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We begin with estimates of genetic and environmental influence on individual differences in learning abilities in the early school years, with subsequent chapters going beyond these rudimentary issues of nature and nurture to address three issues: the relationship between the normal and abnormal, longitudinal analyses of stability and change, and multivariate analyses of covariance within and between domains. After presenting an overview of the results based on the entire sample, we compare results for boys and girls and for children assessed by the same versus different teachers.

The simple cross-twin correlations tell most of the story of genetic and environmental influence. Table 10 lists cross-twin correlations at 7, 9, and 10 years for U.K. National Curriculum (NC) teacher ratings for English, Mathematics, and Science composite scores and for three components within each domain. These results for teacher ratings are followed by results for test data for reading (TOWRE at 7 years, PIAT at 10 years), Mathematics at 10, and “g” at 7, 9, and 10 years. Table 11 presents the model-fitting results for 43 separate analyses; the RMSEA values indicate that the full model with A, C, and E parameters fit the data well. We examine the results in detail below.

Table 10.  INTRACLASS CORRELATIONS BY SEX AND ZYGOSITY
MeasureMZDZallDZssDZosMZMMZFDZMDZF
1. Note.—All correlations were significant at p<.01.

2. The numbers of pairs were as follows:

3. NC measures at 7 years: MZ=1888–1944; DZall=3385–3474.

4. NC measures at 9 years: MZ=877–915; DZall=1547–1620.

5. NC measures at 10 years: MZ=913–954; DZall=1612–1676.

6. Tests at 7 years (TOWRE and General Cognitive Ability): MZ=1769–1791; DZall=3107–3166.

7. Tests at 9 years (General Cognitive Ability): MZ=1139; DZall=1265.

8. Tests at 10 years (PIAT, Mathematics and General Cognitive Ability): MZ=722–931; DZall=1265–1610.

9. MZ, monozygotic; DZall, dizygotic same-sex and opposite-sex twins; DZss, same-sex dizygotic twins; DZos, opposite-sex dizygotic twins; MZM, monozygotic male twins; MZF, monozygotic female twins; DZM, dizygotic male twins; DZF, dizygotic female twins.

1.NC measures
NC measures at 7 years
English: speaking and listening.80.49.53.45.80.79.49.56
English: writing.67.36.38.34.68.66.36.39
English: composite.82.50.52.47.83.81.51.53
Mathematics: using and applying.71.40.45.35.73.70.43.47
Mathematics: numbers and algebra.70.39.41.35.72.68.38.45
Mathematics: shapes, space and measures.74.43.46.39.76.73.44.48
Mathematics: composite.78.44.47.40.78.77.46.49
NC measures at 9 years
English: speaking and listening.68.43.42.45.68.69.37.46
English: writing.72.37.38.35.72.72.36.41
English: composite.78.46.45.46.79.78.43.46
Mathematics: using and applying.73.37.41.34.74.72.40.42
Mathematics: numbers and algebra.71.38.40.35.68.74.38.41
Mathematics: shapes, space and measures.72.41.43.38.70.75.40.46
Mathematics: composite.76.41.44.38.75.78.43.44
Science: scientific enquiry.71.41.43.40.69.72.38.48
Science: life processes.74.41.40.41.76.71.39.42
Science: physical processes.72.41.44.38.75.70.43.44
Science: composite.76.44.45.43.76.76.43.47
NC measures at 10 years
English: speaking and listening.73.44.48.40.78.69.50.45
English: writing.73.42.46.38.73.72.49.41
English: composite.80.49.53.45.81.78.56.50
Mathematics: using and applying.72.41.45.37.71.73.50.40
Mathematics: numbers and algebra.72.41.43.40.69.75.46.40
Mathematics: shapes, space and measures.71.42.48.37.68.74.51.45
Mathematics: composite.76.44.49.40.74.78.52.45
Science: scientific enquiry.71.47.53.41.72.71.57.48
Science: life processes.72.48.54.42.72.73.58.49
Science: physical processes.72.49.56.41.71.73.60.52
Science: composite.76.51.57.44.75.76.62.52
2. Test measures
Towre: word.83.49.52.46.85.82.54.49
Towre: non-word.80.46.50.42.81.79.51.48
Towre: composite.85.50.54.45.85.84.56.52
PIAT.64.44.44.44.66.63.44.43
Mathematics test at 10 years
Understanding Number.59.38.40.36.57.60.36.43
Nonnumerical Processes.56.40.40.39.58.54.41.39
Computation and Knowledge.52.30.37.23.52.53.35.38
Mathematics: composite.68.44.49.37.66.70.46.52
3. General cognitive ability
“g” at 7 years.66.48.49.47.68.64.52.48
“g” at 9 years.76.59.61.57.75.77.56.65
“g” at 10 years.72.51.54.47.72.72.53.55
Table 11.  ACE MODEL-FITTING ESTIMATES WITH 95% CONFIDENCE INTERVALS IN PARENTHESESa
MeasureRMSEAACE
• Note.—

