independence, with the actual

distances calculated under the conditions of actual correlations found in the data.

The greater the difference between the Mahalanobis Distances calculated under the

two versions, the higher correlation in general must be present among the scale

responses. This leads toFig. 2, where the two distance measures are displayed. The

greater the gap between the two curves in Fig. 2, the more correlated are the

responses in general to the eleven scales for the particular country on the X-axis.

The information in Fig. 2 can furthermore be summarized numerically as ratios

between Mahalanobis Distances under correlation to the distance assuming no

correlation. Table 5 lists these ratios and, it can be clearly seen that the countries

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14

13

12

11

10

mahala

A B B C C C C C

C

D D E E F G

GG

H H I

I

L L

L

N

NN N

P P R

R

R

R S

S

S S U

UU F G H H O Y Z E N N S K

K

U T

T

T

T

V V VO OO R

S R R E L L P U U A AAU M K E

W S

ALPHA NUMERIC COUNTRY CODE

Fig. 2. Average Mahalanobis Distances based on data for each country separately. Upper curve (K) is

calculated, cf. (1) assuming that scales correlated. Lower curve (*) is calculated, cf. (2) assuming that scales

are independent.



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enjoying the greatest reduction are Denmark, Sweden, England, Hong Kong,Australia and Bulgaria. This means that student responses from these countries seem

to be highly correlated in general, while students in countries like Czech Republic,

Chile, Russia, Slovak Republic, Cyprus and Hungary seem to respond to the 11

scales with a high degree of independence among the scale responses.

10. Predicting levels of civic knowledge

As a contrast to the described analyses, the Civic Study offers an immediate

possibility to study the correlation structure from the perspective of a regressionanalysis, where correlations between dependent and independent variables are

examined for their ability to predict values of the dependent variables. The following

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Table 5

Average Mahalanobis Distances calculated from data from each country

Abbreviation Distance Distance Ratio Country

Dep. Indep.

HUN 11.40 10.97 1.04 Hungary

CYP 11.57 10.90 1.06 Cyprus

SVK 11.58 10.90 1.06 Slovak Republic

RUS 11.61 10.90 1.06 Russia

CHL 11.68 10.91 1.07 Chile

CZE 11.68 10.85 1.08 Czech Republic

ITA 11.82 10.87 1.09 Italy

ROM 11.84 10.79 1.10 Romania

COL 12.02 10.93 1.10 Colombia

GRC 11.92 10.78 1.11 Greece

POL 12.02 10.87 1.11 Poland

SVN 12.10 10.68 1.13 Slovenia

EST 12.30 10.83 1.14 Estonia

DEU 12.24 10.70 1.14 Germany

PRT 12.46 10.78 1.16 Portugal

FIN 12.50 10.80 1.16 Finland

CHE 12.36 10.66 1.16 Switzerland

LVA 12.53 10.79 1.16 Latvia

NOR 12.87 10.61 1.21 Norway

LTU 13.15 10.73 1.23 Lithuania

BFR 13.34 10.75 1.24 Belgium

DNK 13.36 10.70 1.25 DenmarkSWE 13.39 10.61 1.26 Sweden

ENG 13.57 10.72 1.27 England

HKG 13.65 10.65 1.28 Hong Kong

AUS 13.82 10.47 1.32 Australia

USA 13.89 10.44 1.33 United States

BGR 14.00 10.51 1.33 Bulgaria

Distance dep: eleven scales assumed correlated. Distance indep: eleven scales assumed independent. Ratio:

Distance dep/distance indep.



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analyses consider the eleven scales as independent variables and the Civic knowledge

scale as the dependent variable, recognizing that it is not really an integral point for

the Civic Study to look at these scales from the perspective of dependent variables

to be derived from independent variables.One interesting facet of the regression analysis is its capability to provide

comparisons of adjustedknowledge levels instead of comparing the simple, direct

average values on the knowledge scales, as listed in the first international report

(Torney-Purta et al., 2001, Fig. 3.3 p. 55 lists totalknowledge). In fact,expected(i.e.,

predicted) levels of Civic Knowledge are calculated and compared, based on a

specific student profile xv = (x1v,y, x11v), used for allcountries.

Table 6shows the results of this co variance analysis. Listed first are two kinds of

mean values for the knowledge scale: Mean2 being the international (weighted) mean

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Table 6

Reported knowledge mean values from the international report

Abbreviation Mean1 Mean2 Adj1 Adj2 Country

AUS 100.41 99.35 98.00 98.12 Australia

BFR 95.25 95.28 94.91 96.45 Belgium

BGR 100.44 99.05 104.04 103.46 Bulgaria

CHE 97.52 97.14 96.29 97.05 Switzerland

CHL 89.94 93.82 90.24 91.16 Chile

COL 89.17 88.12 89.17 89.65 Colombia

CYP 107.91 107.48 108.33 106.68 CyprusCZE 103.54 111.61 104.46 104.85 Czech Republic

