Cross-National Patterns of Gender Differences in Mathematics: A Meta-Analysis

Psychological Bulletin
© 2010 American Psychological Association
2010, Vol. 136, No. 1, 103–127
0033-2909/10/$12.00
DOI: 10.1037/a0018053
Cross-National Patterns of Gender Differences in Mathematics:
A Meta-Analysis
Nicole M. Else-Quest
Janet Shibley Hyde
Villanova University
University of Wisconsin—Madison
Marcia C. Linn
University of California, Berkeley
A gender gap in mathematics achievement persists in some nations but not in others. In light of the
underrepresentation of women in careers in science, technology, mathematics, and engineering, increas-
ing research attention is being devoted to understanding gender differences in mathematics achievement,
attitudes, and affect. The gender stratification hypothesis maintains that such gender differences are
closely related to cultural variations in opportunity structures for girls and women. We meta-analyzed 2
major international data sets, the 2003 Trends in International Mathematics and Science Study and the
Programme for International Student Assessment, representing 493,495 students 14 –16 years of age, to
estimate the magnitude of gender differences in mathematics achievement, attitudes, and affect across 69
nations throughout the world. Consistent with the gender similarities hypothesis, all of the mean effect
sizes in mathematics achievement were very small (d
0.15); however, national effect sizes showed
considerable variability (ds
0.42 to 0.40). Despite gender similarities in achievement, boys reported
more positive math attitudes and affect (ds
0.10 to 0.33); national effect sizes ranged from d
0.61
to 0.89. In contrast to those of previous tests of the gender stratification hypothesis, our results point to
specific domains of gender equity responsible for gender gaps in math. Gender equity in school
enrollment, women’s share of research jobs, and women’s parliamentary representation were the most
powerful predictors of cross-national variability in gender gaps in math. Results are situated within the
context of existing research demonstrating apparently paradoxical effects of societal gender equity and
highlight the significance of increasing girls’ and women’s agency cross-nationally.
Keywords: gender differences, mathematics, gender equity, international data sets
The question of gender differences in mathematics achievement,
research on gender differences in math has been based on North
attitudes, and affect is a continuing concern as scientists seek to
American samples, the current study aimed to examine the mag-
address the underrepresentation of women at the highest levels of
nitude of gender differences in mathematics achievement,
science, technology, mathematics, and engineering (STEM; Halp-
attitudes, and affect cross-nationally. Furthermore, some have pro-
ern et al., 2007; National Academy of Sciences, 2006). Stereotypes
posed the gender stratification hypothesis, arguing that cross-
that girls and women lack mathematical ability persist, despite
national patterns of gender differences in math achievement reflect
mounting evidence of gender similarities in math achievement
gender inequities in educational and economic opportunities avail-
(Hedges & Nowell, 1995; Hyde, Fennema, & Lamon, 1990; Hyde,
able in a given culture (Baker & Jones, 1993; Guiso, Monte,
Lindberg, Linn, Ellis, & Williams, 2008). Because much of the
Sapienza, & Zingales, 2008; Riegle-Crumb, 2005). In the current
study, we meta-analyzed two large international data sets to ex-
amine cross-national patterns of gender differences in mathematics
achievement, attitudes, and affect and assessed the links of these
Nicole M. Else-Quest, Department of Psychology, Villanova Univer-
patterns to gender equity at the national level.
sity; Janet Shibley Hyde, Department of Psychology, University of Wis-
consin—Madison; Marcia C. Linn, Graduate School of Education, Univer-
sity of California, Berkeley.
Gender Differences and Similarities in Mathematics
Portions of these data were presented at the Gender Development
Research Conference, San Francisco, California, April 2008, as well as at
Stereotypes about female inferiority in mathematics (Bhana,
the meeting of the Society for Research in Child Development, Denver,
2005; Fennema, Peterson, Carpenter, & Lubinski, 1990; Fennema
Colorado, April 2009. This research was funded through National Science
& Sherman, 1977; Hyde, Fennema, Ryan, Frost, & Hopp, 1990;
Foundation Grant REC 0635444. Any findings, conclusions, or recommen-
Li, 1999) stand in distinct contrast to the actual scientific data
dations expressed in this material are our own and do not necessarily reflect
reported in previous studies. This discrepancy is particularly prob-
the views of the National Science Foundation.
lematic because such negative stereotypes can impair math test
Correspondence concerning this article should be addressed to Nicole
performance and cause anxiety via stereotype threat (Blascovich,
M. Else-Quest, Villanova University, Department of Psychology, 800
Lancaster Avenue, Villanova, PA 19085. E-mail: nicole.else.quest@
Spencer, Quinn, & Steele, 2001; Spencer, Steele, & Quinn, 1999).
villanova.edu
Reviewing evidence from research with infants and preschoolers,
103

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104
ELSE-QUEST, HYDE, AND LINN
Spelke (2005) concluded that gender similarities are the rule in the
not differ significantly from 1.0 or are even significantly less than
development of early number concepts. Girls earn better grades in
1.0. For example, VR equals 0.99 for Denmark and 0.95 for
mathematics courses through the end of high school (Dwyer &
Indonesia. Thus, despite some claims (Machin & Pekkarinen,
Johnson, 1997; Kenney-Benson, Pomerantz, Ryan, & Patrick,
2008), the phenomenon of greater male variance in mathematics
2006; Kimball, 1989).
performance is not universal (Penner, 2008). Another method of
In the United States, gender differences in mathematics perfor-
testing the greater male variability hypothesis is to examine mean
mance are declining. A meta-analysis in 1990 (Hyde, Fennema, &
gender differences in achievement on assessments of varying dif-
Lamon., 1990) found an effect size of d
0.05 for the gender
ficulty level. That is, if males are overrepresented in the upper tails
difference in math performance among the general population,
of the distribution, gender differences in achievement should be
indicating a negligible female advantage (note that positive values
larger on difficult or complex problems than on easy or moderate
of d represent higher scores for males than females, whereas
problems. Although Hyde, Fennema, and Lamon’s (1990) meta-
negative values represent higher scores for females). At that time
analysis showed that males outperformed females in complex
the gender gap increased during high school. Another meta-
problem solving by d
0.29 in high school, recent data suggest
analysis used data sets representing large probability samples of
that this gap has closed. In their analyses of gender differences on
American adolescents and found d
0.03 to 0.26 across the
the math portion of the National Assessment of Educational
different data sets (Hedges & Nowell, 1995). More recent data
Progress, Hyde et al. (2008) found that gender differences were not
indicate that the gender difference in math achievement has been
larger on the most challenging problems. This finding provided
eliminated. A study of statewide mathematics tests administered
little support for the argument that males outperform females in
between 2005 and 2007 for Grades 2–11 found d
0.0065,
complex problem solving.
without the increased gender gap in adolescence found with earlier
data (Hyde et al., 2008). These findings, for U.S. samples, are
consistent with the gender similarities hypothesis, which maintains
Assessing Mathematics Achievement, Attitudes, and
that males and females are similar on most, but not all, psycho-
Affect Cross-Nationally
logical variables (Hyde, 2005).