• a

A full sex-limitation model was used to test for quantitative (boy vs. girls) and qualitative (same-sex vs. opposite-sex DZ pairs), as explained in Chapter II. For all 43 analyses, no significant quantitative or qualitative sex differences emerged. Therefore, estimates are equated for boys and girls and for same-sex and opposite-sex DZ pairs, described in Chapter II as the “null” model.

• b

b Although the best-fitting model was the null model for 42 analyses, the best-fitting model, for Scientific Enquiry at 10 years was the scalar model which allows variance differences between boys and girls but no quantitative or qualitative sex differences.

• RMSEA root mean square error of approximation: √[χ2/df−1)/(N−1)], where N is the sample size and df the degrees of freedom of the model. Models that provide a good fit to the data have a RMSEA less than or equal to .05. A, additive genetic influence; C, shared environmental influence; E, non-shared environmental influence.

1. NC measures
NC measures at 7 years
English: speaking and listening.023.60 (.54–.65).20 (.15–.24).21 (.19–.22)
English: writing.018.65 (.58–.70).03 (.00–.09).32 (.30–.34)
English: composite.007.65 (.60–.71).17 (.12–.22).18 (.17–.19)
Mathematics: using and applying.034.65 (.59–.72).07 (.01–.12).28 (.26–.30)
Mathematics: numbers and algebra.025.64 (.57–.70).06 (.01–0.12).30 (.28–.32)
Mathematics: shapes, space and measures.024.66 (.60–.72).09 (.04–.15).25 (.23–.27)
Mathematics: composite.039.68 (.63–.74).09 (.04–.15).22 (.21–.24)
NC measures at 9 years
English: speaking and listening.024.51 (.41–.60).17 (.09–.25).32 (.29–.35)
English: writing.007.70 (.61–.75).02 (.00–.10).28 (.25–.31)
English: composite.020.67 (.59–.76).11 (.04–.19).21 (.19–.23)
Mathematics: using and applying.027.73 (.64–.76).01 (.00–.09).26 (.24–.29)
Mathematics: numbers and algebra.031.67 (.58–.74).04 (.00–.12).29 (.26–.32)
Mathematics: shapes, space and measures.031.63 (.54–.72).09 (.01–.17).28 (.25–.31)
Mathematics: composite.022.72 (.64–.79).04 (.00–.12).23 (.21–.26)
Science: scientific enquiry.013.58 (.49–.67).13 (.04–.21).29 (.27–.32)
Science: life processes.010.65 (.56–.74).09 (.00–.17).27 (.24–.29)
Science: physical processes.000.65 (.56–.75).08 (.00–.16).27 (.24–.30)
Science: composite.012.63 (.55–.72).12 (.04–.20).24 (.22–.27)
NC measures at 10 years
English: speaking and listening.034.56 (.47–.65).17 (.09–.24).28 (.25–.30)
English: writing.044.64 (.55–.72).10 (.02–.17).27 (.24–.30)
English: composite.020.60 (.52–.67).20 (.12–.26).21 (.19–.23)
Mathematics: using and applying.041.63 (.54–.72).09 (.01–.17).28 (.25–.31)
Mathematics: numbers and algebra.034.62 (.53–.71).10 (.02–.18).28 (.25–.31)
Mathematics: shapes, space and measures.047.59 (.50–.68).13 (.05–.21).28 (.26–.31)
Mathematics: composite.044.64 (.56–.72).12 (.04–.19).24 (.22–.26)
Science: scientific enquiryb.046.48 (.39–.56).23 (.16–.31).29 (.27–.32)
Science: life processes.039.48 (.40–.57).24 (.16–.31).28 (.25–.31)
Science: physical processes.047.45 (.36–.53).27 (.19–.34).29 (.26–.32)
Science: composite.047.48 (.41–.56).27 (.19–.34).25 (.22–.27)
2. Test measures
Towre: word.013.69 (.63–.74).15 (.10–.20).17 (.16–.18)
Towre: non-Word.025.67 (.61–.73).13 (.07–.18).20 (.19–.22)
Towre: composite.030.70 (.64–.75).15 (.10–.20).15 (.14–.17)
PIAT.012.39 (.28–.50).25 (.15–.34).36 (.33–.41)
Mathematics test at 10 years:
Understanding Number.008.41 (.30–.52).18 (.09–.26).41 (.38–.46)
Nonnumerical Processes.009.33 (.22–.44).23 (.14–.31).44 (.40–.48)
Computation and Knowledge.020.46 (.34–.56).07 (.00–.17).47 (.43–.52)
Mathematics: composite.024.49 (.40–.58).19 (.11–.27).32 (.29–.35)
3. General cognitive ability
“g” at 7 years.002.36 (.29–.42).30 (.25–.36).34 (.32–.36)
“g” at 9 years.030.36 (.29–.42).41 (.35–.46).24 (.22–.26)
“g” at 10 years.002.41 (.33–.50).30 (.23–.37).28 (.26–.31)