DEU 100.25 98.64 99.43 99.41 Germany

DNK 102.45 100.54 101.40 102.09 Denmark

ENG 97.81 96.38 94.16 94.75 England

EST 94.61 94.75 95.89 96.57 Estonia

FIN 108.73 107.66 107.09 107.02 Finland

GRC 109.46 109.02 109.15 107.74 Greece

HKG 110.37 107.26 110.49 113.47 Hong Kong

HUN 102.26 102.76 104.39 103.74 Hungary

ITA 105.84 105.73 105.30 105.51 Italy

LTU 95.51 94.82 98.87 97.66 Lithuania

LVA 92.90 93.81 95.53 96.12 Latvia

NOR 104.27 102.70 101.29 100.64 Norway

POL 112.87 110.18 111.75 111.42 Poland

PRT 98.05 97.53 97.86 98.11 Portugal

ROM 93.71 93.53 97.70 96.87 Romania

RUS 102.29 102.08 103.89 103.54 Russia

SVK 106.89 109.71 108.18 108.49 Slovak Republic

SVN 102.09 101.93 103.21 104.61 Slovenia

SWE 98.87 97.85 97.51 97.17 Sweden

USA 104.11 100.55 101.60 100.30 United States

Mean2: Reported knowledge mean values from the international report.Mean1: The same as Mean2, but only students with no missing responses enter the calculations.

Adj1 are adjusted knowledge levels using common regression coefficients across all countries,

Adj2 are adjusted knowledge levels using regression coefficients estimated from each country.



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values (knowledge of content, only, Type 1), which reflect how countries are ranked

using the simple average values. Mean1 is the same as Mean2, but only students with

non-missing responses to all 11 scales (in fact a total ofN= 84000 students) enter

the calculations. Adj1 and Adj2 are the adjusted, or predicted, knowledge valuesestimated from the regression model using the student profile xv= (x1v,y, x11v) =

(10,10,10,y,10). Two adjusted values are given, one based on equal regression

coefficients equal for all countries (Adj1), the other (Adj2) based on local regression

coefficients estimated from specific country data.

In the last case, interpretation of differences in (expected) knowledge levels across

countries depends heavily on the choice of reference student xv = (x1v,y, x11v).

By comparing Mean2 values to either of the columns Adj1 or Adj2, we see that the

top ranking based on the international Mean2 values change slightly for Czech

Republic and Hong Kong. A position in the middle ranking, like Norway, changes

to a slightly lower value, while Romania moves up from a low ranking position to a

place near the middle. The lowest position, held by Colombia, remains the same with

or without adjustments. In the same way, Poland keeps its position as the top-ranked

country.

It is tempting to conclude that only minor changes in the rankings take place

between unadjusted and adjusted knowledge values. This analysis confirms, to an

extent, that the international rankings carried out by Mean2 reflect scale-eleven

independent information, and that the international rankings are objective in the

sense that they change only slightly, when information from the 11 scales is used as a

conditional prerequisite for the comparisons. This impression is supported bymultiple correlations R2 for the regression, found to be around 13% to 25%.

One of the controversies of the displayed co variance adjustment technique is that

the fixed reference studentxv= (x1v,y,x11v) may not be part ofany of the country-

specific clusters of responses to the eleven scales, the likelihood of which can, in fact,

be judged fromFig. 1, since this figure displays the (student average) Mahalanobis

Distance to this reference student.

While the adjusted levels of knowledge across countries in many instances were

almost the same as the unadjusted values, the analysis of adjusted gender differences

reveals a greater change in difference. In fact, considering students in grades eight

and nine in Denmark, for example, it can be shown that the original, raw knowledgedifference (Mean2 values for boys minus girls): 101.1297.52 = 3.60 (grade eight)

and 108.75104.46 = 4.29 (grade nine) became greater when adjusted (Adj1

adjustments, cf. Table 6) according to the eleven scales: 107.4397.40 = 10.03

(grade eight) and 114.53103.51 =11.02(grade nine). All differences are significant,

at a 5% level of significance. It can furthermore be noted that the adjustment

procedure has the greatest impact on expected levels for boys.

11. Summary and conclusions

The paper presents analyses of complete student attitude profiles, considered as

simultaneous response vectors holding 11 Civic scales scores. By means of a general

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distance measure developed by Mahalanobis (Rao, 1965) it is demonstrated how

participating countries can be arranged and compared using information from all 11

scales simultaneously. Gender differences in response behaviour on the underlying

ordinal scale are detected. The general distance measure takes into account scalecorrelations and facilitates the assessment of a correlation level assigned to the

scales, looked upon as one multidimensional response. Finally, the relationship

between Civic knowledge and the 11 attitude scales is explored by means of multiple

regression analysis and the model is used for predicting expected, or adjusted levels

of Civic knowledgeacross countries and across gender.

References

Allerup, P. (1994). Rasch measurement theory of. The international encyclopaedia of education (2nd ed.).New York: Pergamon Press.

Beaton, Albert, et al. (1996). Mathematics Achievement in the Middle School Years. IEAs third

international mathematics and science study. USA: Boston College.

Bruun, J. (2001). Politisk Dannelseunges synspunkter pa demokratiske vrdier I skole og samfund.

Copenhagen: The Danish Institute for Educational Research.

Elley, W. (1992). How in the world do students read. IEA study of reading literacy. The Hague: IEA.

Fischer, G., & Molenaar, I. (1995). Rasch modelsfoundations, recent developments, and applications. New

York: Springer-Verlag.

Rao, C. R. (1965). Linear statistical inference and its applications. New York: Wiley.

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: The

National Danish Institute for Educational Research.

Torney-Purta, J., Lehman, R., Oswald, H., & Schulz, W. (2001). Citizenship and education in twenty-eightcountries: civic knowledge and engagement at age fourteen. Amsterdam: IEA.

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