How smart is my child? The judgment accuracy of parents regarding their children's cognitive ability

Abstract

Parents' judgment of their children's cognitive ability is important for providing adequate learning environments. This study examined parents' judgment accuracy with 2346 children (M = 8.94 years; 48.3% girls) and their parents (1283 mothers, 426 fathers, and 637 parental pairs). The data were collected between September 2012 and February 2014 in Germany. Latent regression analyses were conducted for the overall sample and by grade (n _Grade1&2 = 830; n _Grade3&4 = 1516). Characteristics of the child (gender, birth order) and parents (gender, socioeconomic background) were investigated as moderators. Children's cognitive ability explained 34%/25%/37% (overall sample/Grade1&2/Grade3&4) of the variance in parental judgments. Judgments depended more on children's academic achievement than on cognitive ability. Parents judged their son's intelligence more accurately than their daughter's and first‐born children more accurately than last‐born children. Higher‐educated parents showed higher judgment accuracy.

For most children, the family is the primary educational environment that lays the foundation for their development (Landry et al., 2006). This includes children's cognitive ability, which can be defined as a general mental capability involving reasoning, planning, problem‐solving, abstract thinking, complex idea comprehension, and learning from experience (Gottfredson, 1997). Parents strongly contribute to the development of children's cognitive ability by providing stimulating play materials, offering opportunities for active learning, being responsive and sensitive to their children's questions, and promoting their self‐confidence and interest in learning (Lugo‐Gil & Tamis‐LeMonda, 2008). Parents can better support their children's development when they know about their children's cognitive ability and adapt their behavior and demands to their current level (Frischknecht et al., 2014; Voß, 1994). This includes parents' responsivity to the child, especially in the form of verbal communication or by engaging the child in activities that promote learning (Lugo‐Gil & Tamis‐LeMonda, 2008). Parents often foster their children unintentionally, for example, while playing and engaging with them at home (Tamis‐LeMonda et al., 2004). Misjudging children's cognitive ability bears the risk of over‐ or underchallenging them. Slight overestimation has a positive impact on students' achievement, due to its motivating effect (Helmke et al., 2004). However, both pushing children before they are ready and failing to provide a cognitively stimulating learning environment can hinder or even decrease children's cognitive development (Becker et al., 2012; Niklas & Schneider, 2017). Parents' judgments of children's ability also affect decisions about children's education and future academic path. For example, children's academic self‐perceptions and achievement are affected by parents' educational aspirations (Buchmann et al., 2022), which in turn, are positively related to children's cognitive ability (e.g., Murayama et al., 2016) and therefore to their judgments of children's cognitive ability (e.g., Rothenbusch et al., 2018). In addition, parental nomination is often the first step in the process of identifying cognitively highly able students for early entrance to school, grade skipping, or gifted programs (Marsili & Pellegrini, 2022). Without this nomination, children may miss out on opportunities for support. That is, children benefit when their parents accurately judge their cognitive ability.

Prior studies applied different operationalizations of parents' judgment accuracy for children's cognitive ability, which impedes the integration of findings. The present study reviews the different operationalizations, their strength and limitations, and related research findings of parents' judgment accuracy for children's cognitive ability. It further investigates a large sample of mothers and fathers of elementary school children using latent regression and moderator analyses. By doing so, the present study aims to significantly contribute to our knowledge base on the important topic of parents' judgment accuracy for their children's cognitive ability.

Parents' judgment accuracy for children's cognitive ability

Parents' judgments rely on their diagnostic competencies defined as parents' ability to appropriately judge children's states and characteristics, such as their cognitive ability. Parents mostly make these judgments implicitly, through casual observations (Schrader, 2010). Because children's cognitive ability is not directly observable, it must be deduced by the parents from children's behavior (Urhahne & Wijnia, 2021). This deductive process is described in the Realistic Accuracy Model (Funder, 2012; see Figure 1). To reach an accurate judgment, a person must first display relevant behavior related to the trait (e.g., a child learns new content fast). Second, this behavior must be available to and detected by the judge (e.g., a parent perceives this learning progress and its speed). Third, the judge must utilize the relevant, available, and detected information correctly to achieve an accurate judgment (e.g., the parent interprets learning speed as an indicator of cognitive ability and has a valid standard of comparison for evaluating it as “fast”).

FIGURE 1.

Realistic Accuracy Model (based on Funder, 2012; adapted by the authors).