For the United States, meta-analytic studies of gender differ-
Efforts to measure the mathematics achievement, attitudes, and
ences in attitudes and affect toward mathematics demonstrate that
affect of students cross-nationally have produced two large-scale
males tend to hold more positive attitudes about math, though the
recurring assessments, the Trends in International Mathematics
gap is small (Hyde, Fennema, Ryan, et al., 1990). Hyde et al.
and Science Study (TIMSS) and PISA. TIMSS is an international
(1990) found that, developmentally, the gap widens during high
assessment of mathematics and science learning in eighth graders,
school, when males report greater self-confidence (d
0.25).
conducted on a 4-year cycle by the International Association for
Gender differences in math anxiety and self-concept have received
the Evaluation of International Achievement (IEA), in collabora-
considerable research attention, with girls tending to report higher
tion with Statistics Canada and the Educational Testing Service.
anxiety and lower self-concept about their math abilities (Casey,
PISA is an international assessment of mathematics, reading, sci-
Nuttall, & Pezaris, 1997; Fredricks & Eccles, 2002; Hyde, Fen-
ence, and problem-solving literacy in 15-year-olds, conducted on a
nema, Ryan, et al., 1990; McGraw, Lubienski, & Strutchens, 2006;
3-year cycle by the Organisation for Economic Co-operation and
Meece, Wigfield, & Eccles, 1990; Pajares & Miller, 1994); yet,
Development (OECD). The current study uses data from the 2003
these effects tend to be small to medium in magnitude. Although
round of TIMSS (Mullis, Martin, Gonzalez, & Chrostowski, 2004)
cross-cultural research has demonstrated similar findings (Stet-
and PISA (OECD, 2004). With regard to issues such as measure-
senko, Little, Gordeeva, Grasshof, & Oettingen, 2000), most of
ment and sampling, in light of the complex methodological issues
these reports have been based on North American samples; thus, it
involved in analyzing cross-national surveys of student achieve-
is unclear if these patterns of gender differences are generalizable
ment, experts regard the TIMSS and PISA data sets as high-quality
to other cultures. Therefore, a focus in this paper is to estimate the
(e.g., Porter & Gamoran, 2002). Nonetheless, it is important to
magnitude of gender differences in math achievement, attitudes,
note the differences between these two oft-cited data sets, as well
and affect across two international data sets totaling 69 nations.
as to acknowledge any limitations.
Others have focused not on mean gender differences but on
At the outset, it is important to recognize that TIMSS and PISA
gender differences in the upper tail of the distribution and the
have explicitly different goals. TIMSS focuses on assessing the
greater male variability hypothesis (Hyde & Mertz, 2009). The
attained curriculum, or what students have learned in the class-
argument is that greater variance in test scores is displayed by
room, as well as teacher- and school-level variables. In contrast,
males than females, so that, even if there is no average gender
OECD emphasizes that the PISA test of mathematics assesses
difference, there will still be more males among the very top
mathematics literacy, which is defined as “the capacity to identify
performers. One statistic used to test this hypothesis is the variance
and understand the role that mathematics plays in the world, to
ratio, VR, or the male variance divided by the female variance.
make well-founded judgments and to use and engage with math-
Analysis of variance ratios in cross-national data (using the 2003
ematics in ways that meet the needs of that individual’s life as a
cycle of the Programme for International Student Assessment, or
constructive, concerned and reflective citizen” (OECD, 2004, p.
PISA) indicates that males are sometimes more variable, although
26). In light of these differing aims, one can expect TIMSS to be
the variance ratios do not indicate widely divergent differences
more curriculum-based and PISA to be more applied. The impli-
(Hyde & Mertz, 2009; Machin & Pekkarinen, 2008). For example,
cation that this distinction has for comparing results from the data
VR equals 1.19 for the United States and 1.06 for the United
sets is that PISA may be a more challenging assessment requiring
Kingdom. However, other countries display variance ratios that do
a deeper understanding of mathematics.

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GENDER DIFFERENCES IN MATH
105
The quality of any academic achievement assessment is partly
that year on? Provide an argument to support your answer.” An
determined by the depth of knowledge (DoK) or degree of diffi-
emphasis in the PISA on more challenging and complex mathe-
culty assessed with its items. Ideally, a standardized indicator of
matics is evident from the breakdown of items within each cog-
DoK would be applied to TIMSS and PISA to determine whether
nitive cluster. Thus, it may be surmised that PISA is a more
one assessment is more challenging than the other. Because the
challenging mathematics assessment than is TIMSS. Previous re-
IEA and OECD do not release to the public the full batteries of
ports have suggested that gender differences in mathematics ap-
TIMSS and PISA items, respectively, it is not possible to code the
pear only at the level of complex problem solving (Hyde, Fen-
DoK assessed by the test items on both assessments. However,
nema, & Lamon, 1990), and the greater male variability hypothesis
both the IEA and OECD attempt to address this concern with their
predicts larger gender differences in more challenging mathemat-
own respective coding scheme. The IEA classifies TIMSS items
ics assessments. Thus, this apparent difference in DoK accessed on
into three “cognitive domains,” which reflect the complexity of
the two assessments might foreshadow larger gender differences
cognitive processes required for those items (International Asso-
on PISA than on TIMSS, as would be consistent with the greater
ciation for the Evaluation of International Achievement [IEA],
male variability hypothesis.