### NC TEACHER RATINGS

The pattern of twin correlations in Table 10 for NC teacher ratings consistently suggests substantial genetic influence and modest shared and nonshared environmental influence across domains and across ages. Consider the first two columns of correlations, which are based on the entire sample of MZ twins and DZ twins. (The other columns show results separately by sex, which we will discuss later.) The first row shows twin correlations for English: Speaking and Listening at 7 years. The MZ and DZ correlations of .80 and .49 suggest substantial heritability of .62 [2 (rMZ−rDZ)], .18 shared environmental influence (rMZ−heritability), and .20 nonshared environmental influence (1−rMZ), which includes error of measurement.

A similar pattern of results is seen for all three components of English at 7 years, although Writing shows the least shared environmental influence (.05). A remarkably similar pattern of results can also be seen at 9 and 10 years for the three components of English. For the English composite, the twin correlations yield heritability estimates of .64, .64, and .62, respectively, at 7, 9, and 10 years; estimates of shared environmental influence are .18, .14, and .18.

Results are also similar for the Mathematics composite at 7, 9, and 10 years for heritability (.68, .70, and .64) and shared environment (.10, .06, .12). The Science composite also yielded similar results at 9 years (.64 heritability, .12 shared environment), but at 10 years it suggested somewhat less heritability (.50) and somewhat greater shared environment (.26), a pattern seen for all three components of Science at 10 years.

The model-fitting results for NC measures shown in Table 11 confirm these estimates and conclusions based on the twin correlations: Heritabilities are substantial and shared environmental estimates are modest within each domain, across domains, and across ages. For example, as noted above, the twin correlations for the first row of Table 10 suggested estimates of .62 for heritability, .18 for shared environment, and .20 for nonshared environment. The model-fitting estimates shown in Table 11 are .60, .20, and .21, respectively. The twin correlations suggested that Writing at 7 years showed less shared environmental influence (.05), and this is also confirmed with a model-fitting estimate of .03; the nonoverlapping confidence intervals in the shared environmental estimates indicate that the shared environmental estimate for Writing is significantly lower than for Speaking/Listening. Also, the twin correlations suggested that the Science composite at 10 years was less heritable (.50) and more influenced by shared environment (.26) than any of the other domains. Model-fitting estimates were similar (.48 and .27, respectively); however, the overlapping confidence intervals from the model-fitting analyses indicate that these differences are not significant for the composite measures. The average model-fitting heritability estimate across the NC composite scores and across age is .63, the average estimate of shared environment is .14 and the average estimate of nonshared environment is .22.