That is, parents' judgments and their accuracy rely on a complex process that can be affected by the characteristics of the target, trait, and judge. For example, two characteristics of children that are both readily available and detectable but that differ in their relevance (i.e., in their relationship with children's cognitive ability) are attractiveness and academic achievement. Both characteristics are related to judgments of children's cognitive ability. More attractive children are judged by others to be more intelligent compared with less attractive children (Langlois et al., 2000), and children with higher academic achievement are judged by parents and teachers to be more intelligent than children with lower achievement (Fisicaro & Lance, 1990; Machts et al., 2016). Attractiveness is not or only weakly related to cognitive ability (Langlois et al., 2000; Mitchem et al., 2015). Its biasing influence on judgments of a person's cognitive ability can be described as a halo effect, which occurs when one characteristic of the person overshadows the judgment of their other characteristics (Sanrey et al., 2020). Other examples of halo effects include the influence of a person's gender or social status on other judgments. Academic achievement, on the other hand, is strongly related to cognitive ability (e.g., meta‐analytic correlation with school grades: ρ = .54; Roth et al., 2015). Thus, utilizing academic achievement as an indicator of children's cognitive ability would lead to more accurate judgments than utilizing children's attractiveness. However, using children's academic achievement as the sole indicator would lead to insufficient judgment accuracy, as approximately 50% to 75% of the differences in academic achievement cannot be explained by differences in cognitive ability. Especially for children for whom achievement is not a good indicator of cognitive ability, such as underachievers, using academic achievement as a cue leads to errors in parental judgment. However, other behavioral indicators of children's cognitive ability may be less recognized or known (e.g., the speed of learning new material or problem‐solving and creative behavior; Krischler et al., 2021) and therefore utilized less by parents.

Review of findings on the accuracy of parents' judgments

Parents' judgments of children's cognitive ability can be compared to children's actual scores in a cognitive ability test using percentage agreement or discrepancy, mean comparison, correlational analyses, or regression analysis. Table 1 presents existing research of judgment accuracy using these operationalizations. It includes empirical papers written in the English language that were published after 1980 in peer‐reviewed journals and referred to K12 children. We found 16 studies; most older but also some more recent ones were based on small samples (i.e., 50 or less; Maas & Hox, 2005). Only one study controlled for the nested data structure or used a latent variable approach (Rothenbusch et al., 2018). Three studies used percentage agreement or discrepancy without significance testing (i.e., Hunt & Paraskevopoulos, 1980; Miller, 1986; Stoiber, 1992). Their findings depend on the categories used and are difficult to compare across studies. Agreements between parents' judgment and children's cognitive ability ranged between 6% to 61% and discrepancies between 10% and 30% (e.g., Miller et al., 1991; Stoiber, 1992). Two studies using mean comparisons point to a significant difference between parents' judgments and children's actual cognitive ability, with parents—especially fathers—overestimating their children (e.g., Chamorro‐Premuzic et al., 2009). Twelve studies used measures of association and show that parents are fairly accurate in judging children's cognitive ability, with correlations ranging from .50 to .70 (for a review see Schrader & Praetorius, 2018), and regression coefficients ranging from .07 to .55 (Chan, 2000; Rothenbusch et al., 2018). Judgment accuracy varies greatly between studies (r = .18–.83, see Table 1) and parents (Miller et al., 1991). Studies used different measures of cognitive ability, such as standardized tests or developmental screenings. Measures of parental judgments also differed (e.g., yes/no judgments about whether children answered an item correctly or estimates of mental age). Parents tended to overestimate children's cognitive ability (e.g., Chamorro‐Premuzic et al., 2009; Willinger & Eisenwort, 2005) and to underestimate the variation in development (Voß, 1994). Parents judged their children more accurately when rating them relative to other children than when estimating absolute values (Miller, 1986; Miller et al., 1991).

TABLE 1.

Empirical studies on parents' accuracy in judging their children's cognitive ability.