2007). Items in the Knowing Facts, Procedures, and Concepts
In terms of samples, PISA differs from TIMSS insofar as it is
domain make up 33.5% of the TIMSS items; they require recall of
based on age (15 years 3 months to 16 years 2 months) rather
facts, procedures, and mathematical concepts; computation; rec-
than grade level. Because the majority of nations begin formal
ognition and identification of mathematical equivalence; and use
schooling at age 6, most of the eighth graders assessed in
of mathematics and measuring instruments. For example, “If x
TIMSS were between 14 and 15 years of age, approximately
3, what is the value of
3x?” The Applying Knowledge and
one year younger than those in the PISA sample. The develop-
Understanding domain entails the application of mathematical
mental importance of this age difference in samples is unclear.
knowledge of facts, skills, procedures, and concepts to create
Although previous reports have demonstrated a widening of the
representations and solve routine problems. For example, “Jack
gender gap in math achievement and attitudes during this de-
wants to find how far an airplane will travel in 3.5 hours at its top
velopmental period (Hyde, Fennema, & Lamon, 1990; Hyde,
speed of 965 kph. He uses his calculator to multiply 3.5 by 965 and
Fennema, Ryan, et al., 1990), recent data suggest that the gap
tells his friend Jenny that the answer is 33,775 km. Jenny says ‘that
has closed (Hyde et al., 2008). Regardless, students of this age
can’t be right.’ How does she know?” This domain represents the
range (14 –16 years) are old enough to be capable of complex
largest component of the assessment and includes 43.9% of the
mathematical problem solving.
items. At the deepest level is the Reasoning domain, which con-
Both TIMSS and PISA hold participating nations to strict stan-
stitutes 18.6% of the items. It requires logical, systematic thinking,
dards in terms of sampling and test administration. This provides
such as the ability to hypothesize, analyze, evaluate, generalize,
confidence in the reliability and quality the data. Yet, these stan-
synthesize, and prove, as well as nonroutine problem solving. For
dards incur major costs on the nations that participate in these
example, “Twin primes are prime numbers with one other number
voluntary assessments (Hutchison & Schagen, 2007); thus, nations
between them. Thus, 5 and 7, 11 and 13, and 17 and 19 are pairs
must have organized formal schooling systems and enjoy a certain
of twin primes. Make a conjecture about the numbers between twin
level of prosperity in order to participate. None of the nations in
primes.” Based on the breakdown of items within each cognitive
the TIMSS or PISA data sets are characterized as low in human
domain, an emphasis in the TIMSS on basic knowledge and
development (i.e., having a Human Development Index, or HDI, of
routine problem-solving is evident.
less than 0.50), according to the1995 Human Development Report
OECD attempts to address the DoK issue by classifying PISA
(UN Development Programme, 2003). Instead, over half of the
math items into three “competency clusters,” which are based on
nations included in TIMSS and 84% of the nations in PISA sample
the cognitive processes used to complete the items (OECD, 2003).
were characterized as high in human development in 2003. It is
Items in the Reproduction cluster make up 31% of the assessment
noteworthy that TIMSS represents a more diverse and less devel-
and involve recall of facts, recognition of equivalents, manipula-
oped sample of nations than does PISA, as the PISA sample
tion of expressions, routine procedures, computations, and appli-
reflects membership in the OECD. The overrepresentation of de-
cation of standard algorithms and skills. For example, “Write 69%
veloped nations in the TIMSS and PISA samples is a limitation
as a fraction.” The Connections cluster represents nearly half of the
that is difficult to overcome with international academic achieve-
PISA math test (47%) and involves solving nonroutine problems in
ment assessments.
familiar or quasifamiliar situations. For example, “A pizzeria
In sum, TIMSS and PISA differ somewhat with regard to the
serves two round pizzas of the same thickness in different sizes.
sample age and level of development and the difficulty level of
The smaller one has a diameter of 30 cm and costs 30 zeds. The
the test items. These differences could be reflected in the
larger one has a diameter of 40 cm and costs 40 zeds. Which pizza
findings of the current study, insofar as results from TIMSS and
is better value for money? Show your reasoning.” The third clus-
PISA may vary. Insofar as the greater male variability hypoth-
ter, Reflection, comprises 22% of the items and involves advanced
esis maintains that males should be overrepresented at the upper
reasoning, insight, and creativity, requiring students to plan and
tails of the distribution in mathematics ability, a male advantage
implement problem-solving strategies. For example, students are
in the most difficult math problems should exist. Thus, if the
shown a graph modeling combined fish growth (in kilograms) over
greater male variability hypothesis is valid, we would expect
time (in years); the item states “Suppose a fisherman plans to wait
larger gender differences in more challenging assessments of
a number of years and then start catching fish from the waterway.
math achievement, such as PISA, or on problems assessing
How many years should the fisherman wait if he or she wishes to
deeper levels of processing, such as the TIMSS cognitive do-
maximize the number of fish he or she can catch annually from
main of Reasoning.

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106
ELSE-QUEST, HYDE, AND LINN
Theoretical Framework
or by taking elective math courses. She may see math as less useful
or valuable and may think she is not capable of doing math. The
What factors might contribute to gender differences or similar-
theory has received abundant empirical support (e.g., Eccles, 1994;
ities in math achievement, attitudes, and affect? Dozens of expla-
Frome & Eccles, 1998) and provides a clear model for why
nations have been proposed, including hormones and prenatal
cultural inequities in educational or career opportunities have an
brain differentiation, stereotype threat, and other factors (Byrnes,
adverse impact on girls and women considering STEM careers.
2005; Ceci & Williams, 2007; Halpern et al., 2007). Of primary
Eccles’s (1994) expectancy-value theoretical model is consistent
interest here is a sociological hypothesis proposed by Baker and
with the gender stratification hypothesis in maintaining that indi-
Jones (1993), who argued that girls’ poorer math achievement and
viduals do not engage in tasks that are perceived to have little
more negative math attitudes are the result of societal gender
value and arguing that individuals make cost– benefit judgments
stratification. The gender stratification hypothesis proposes that in
regarding their academic choices.