### TESTS OF READING AND MATHEMATICS

The second panel of Table 10 presents MZ and DZ twin correlations for two subtests and a composite of the TOWRE at 7 years, the PIAT reading recognition test at 10 years, and three subtests and a composite of the Mathematics test at 10 years. The TOWRE at 7 years yields results similar to those for NC teacher ratings: heritability of .70 and shared environment of .15 for the composite measure. The word and nonword subtests of the TOWRE yield very similar results. However, the results for the PIAT at 10 years differ from the results for the NC teacher ratings and for the TOWRE: MZ correlations are lower, which results in somewhat lower heritability estimates (.40) and higher shared environment estimates (.24).

Twin correlations for the web-based mathematics tests also suggest moderate heritability (.48 for the composite) and modest shared environment (.20 for the composite). Results for the three component tests in the mathematics battery are similar.

The model-fitting results shown in the second panel of Table 11 confirm these conclusions for the tests of reading and mathematics. The confidence intervals indicate that the heritability of the TOWRE at 7 years is significantly greater than for the PIAT at 10 years.

### TESTS OF GENERAL COGNITIVE ABILITY (“g”)

Despite the different modes of measurement for “g” at 7 (telephone), 9 (mailed booklets), and 10 (web-based tests), the results are similar across the three ages. Heritability estimates for “g” based on the twin correlations shown in the third panel of Table 10 are lower than for the measures of academic performance: .36 at 7 years, .34 at 9 years, and .42 at 10 years. Shared environmental estimates are higher than for the measures of academic performance: .30, .42, .30, respectively.

The model-fitting estimates shown in Table 11 are similar. Nonoverlapping confidence intervals suggest that at each age “g” is significantly less heritable and shows significantly more shared environmental influence than the NC composite measures except for Science at 10. One possibile explanation of the greater heritability of achievement scores is that the expression of genetic potential for achievement takes place in the context of active genotype-environment correlations, driven by variance in interest, motivation, and engagement. In other words, in respect to genetic influences on achievement, genes code for appetites, not aptitudes. Finding genes for both general cognitive ability and different areas of academic achievement will facilitate understanding the mechanisms that lead to the observed differences in heritability between g and achievement.

### BOYS VERSUS GIRLS

So far we have focused on results for the entire sample without regard to sex. The last four columns of Table 10 show the twin correlations separately for boys and girls. In general across measures and ages, estimates derived from the twin correlations are similar for boys and girls. For example, for the NC ratings, the average heritability estimates are .56 for boys and .59 for girls; estimates of shared environment are .21 for boys and .19 for girls. The largest differences are for NC Mathematics and NC Science at 10 years where heritability is lower for boys than girls (.44 vs. .66 for NC Mathematics composite and .26 vs. .48 for NC Science composite) and shared environment is greater for boys than girls (.30 vs. .12 and .49 vs. .28). However, for the Mathematics test-score data at 10 years, the results are similar for both boys and girls: The average heritability estimates are .42 for boys and .38 for girls; shared environment estimates are .30 and .33.

These interpretations based on the twin correlations are confirmed by fitting sex-limitation models, which yielded no significant quantitative sex differences. The best-fitting sex-limitation model for all but one of the 43 analyses was the “null” model that allows no sex differences in parameter estimates.

In summary, ACE parameter estimates are similar for boys and girls in our most powerful analyses that capitalize on the entire TEDS dataset. Analyses in subsequent chapters are less powerful in that they involve sub-samples—sub-samples at the low extremes of the distribution (Chapter IV), sub-samples with longitudinal data at all three ages (Chapter V), and sub-samples with complete data on all measures for multivariate analyses (Chapter VI). In order to maximize power for these analyses and to simplify our presentation of the results, we will focus on analyses of the total dataset with sexes combined.

### SAME-SEX VERSUS OPPOSITE-SEX DZ TWINS

Table 10 shows that twin correlations are similar for same-sex and opposite-sex DZ twins. On average, correlations for the same-sex DZ twins are .06 greater than for opposite-sex DZ twins for NC ratings, reading and mathematics tests, and “g.” Even with these large sample sizes, such differences are not nearly significant. As expected from these results, sex-limitation model fitting shows no significant qualitative sex differences. Because same-sex and opposite-sex DZ twins yield similar results, subsequent analyses will maximize power by combining same-sex and opposite-sex DZ twins.

### SAME TEACHERS VERSUS DIFFERENT TEACHERS

As mentioned in Chapter II, some twins were in the same classroom: 67% at 7 years, 63% at 9 years, and 58% at 10 years. For the teacher ratings, when twins were in the same classroom, they were rated by the same teacher; when they were in different classrooms, they were rated by different teachers. In this section, we examine the effect of having the same versus different teachers on ACE estimates.