Authors (year)	Sample N	Children's age	Grade level	Cognitive ability measures	Judgment measures	Operationalization of accuracy	Results on accuracy	Moderators a
Chamorro‐Premuzic et al. (2009)	54 children and their parents (54 mothers and 54 fathers, both judged their child separately)	13–15 years M = 14.33 SD = 0.32	Grade 9	Cognitive Abilities Test	Questionnaire (mathematical, spatial, and verbal intelligence)	Mean comparison	M mothers = 112.45 M fathers = 116.13 M children = 108.52 t(53) = 3.51–5.66, p < .01	PG ●
						Correlation	r mothers = .65** r fathers = .58**
Chan (2000)	109 students and their parents	12–18 years M = 14.61 SD = 1.43	Grade 7–12, gifted program	Cognitive battery (Raven's Standard Progressive Matrices)	Questionnaire on students' learning characteristics (e.g., advanced vocabulary, ability to generalize)	Correlation	r = −.24, p < .05
						Regression	R = .44, p < .05
Furnham and Valgeirsson (2007)	305 children and their parent(s) (79 mothers & 79 fathers, one parent judged 1–3 children)	M = 10.5 years SD = 4.3		Wechsler Intelligence Scale for Children	Questionnaire on general cognitive ability	Regression	β = .31**–.55**
Glascoe and Sandler (1995)	134 children and their parent (one parent judged their child; 82% were mothers)	12–77 months Mdn = 42		Battelle Developmental Inventory Screening Test	Estimate of children's mental age	Correlation	r = .65**–.78**	CG ● PG ● SB ●
Hunt and Paraskevopoulos (1980)	50 children and their mothers	45–64 months M = 52 SD = 6.5	Preschool	Cognitive Battery (e.g., items from the Stanford‐Binet Intelligence Test and the Peabody Picture Vocabulary Test)	Interview on expected performance per test item	Discrepancy	Difference between the mean number of test items passed by the children and the mean number their mothers predicted they would pass, based on 96 items in total: M = 16.50	SB +
Kirkcaldy et al. (2007)	415 children and their parents (both judged their child separately)	10–13 years M = 10.6 SD = 0.58	Grade 5	Raven Progressive Matrices test	Questionnaire on general cognitive ability	Correlation	r mothers = .21*** r fathers = .19***
						Regression	β mothers = .07, ns β fathers = .08 +
Malhi et al. (2005)	100 children and their mothers	16–60 months M = 42.2 SD = 11.5		Developmental Profile II	Estimate of children's mental age	Correlation	r = .83***	CG ● BO ● SB ●
Miller (1986)	49 children and their mothers	6.1–7.4 years M = 6.9	Grade 1	Cognitive Battery (e.g., items from the Stanford‐Binet Intelligence Test and the Peabody Picture Vocabulary Test)	Interview on expected performance per test item	Agreement	Number of correctly judged items out of 18 items in total: M = 11.29–14.24 (SD = 2.09–3.30)
Miller et al. (1991)	50 children and their parent(s) (48 mothers, 34 fathers, at least one parent judged their child)	M = 8.2–11.3 years	Grade 2 (n = 26) Grade 5 (n = 24)	Cognitive Battery (e.g., items from the Kaufman Assessment Battery for Children)	Interview on expected performance per test item	Percentage agreement	M mothers = 6%–8% M fathers = 6%–16%	CG ● PG ●
						Percentage discrepancy	M mothers = 13%–30% M fathers = 10%–30%
						Correlation	r mothers = .44*–.71** r fathers = .40*–.50*
Miller and Davis (1992)	56 children and their mothers	M = 8.5–11.5 years	Grade 2 (n = 33) Grade 5 (n = 27)	Cognitive Battery (e.g., items from the Stanford‐Binet Intelligence Test and the Peabody Picture Vocabulary Test)	Interview on expected performance per test item	Percentage discrepancy	M = 18%	SB ●
						Correlation	r = .19–.43**
Rothenbusch et al. (2018)	572 gifted students and their parent(s) (at least one parent judged their child)		Grades 3 and 4	Cognitive Ability Test for the Gifted	Questionnaire on cognitive abilities (e.g., verbal abilities, deductive reasoning)	Correlation (consideration of nested data structure)	r = .18**–.31***
Sommer et al. (2008)	93 children and their parents (87 mothers & 6 fathers)	9.3–11.2 years M = 9.10 SD = 0.41	Grade 4	Cognitive Ability Test (Kognitiver Fähigkeitstest, KFT)	Questionnaire on general cognitive ability	Correlation	r = .50* r girls = .54* r boys = .48*	PG ●
Spinath and Spinath (2005)	595 children and their parents (82.6% mothers)	7–11 years M = 8.7 SD = 1.2	Grades 1–4	Cognitive Ability Test (CFT 1 and CFT 20)	Questionnaire (Absolute School‐Based Ability Perception scale)	Correlation	r = .32**
Stoiber (1992)	24 children and their mothers	3–4 years M = 50 month SD = 10	Preschool	Cognitive Battery (e.g., block counting, word recognition)	Interview on expected performance per test item	Percentage agreement	M = 61%
Waschbusch et al. (2000)	145 children and their parent (mostly mothers)	5–12 years M = 8.04 SD = 2.06		Woodcock‐Johnson Psycho‐Educational Battery; Wechsler Intelligence Scale for Children	Questionnaire on general cognitive ability	Correlation	r girls = .43**–.51*** r boys = .49***–.51***	CG ●
Willinger and Eisenwort (2005)	55 children and their mothers	3–6 years M = 55.2 month SD = 9.9		Columbia Mental Maturity Scale; Vienna Developmental Test	Questionnaire on children's active vocabulary	Mean comparison	M mothers = 63.8 M children = 26.2 t(54) = −21.05, p < .001	CG ● BO ● SB ●