patriarchal cultures, male students link their achievement to future
opportunities and outcomes. As a result of the decreased opportu-
Another psychological theory that is consistent with the gender
nities afforded to females, girls do not perceive such a link and
stratification hypothesis is cognitive social learning theory (Ban-
thus do not achieve as boys do in domains that they perceive to be
dura, 1986; Bussey & Bandura, 1999), which maintains that a
less useful. Baker and Jones (1993) argued that
number of social processes contribute to the development of
gender-typed behavior, including reinforcements, modeling, and
female students, who are faced with less opportunity, may see math-
cognitive processes, such as self-efficacy. Role models and social-
ematics as less important for their future and are told so in a number
izing agents, as well as perceptions of gender-appropriate behav-
of ways by teachers, parents, and friends. In short, opportunity struc-
ior, have an important influence on an individual’s academic
tures can shape numerous socialization processes that shape perfor-
choices. As with Eccles’s model, this theory also emphasizes the
mance. (p. 92)
role of self-efficacy in gender-typed behaviors, such as choosing to
Broadly, the gender stratification hypothesis proposes that, where
major in physics. This theory maintains that girls are attentive to
there is more societal stratification based on gender, and thus more
the behaviors that women in their culture engage in and thus feel
inequality of opportunity, girls will report less positive attitudes
efficacious in and model those behaviors. That is, if girls observe
and more negative affect and will perform less well on mathemat-
that women in their culture do not become engineers or scientists,
ics achievement tests than will their male peers. Yet, where there
they may believe that such careers (and, by extension, STEM
is greater gender equity, gender similarities in math will be evi-
subjects) are outside the realm of possibilities for girls and feel
dent.
anxious about and/or avoid these subjects. In emphasizing the roles
Three theoretical approaches within psychology provide some
of observational learning and the internalization of cultural norms,
insight into socialization processes that might account for the
cognitive social learning theory provides an individual-level ex-
effects proposed by the gender stratification hypothesis. Eccles and
planation of why girls and women make gendered educational and
her colleagues (e.g., Eccles, 1994; Jacobs, Davis-Kean, Bleeker,
vocational choices that recapitulate societal-level gender stratifi-
Eccles, & Malanchuk, 2005; Meece, Eccles-Parsons, Kaczala,
cation.
Goff, & Futterman, 1982) have proposed and tested an
Social structural theory (sometimes referred to as social role
expectancy-value theoretical model to explain the gender gap in
theory; Eagly, 1987; Eagly & Wood, 1999) is another relevant
mathematics achievement, attitudes, and affect and the underrep-
psychological theory in that it maintains that psychological gender
resentation of women in careers in science and engineering. Ac-
differences are rooted in sociocultural factors, such as the gendered
cording to the Eccles model, people do not undertake a challenge
division of labor. A society’s gendered division of labor fosters the
unless they value it and have some expectation of success. Per-
development of gender differences in behavior by affording dif-
ceptions of the value of the task (e.g., taking a challenging math-
ferent restrictions and opportunities to males and females on the
ematics course) are shaped by the cultural milieu (e.g., gender
basis of their social roles. Accordingly, if girls are expected to care
segregation of occupations, cultural stereotypes about the subject
for younger siblings or prepare meals rather than learn algebra,
matter) and the person’s short-term and long-term goals (e.g.,
their access to formal schooling may be limited. Eagly and Wood’s
becoming an elementary school teacher and thinking one does not
(1999) cross-cultural analyses tend to support social structural
need advanced mathematics or becoming a civil engineer and
theory, demonstrating substantial correlations between composite
knowing that one does). Expectations of success are shaped by
indicators of gender equity and gender differences in mate prefer-
the person’s aptitude, relevant past events such as grades in the
subject and scores on standardized tests, the person’s interpre-
ences (including earning capacity, domestic skills, and age). Al-
tations of and attributions for these events, and the person’s
though Eagly and Wood did not analyze gender differences in
self-concept of ability. Sociocultural forces such as parents’ and
mathematics, social structural theory can be applied to access to
teachers’ attitudes and expectations, including stereotypes, also
mathematics education. That is, if the cultural roles that women
shape self-concept and attitudes toward the subject; empirical
fulfill do not include math, girls may face both structural obstacles
research on the awareness of negative stereotypes supports this
(e.g., formal access to education is limited to boys) and social
link (Aronson & McGlone, 2008; Pinel, 1999). According to the
obstacles (e.g., stereotypes that math is a male domain) that im-
expectancy-value model, if a girl believes that the career oppor-
pede their mathematical development. According to social struc-
tunities available to or appropriate for women do not require
tural theory, across nations, gender equity in educational and
mathematics skills, she is less likely to invest in developing her
employment opportunities should be associated with gender sim-
mathematics skills by working hard in her required math courses
ilarities in mathematics achievement, attitudes, and affect.

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GENDER DIFFERENCES IN MATH
107
Previous Tests of the Gender Stratification Hypothesis
gender gap in math achievement. These findings indicate that the
picture is more complex than first theorized. They provide mixed
To test the gender stratification hypothesis, Baker and Jones
support for the gender stratification hypothesis, suggesting that
(1993) used cross-national data from the Second International
specific domains of gender equity are important in understanding
Mathematics Study (SIMS; an early precursor to TIMSS), which
how societal gender inequities are linked to the gender gap in math
administered the same mathematics test to a representative sample
performance.
of 13-year-old students in each of 19 countries around the globe in
In a more widely publicized report, Guiso et al. (2008) tested the
1982. Using United Nations Development Programme (UNDP)
gender stratification hypothesis using different indicators of both
data, Baker and Jones constructed several variables measuring
math achievement and gender equity than those Baker and Jones
gender equity in the countries (e.g., percentage of females in
and Riegle-Crumb had used in their studies. To measure the gender
higher education and percentage of females in the labor force).
gap in math performance, Guiso et al. used the 2003 PISA data. To
They then computed correlations between the magnitude of gender
assess gender equity, they used the World Economic Forum’s
differences in mathematics achievement and each of the gender
Gender Gap Index (GGI; Hausmann et al., 2007), a composite
inequality variables, essentially testing whether gender equity
indicator that includes many of the social, economic, and political
moderated the gender difference in math performance on the
variables used by both Baker and Jones (1993) and Riegle-Crumb
SIMS. Their results showed that boys significantly outperformed
(2005). Guiso et al. found that girls’ performance was, on average,
girls in seven of the 19 nations and that girls significantly outper-
only 2% lower than boys’ performance. Their analyses supported
formed boys in four. There were no significant gender differences
in the remaining eight nations. Baker and Jones also found support
the gender stratification hypothesis in that the GGI significantly
for the gender stratification hypothesis; a smaller gender gap in
predicted the magnitude of the (albeit small) gender gap in math
math was significantly correlated with greater women’s labor force
performance. In addition, analyses of genetic distance suggested
participation, the percentage of women in higher education, and
that biological differences across countries could not explain the
the percentage of women working in the industrial and service
cross-national pattern of gender differences in math performance.