#### Teacher Ratings

In general, twin correlations were higher when the same teacher rather than different teachers rated members of a twin pair. However, differences in twin correlations for MZ and DZ twins were similar for same-teacher and different-teacher ratings. In other words, heritability estimates were similar regardless of whether the same teacher or two different teachers rated members of a twin pair, but shared environment estimates were greater when twins were rated by the same teacher. For example, for the English composite at 7 years, the MZ and DZall correlations for same-teacher ratings were .88 and .55; for different-teacher ratings the correlations were .71 and .39. These twin correlations suggest heritabilities of .66 for same-teacher ratings and .64 for different-teacher ratings. Shared environment estimates were greater for same-teacher ratings (.22) than for different-teacher ratings (.07).

Similar results were obtained for all of the NC ratings at all three years: The average heritability estimates were .64 for same-teacher ratings and .59 for different-teacher ratings; the average shared environment estimates were .22 and .05, respectively. Differences of this magnitude in heritabilities and shared environment were not significantly different in model-fitting analyses, despite the large sample size.

##### Tests

Although the estimates of shared environment for same-teacher ratings as compared with different-teacher ratings are not significantly different, the somewhat higher shared environment estimates for same-teacher ratings might signal a bias when one teacher rates both twins. However, children rated by the same teacher have been in the same classroom and experiencing the same instruction, so another possibility is that they might show a true shared environmental effect as compared with children in different classrooms. These hypotheses can be tested by comparing the results for NC ratings to those for test data. If the rating bias hypothesis is correct, test data should not show a difference in shared environment estimates for twins in the same classroom versus twins in different classrooms. On the other hand, if the twins in the same classroom truly evidence more effect of shared environment than children in different classrooms for NC teacher ratings, the test data should show the same pattern of results.

For three of the tests, the results appear to support the rating bias hypothesis: Averaged across the three ages, the shared environmental estimates for children in the same classroom versus in different classrooms were, respectively, .24 and .24 for the PIAT, .17 and .21 for the web-based Mathematics composite, and .35 and .31 for “g.” In contrast, the results for the TOWRE at 7 years appear to support the second hypothesis: Shared environment estimates for twin pairs taught by the same teacher in the same classroom and those taught by different teachers in different classrooms were .17 and .07 for the TOWRE composite, although this difference in estimates of shared environment is not nearly significant.

Averaging estimates of shared environment across all four tests at all ages, the test-score data yield highly similar estimates for twins with the same teacher (.27) and those with different teachers (.24), suggesting that there is no added shared environmental effect when children share the same classroom. Taken together, these findings for the test-score data support the rating bias interpretation of the teacher-rating results (when one teacher rates both twins, estimates of shared environment are inflated).

However, there is another twist: The results for the test-score data do not support the most straightforward version of the rating bias hypothesis, because the average shared environment estimate for test-score data across ages (.22) is similar to the average shared environment estimate for same-teacher ratings (.20), not to the average estimate for different-teacher ratings (.07) as might have been expected. Thus, same-teacher ratings of academic performance do not inflate estimates of shared environment as compared with test-score data. Instead, it is possible that different-teacher ratings inflate estimates of nonshared environment by introducing between-rater variance. For example, although it seems reasonable to assume that the results for different-teacher assessments are more valid as they eliminate rating bias, seeing the two twins together all day long may make same-teacher ratings more valid. However, a less interesting, but more parsimonious, hypothesis is that the nonsignificant differences in shared environmental estimates for NC ratings by same versus different teachers are not real.

As was the case for same-teacher and different-teacher NC ratings, heritability estimates for the test-score data were similar for members of twin pairs, whether taught by the same teacher or by different teachers: .68 and .78 for TOWRE composite, .38 and .42 for PIAT, .52 and .46 for web-based Mathematics composite, and .35 and .41 for “g” on average across the 3 years.

Twin correlations and model-fitting estimates for same- and different-teacher ratings are available from the authors. Because results are generally similar for twins taught by the same teacher and those taught by different teachers, subsequent analyses were conducted on the combined sample in order to maximize power and simplicity of presentation.