economic sectors. Gender occupational segregation, the ratio of
Although this study suggests that a multidimensional indicator of
women in university–nonuniversity programs, and the percentage
gender equity is a good predictor of gender differences in math test
of women working in the agricultural economic sector were not
scores, it does not shed light on the specific domains of gender
significantly correlated with the gender gap in math performance
equity that are most relevant to math achievement and leaves the
but were significantly correlated with perceived parental encour-
debate about the mechanisms of the gender stratification hypoth-
agement for math achievement. Although these findings provide
esis unresolved.
evidence of cultural influence—specifically, the importance of
Several studies have assessed the gender stratification hy-
equal opportunity in a culture—they are limited by several meth-
pothesis with regard to greater male variability, though with
odological constraints.
somewhat conflicting findings. Machin and Pekkarinen (2008),
The SIMS is now more than 26 years old, and international math
using 2003 PISA data, found no correlation between VR in
assessments have improved greatly since then in terms of items
math achievement and national gender equity. In contrast, Hyde
and administration (Mullis & Martin, 2007). The sample of nations
and Mertz (2009) used PISA 2003 data and found a negative
participating in the SIMS was primarily limited to developed
correlation between gender equity and the ratio of males to
nations, in which there tends to be relatively greater gender equity
females scoring above the 95th percentile on the 2003 PISA.
(Hausmann, Tyson, & Zahidi, 2007; UN Development Programme
Similarly, Penner (2008) used TIMSS-1995 data and found that
[UNDP], 1995; but see Riegle-Crumb, 2005, for an opposing
the proportion of girls scoring above the 95th percentile was
view). What do analyses with more recent data suggest about the
linked to national gender equity.
gender stratification hypothesis?
Considered together, the results of previous tests of the
Riegle-Crumb (2005) used cross-national data from the Third
gender stratification hypothesis indicate the need for several
International Mathematics and Science Study (TIMSS-1995) to
methodological revisions. With regard to cross-national pat-
test the gender stratification hypothesis. An update to the SIMS
terns of gender differences in math achievement, it must first be
and precursor to the TIMSS 2003 used in the current study,
demonstrated that a gap still exists. There is increasing agree-
TIMSS-1995 included more than twice as many countries as did
ment among researchers that the gender difference in math
the 1982 SIMS assessment. Riegle-Crumb argued that, when girls
performance is very small in some nations, such as the United
witness a lack of women in power, the status quo in gender
inequality is maintained by limiting their expectations of success
States (Hedges & Nowell, 1995; Hyde, Fennema, & Lamon,
and achievement. To measure gender equity in the domains of
1990; Hyde et al., 2008); however, it is unclear to what extent
labor force and government representation, Riegle-Crumb used
this gender gap varies across countries. Similarly, the extent of
variables similar to those used by Baker and Jones and added
cross-national variations in gender differences in math attitudes
measures to assess gender equity in the home and family (indicated
and affect is not well understood, despite their links to math
by fertility rate and availability of legal abortion). Her analyses
achievement (e.g., Bandura, Barbaranelli, Caprara, & Pastorelli,
demonstrated that boys outperformed girls in 80% of the nations
2001; Eccles, 1994). Also, the sample of nations included in the
sampled. In addition, although greater female representation in
analyses should be maximized, as occurs in the more recent
national governments predicted a smaller gender difference in
cross-national assessments. Use of multiple cross-national as-
math achievement, women’s economic development and relative
sessments of math achievement would ensure a more reliable
status in the home and family did not significantly predict the
and thorough test of the gender stratification hypothesis.

---

108
ELSE-QUEST, HYDE, AND LINN
Defining Gender Equity
types of composite indices typically are computed using male-to-
female ratios in a variety of domains, such as health (e.g., life
In terms of assessing gender equity across nations, these find-
expectancy and legal access to elective abortion), education (e.g.,
ings point to the importance of how gender equity is defined and
enrollment ratios and literacy rates), economics (e.g., earned in-
measured in the context of predicting gaps in math achievement,
come, economic activity rates, labor market participation), and
attitudes, and affect. Various composite indicators of national
politics (e.g., proportion of parliamentary seats held by women),
gender equity have been developed, though there is controversy
with some domains being weighted more than others (Dijkstra,
regarding their use and relative strengths. Table 1 lists the most
2006). Because these composite indices are each computed differ-
widely used composite indicators, their components, and limita-
ently, reflecting some domains more than or instead of others, their
tions. It is noteworthy that one of the most widely used indices, the
predictive validity also varies.
Gender Development Index (GDI; UNDP, 1995), is not actually an
Some aspects of gender equity may be more germane to math
indicator of gender equity per se. The GDI, which was first
achievement than others; for example, equal access to formal
published in the 1995 Human Development Report (HDR 1995)
schooling (at all levels) surely has a profound impact on girls’
focusing on women’s empowerment, has been and continues to be
math skills, but women’s greater life expectancy is probably less
misconstrued as an indicator of national gender equity and misused
relevant. A cross-national measure of women’s involvement in
as such in a variety of popular press and academic publications
STEM careers would test the gender stratification hypothesis more
(Schu¨ler, 2006). For example, Eagly and Wood (1999) as well as
directly. Thus, indicators in multiple individual domains germane
Schmitt, Realo, Voracek, and Allik (2008) used the GDI, among
to math achievement, attitudes, and affect—including educational,
other indicators, as a measure of gender equality in their analyses.
economic, and political—as well as composite measures (e.g.,
In fact, the GDI is an indicator of human development that is
GEQ, SIGE, GGI, GEM) should be used to provide the broadest
discounted for gender inequity. Also developed by the UNDP for
test of the gender stratification hypothesis. This approach would
HDR 1995, the Gender Empowerment Measure (GEM) assesses
also indicate the societal domains with the strongest links to the
national gender equity in political, health, and economic domains.
gender gap in math, thus providing insight into the mechanisms in
Although the GEM is perhaps the most widely used composite
question.
indicator, its utility is limited by its omission of gender equity in
education, which is of particular relevance for the current study.
The Current Study
In response to the challenge of measuring societal or national
gender equity, social scientists have developed several composite
There were two major goals in the current study. The first was
indices, including the Gender Equality Index (GEQ; White, 1997),
to use meta-analysis to estimate the magnitude of gender differ-
the Standardized Index of Gender Equality (SIGE; Dijkstra, 2002),
ences in mathematics achievement, attitudes, and affect using the
and the GGI used by Guiso et al. (2008). Like the GEM, these
most recent data from TIMSS and PISA. Because recent research
Table 1
Composite and Domain-Specific Indicators of Societal Gender Equity
Indicator type
Description
Composite
Gender Empowerment Measure (GEM)
Includes women’s and men’s percentage shares of parliamentary seats; positions as legislators,
senior officials, and managers; and professional and technical positions; includes women’s
and men’s estimated earned income; omits education domain
Gender Equality Index (GEQ)
Assesses underlying gender equality in Gender Development Index (GDI); calculated as GDI/
HDI; omits political domain
Standardized Index of Gender Equality (SIGE)
Includes relative female-to-male access to education, life expectancy, economic activity rate;
women’s share in higher labor market occupations; women’s share in parliamentary seats;
weights economic domain heavily
Gender Gap Index (GGI)
Composed of four subindices based on economic participation and opportunity, educational
attainment, political empowerment, and health/survival
Domain-specific
Primary enrollment ratio
% of female population of official school age enrolled in primary education/% of male
population of official school age enrolled in primary education
Secondary enrollment ratio
% of female population of official school age enrolled in secondary education/% of male
population of official school age enrolled in secondary education
Tertiary enrollment ratio
% of female population of official school age enrolled in tertiary education/% of male
population of official school age enrolled in tertiary education
Economic activity rate ratio
the ratio of the proportion of females age 15 or older who supply or are available to supply
labor for the production of goods and services to the proportion of males age 15 or older
who supply or are available to supply labor for the production of goods and services
Women’s share of higher labor market positions
% of higher labor market positions (technical and professional, as well as administrative and
management positions) held by women
Women’s share of research positions
% of research positions (according to International Labour Organization, 1990) held by women
Women’s share of parliamentary seats
% of parliamentary seats held by women
Note.
For all indicators, higher values indicate higher status of women. HDI
Human Development Index.

---

GENDER DIFFERENCES IN MATH
109
with North American samples has indicated little evidence of
(Mullis et al., 2004). The TIMSS data used in the meta-analysis are
gender differences in math achievement, and as consistent with the
from the remaining 46 countries and represent the achievement,
gender similarities hypothesis, we predicted that the data would
attitudes, and affect of 219,612 students. Countries and their sam-
show a pattern of gender similarities in math achievement in many
ple sizes appear in Table 2.
nations. However, because TIMSS and PISA appear to differ in the
Achievement.
To assess mathematics achievement, TIMSS
difficulty level of the items, it was expected that mean effect sizes
2003 included five content domains in addition to a Math com-
from PISA would be slightly larger than those found with TIMSS.
posite, which comprises the five content domains; these content
On the basis of previous findings in math attitudes and affect, we
domains are Number, Algebra, Measurement, Geometry, and Data.
predicted that males would show more positive math attitudes and
The Number content domain includes whole numbers, fractions,
affect. We also predicted that there would be variability in the
decimals, integers, ratios, proportion, and percentages. The content
direction and magnitude of gender differences in math achieve-
domain of Algebra assesses understanding of patterns, algebraic
ment, attitude, and affect across nations.
expressions, equations and formulas, and relationships. Measure-
The second goal in the current study was to explain cross-
ment includes the topics of attributes and units and tools, tech-
national variability in these gender differences, using the most
niques, and formulas. The Geometry content domain assesses
recent data from two international data sets (TIMSS and PISA),
knowledge of lines and angles, two- and three-dimensional shapes,
expanding upon the findings of Baker and Jones (1993), Riegle-
congruence and similarity, locations and spatial relationships, and
Crumb (2005), and Guiso et al. (2008), and testing the gender
symmetry and transformations. The Data domain includes the
stratification hypothesis. Our study improves upon those reports
topics of data collection and organization, data representation, data
insofar as it includes data that (a) are from the most recent years
interpretation, and uncertainty and probability. As described in the
available; (b) are from a larger sample of nations; (c) are from two
Introduction, TIMSS items fall into three cognitive domains
international studies; (d) assess gender differences in math atti-
(Knowing, Applying, and Reasoning). Gender differences in these
tudes and affect in addition to achievement; and (e) reflect multiple
three cognitive domains appear in Mullis, Martin, and Foy (2005)
domains of societal gender equity. This study is therefore well
and are meta-analyzed in the current study.
positioned to provide powerful clues regarding the cultural factors
Attitudes and affect.
In addition to assessing achievement,
associated with narrowing or perhaps reversing the gender gaps in
TIMSS administered two scales of students’ math attitudes and
mathematics achievement, attitudes, and affect. We hypothesized
affect (Martin, Mullis, & Chrostowski, 2004). The first scale,
that global composite indicators of societal gender equity (includ-
Self-Confidence in Mathematics, is based on the mean of four
ing GEM, GEQ, SIGE, and GGI) would explain the cross-national
items with which students rate their agreement (e.g., “I learn things
variation in the math gender gap. To focus on specific mecha-
quickly in mathematics”). The second scale, Students’ Valuing
nisms, we predicted that indicators from domains most germane to
Mathematics, is composed of the mean of seven items with which
mathematics achievement, attitudes, and affect would be the most
students rate their agreement (e.g., “I need to do well in mathe-
robust moderators of the gender gap; these indicators include
matics to get the job I want”). Effect sizes for gender differences
women’s representation in scientific research, technical/
in achievement and attitudes on the TIMSS appear in Table 2.
professional, and administrative/management jobs, as well as girls’
PISA 2003.
PISA 2003 included 41 countries and represented
access to primary, secondary, and tertiary education. It was ex-
the achievement, attitudes, and affect of 273,883 students. The
pected that indicators that most directly and closely reflect the
current study meta-analyzed findings from the 2003 assessment
mechanisms specified by theoretical models such as Eccles’s
because it focused predominantly on mathematics. Countries and
expectancy-value theory, Bandura’s social cognitive theory, and
their sample sizes are displayed in Table 2.
Eagly and Wood’s social structural theory would be the best
Achievement.
The mathematics section of PISA includes four
predictors of gender differences in math. For example, the indica-
content domains in addition to a Math composite that comprises
tor of women’s share of research positions was expected to be the
the content domains; these content domains are Quantity, Space/
strongest predictor of the gender gap in math because it measures
Shape, Change/Relationships, and Uncertainty. The Quantity con-
women’s STEM representation, which signifies the STEM-related
tent domain assesses understanding of numeric phenomena, quan-
opportunity structures available to girls and women. Indicators of
titative relationships, and patterns; it is somewhat comparable to
societal gender equity that seem less directly related (but still
the TIMSS content domain of Number. The content domain of
relevant) to girls’ and women’s opportunities in STEM—such as
Space/Shape assesses understanding of spatial and geometric phe-
parliamentary representation—were expected to be less robust
nomena and relationships; it is somewhat comparable to the
predictors of gender differences in math achievement, attitudes,
TIMSS content domain of Geometry. The Change/Relationships
and affect.
content domain assesses understanding of mathematical manifes-
tations of change, functional relationships, and dependency among
Method
variables; it is to some extent comparable to the TIMSS content
domain of Algebra. The content domain of Uncertainty assesses
International Data Sets of Mathematics Achievement,
understanding of probabilities and statistics; this content domain is
somewhat comparable to the TIMSS domain of Data.
Attitudes, and Affect
Attitudes and affect.
PISA assessed attitudes and affect about
TIMSS 2003.
TIMSS 2003 was conducted in 49 countries,
mathematics with five scales (OECD, 2003). Extrinsic Motivation
although two (Syrian Arab Republic and Yemen) were excluded
is based on the mean of four items; students rated their agreement
because of sampling problems; in addition, the data from one
with statements such as “I will learn many things in Mathematics
nation (Argentina) were not available for the final TIMSS report
that will help me get a job.” Intrinsic Motivation is composed of

---

110
ELSE-QUEST, HYDE, AND LINN
Table 2
Sample Sizes and Unweighted Effect Sizes (d) for Gender Differences in Math Achievement, Attitudes, and Affect, by Nation
TIMSS
Nation
N
N
Math
Algebra
Data
Geometry
Measurement
Number
SCM
VM
F
M
Armenia
3,035
2,691
0.12
0.16
0.14
0.13
0.01
0.13
0.04
0.18
Australia
2,443
2,348
0.15
0.06
0.12
0.15
0.18
0.20
0.19
0.17
Austria
b
b
b
b
b
b
b
b
b
b
Bahrain
2,100
2,100
0.42
0.55
0.36
0.43
0.13
0.28
0.12
0.11
Belgium
2,684
2,286
0.14
0.07
0.15
0.14
0.18
0.22
0.25
0.38
Botswana
2,627
2,524
0.04
0.14
0.01
0.17
0.04
0.12
0.10
0.12
Brazil
b
b
b
b
b
b
b
b
b
b
Bulgaria
1,976
2,141
0.01
0.10
0.09
0.04
0.03
0.01
0.21
0.07
Canada
b
b
b
b
b
b
b
b
b
b
Chile
3,061
3,316
0.18
0.10
0.16
0.19
0.28
0.20
0.29
0.19
Chinese Taipei
2,582
2,797
0.07
0.12
0.05
0.13
0.03
0.06
0.25
0.20
Cyprus
1,961
2,041
0.19
0.31
0.19
0.17
0.09
0.17
0.03
0.00
Czech Republic
b
b
b
b
b
b
b
b
b
b
Denmark
b
b
b
b
b
b
b
b
b
b
Egypt
3,264
3,831
0.01
0.10
0.01
0.02
0.10
0.01
0.22
0.12
England
1,415
1,415
0.01
0.05
0.00
0.05
0.03
0.03
0.32
0.23
Estonia
2,020
2,020
0.03
0.02
0.08
0.02
0.05
0.07
0.06
0.02
Finland
b
b
b
b
b
b
b
b
b
b
France
b
b
b
b
b
b
b
b
b
b
Germany
b
b
b
b
b
b
b
b
b
b
Ghana
2,295
2,805
0.19
0.12
0.13
0.33
0.11
0.13
0.20
0.04
Greece
b
b
b
b
b
b
b
b
b
b
Hong Kong
2,486
2,486
0.03
0.06
0.06
0.03
0.03
0.03
0.43
0.19
Hungary
1,651
1,651
0.09
0.04
0.06
0.14
0.19
0.11
0.15
0.11
Iceland
b
b
b
b
b
b
b
b
b
b
Indonesia
2,881
2,881
0.01
0.09
0.04
0.12
0.00
0.07
0.11
0.07
Iran, Islamic Republic of
1,977
2,965
0.12
0.38
0.05
0.19
0.11
0.08
0.10
0.10
Ireland
b
b
b
b
b
b
b
b
b
b
Israel
2,245
2,073
0.09
0.03
0.12
0.01
0.18
0.13
0.15
0.19
Italy
2,139
2,139
0.06
0.04
0.15
0.07
0.15
0.08
0.18
0.27
Japan
2,379
2,477
0.03
0.05
0.07
0.04
0.00
0.07
0.38
0.23
Jordan
2,200
2,289
0.30
0.38
0.26
0.21
0.18
0.27
0.07
0.05
Korea, Republic of
2,548
2,761
0.07
0.02
0.14
0.09
0.05
0.08
0.34
0.23
Latvia
1,779
1,851
0.07
0.19
0.16
0.08
0.10
0.03
0.09
0.13
Lebanon
2,174
1,640
0.15
0.01
0.08
0.21
0.30
0.10
0.16
0.10
Liechtenstein
b
b
b
b
b
b
b
b
b
b
Lithuania
2,482
2,482
0.05
0.19
0.02
0.04
0.03
0.04
0.13
0.02
Luxembourg
b
b
b
b
b
b
b
b
b
b
Macao
b
b
b
b
b
b
b
b
b
b
Macedonia
1,908
1,985
0.09
0.21
0.05
0.08
0.02
0.09
0.07
0.14
Malaysia
2,657
2,657
0.09
0.17
0.06
0.01
0.02
0.14
0.02
0.14
Mexico
b
b
b
b
b
b
b
b
b
b
Moldova, Republic of
2,057
1,976
0.12
0.20
0.08
0.10
0.00
0.14
0.02
0.06
Morocco
1,472
1,472
0.18
0.03
0.25
0.23
0.22
0.25
0.26
0.05
Netherlands
1,502
1,563
0.10
0.03
0.11
0.03
0.19
0.15
0.39
0.46
New Zealand
1,977
1,824
0.03
0.12
0.10
0.05
0.06
0.04
0.23
0.18
Norway
2,067
2,067
0.04
0.10
0.04
0.06
0.06
0.03
0.24
0.24
Palestinian National Authority
2,946
2,411
0.09
0.26
0.18
0.08
0.13
0.04
0.01
0.05
Philippines
4,012
2,905
0.15
0.19
0.14
0.02
0.04
0.20
0.02
0.16
Poland
b
b
b
b
b
b
b
b
b
b
Portugal
b
b
b
b
b
b
b
b
b
b
Romania
2,134
1,970
0.04
0.15
0.00
0.06
0.03
0.06
0.14
0.05
Russian Federation
2,287
2,380
0.04
0.17
0.03
0.05
0.06
0.02
0.08
0.00
Saudi Arabia
1,847
2,448
0.13
0.04
0.13
0.01
0.27
0.29
0.06
0.19
Scotland
1,758
1,758
0.07
0.11
0.05
0.07
0.00
0.05
0.27
0.15
Serbia
2,105
2,191
0.08
0.18
0.04
0.09
0.02
0.06
0.02
0.04
Singapore
2,949
3,069
0.13
0.16
0.04
0.11
0.06
0.14
0.20
0.09
Slovak Republic
2,023
2,192
0.00
0.13
0.16
0.09
0.08
0.00
0.12
0.17
Slovenia
1,789
1,789
0.06
0.21
0.04
0.08
0.08
0.01
0.10
0.09
South Africa
4,566
4,386
0.02
0.02
0.03
0.01
0.05
0.01
0.05
0.06
Spain
b
b
b
b
b
b
b
b
b
b
Sweden
2,171
2,085
0.00
0.05
0.01
0.05
0.09
0.03
0.34
0.22
Switzerland
b
b
b
b
b
b
b
b
b
b

---

GENDER DIFFERENCES IN MATH
111
PISA
N
N
Math
Quantity
Space
Change
Uncertainty
EM
IM
Anx.
MSC
MSE
F
M
a
a
a
a
a
a
a
a
a
a
a
a
6,171
6,380
0.06
0.01
0.11
0.04
0.07
0.24
0.23
0.31
0.34
0.37
2,294
2,303
0.08
0.04
0.17
0.05
0.08
0.58
0.40
0.36
0.44
0.46
a
a
a
a
a
a
a
a
a
a
a
a
4,210
4,586
0.07
0.01
0.16
0.07
0.07
0.32
0.20
0.32
0.35
0.36
a
a
a
a
a
a
a
a
a
a
a
a
2,383
2,067
0.16
0.17
0.15
0.16
0.18
0.10
0.17
0.34
0.33
0.30
a
a
a
a
a
a
a
a
a
a
a
a
13,037
12,688
0.13
0.05
0.20
0.15
0.15
0.12
0.17
0.33
0.33
0.34
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
3,118
3,202
0.16
0.06
0.25
0.13
0.18
0.26
0.26
0.26
0.36
0.42
2,147
2,071
0.18
0.10
0.16
0.21
0.24
0.43
0.29
0.38
0.48
0.45
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
2,906
2,890
0.09
0.04
0.03
0.12
0.14
0.36
0.34
0.39
0.45
0.56
2,262
2,038
0.09
0.02
0.17
0.04
0.12
0.35
0.24
0.39
0.37
0.31
2,290
2,322
0.09
0.01
0.10
0.11
0.19
0.45
0.37
0.38
0.50
0.46
a
a
a
a
a
a
a
a
a
a
a
a
2,392
2,234
0.21
0.23
0.19
0.17
0.23
0.26
0.31
0.26
0.30
0.44
2,231
2,247
0.04
0.03
0.04
0.01
0.12
0.20
0.27
0.28
0.35
0.30
2,251
2,514
0.08
0.02
0.14
0.10
0.09
0.22
0.12
0.20
0.24
0.35
1,620
1,730
0.17
0.30
0.16
0.10
0.08
0.06
0.07
0.27
0.22
0.25
5,419
5,342
0.04
0.02
0.18
0.04
0.07
0.05
0.08
0.13
0.18
0.08
a
a
a
a
a
a
a
a
a
a
a
a
1,925
1,955
0.17
0.10
0.27
0.14
0.17
0.32
0.04
0.28
0.23
0.30
a
a
a
a
a
a
a
a
a
a
a
a
6,041
5,598
0.19
0.12
0.17
0.20
0.25
0.23
0.11
0.17
0.14
0.36
2,433
2,273
0.08
0.03
0.08
0.06
0.14
0.31
0.26
0.26
0.36
0.31
a
a
a
a
a
a
a
a
a
a
a
a
2,206
3,238
0.25
0.24
0.23
0.25
0.24
0.20
0.16
0.14
0.26
0.20
2,408
2,219
0.03
0.03
0.14
0.01
0.00
0.18
0.20
0.26
0.31
0.34
a
a
a
a
a
a
a
a
a
a
a
a
162
170
0.29
0.23
0.36
0.24
0.32
0.89
0.60
0.61
0.77
0.65
a
a
a
a
a
a
a
a
a
a
a
a
1,992
1,931
0.19
0.09
0.28
0.14
0.23
0.42
0.32
0.44
0.46
0.43
642
608
0.24
0.19
0.24
0.20
0.20
0.24
0.34
0.46
0.47
0.38
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
15,546
14,437
0.13
0.13
0.18
0.08
0.06
0.03
0.16
0.13
0.15
0.18
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
1,956
2,036
0.06
0.04
0.09
0.06
0.11
0.50
0.34
0.38
0.55
0.59
2,256
2,255
0.15
0.12
0.17
0.17
0.12
0.17
0.23
0.31
0.35
0.37
2,015
2,049
0.07
0.00
0.07
0.04
0.10
0.23
0.25
0.36
0.42
0.37
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
2,197
2,186
0.06
0.02
0.12
0.08
0.03
0.05
0.11
0.03
0.18
0.17
2,416
2,192
0.14
0.15
0.16
0.13
0.12
0.06
0.03
0.22
0.21
0.24
a
a
a
a
a
a
a
a
a
a
a
a
3,007
2,967
0.11
0.07
0.18
0.03
0.09
0.09
0.01
0.16
0.07
0.33
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
2,228
2,177
0.01
0.03
0.03
0.01
0.06
0.21
0.18
0.04
0.14
0.27
a
a
a
a
a
a
a
a
a
a
a
a
3,585
3,761
0.20
0.13
0.30
0.16
0.20
0.23
0.17
0.25
0.30
0.33
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
5,482
5,308
0.10
0.05
0.20
0.08
0.09
0.09
0.03
0.34
0.25
0.28
2,310
2,314
0.07
0.04
0.10
0.01
0.09
0.32
0.19
0.30
0.35
0.27
4,063
4,357
0.17
0.07
0.23
0.13
0.20
0.67
0.58
0.44
0.67
0.54
(table continue