Note: Listed are only empirical papers written in the English language, published after 1980 in peer‐reviewed journals, and referring to kindergarten, preschool, or school‐aged children; r = correlations between parents' judgments and children's cognitive ability measures; β = standardized regression coefficient from predicting parents' judgments through children's cognitive ability measures; ● = not significant; ⁺ = positive effect; − = negative effect.

Abbreviations: BO, birth order; CG, children's gender; ns = statistically nonsignificant; PG, parental gender; SB, socioeconomic background.

^a Only moderators of accuracy that were examined in the present study are listed.

⁺ p < .10;

^* p < .05;

^** p < .01;

^*** p < .001.

Operationalizations of parents' judgment accuracy

Table 2 summarizes the diagnostic information that can be taken from the different operationalizations of parents' judgment accuracy and their limitations.

TABLE 2.

Operationalizations of parents' judgment accuracy for children's cognitive ability.

Method	Calculation	Diagnostic information	Limitations	Examples of studies
Percentage agreement	Percentage of correct predictions by parents	Describes the percentage of correctly judged answers or responses of the child	These operationalizations depend on the number of categories used, and each category must be clearly defined and known by the judge. Therefore, percentage agreement and discrepancies are difficult to compare across studies (Südkamp et al., 2012)	Miller et al. (1991) Stoiber (1992)
Percentage discrepancy	Absolute difference between parents' judgments and children's cognitive ability divided by the point total for the task	Indicates the average discrepancy between the judgment and the actual performance (e.g., parents' inaccuracy)	These operationalizations depend on the number of categories used, and each category must be clearly defined and known by the judge. Therefore, percentage agreement and discrepancies are difficult to compare across studies (Südkamp et al., 2012) Parents' judgments and ability measures must be recorded on the same scale and in the same response format	Miller et al. (1991) Miller and Davis (1992)
Mean comparison	Comparison of parents' judgments and children's cognitive ability scores, such as by paired sample t‐tests	Systematic judgment tendencies (e.g., severity) can be detected		Chamorro‐Premuzic et al. (2009) Willinger and Eisenwort (2005)
Correlations	Correlation between parents' judgments and children's cognitive ability as assessed by tests	Describes the extent to which judgments discriminate between relative levels of children's cognitive abilities. Higher correlations indicate higher accuracy of parental ratings concerning cognitive ability measures	High correlations can be achieved despite systematic over‐ or underestimation and no information about parents' judgment tendencies is available (Feinberg & Shapiro, 2003; Südkamp et al., 2012)	Sommer et al. (2008) Spinath and Spinath (2005)
Regression analysis	Regression of parents' judgments on children's cognitive ability as assessed by tests	Regression analyses provide estimates of the overall relationship and deviations between judgments and test results; they allow the consideration of possible influencing factors on judgment accuracy (i.e., moderators), for testing the functional form of relations, and can account for nested data structures	High relations can be achieved despite systematic over‐ or underestimation and no information about parents' judgment tendencies is available	Furnham and Valgeirsson (2007) Kirkcaldy et al. (2007)

Each operationalization has different advantages and disadvantages, such as that all but mean comparisons do not show whether parents tend to over‐ or underestimate their children (Feinberg & Shapiro, 2003; Südkamp et al., 2012). Further, measures of association such as correlations or regressions are not optimal measures of judgment accuracy because high associations can result from systematic over‐ or underestimation. For example, parents tend to overestimate their children's intelligence (e.g., Chamorro‐Premuzic et al., 2009). If this general tendency is shown to a similar extent for each individual child (i.e., similar variation of values), this would lead to strong correlations between parents' judgments with children's intelligence. Nevertheless, both operationalizations are often and increasingly used (e.g., Chamorro‐Premuzic et al., 2009). Regression analysis has specific advantages. It allows the consideration of factors that might impact parents' judgments of children's cognitive ability such as children's academic achievement and parents' educational level. It further allows to account for nested data structures. Children in the same classroom are more similar than children in different classrooms (Raudenbush & Bryk, 2002) as they are exposed to common influences such as the same teachers. This may impact parents' perceptions, too, because parents receive feedback about their children from the same teacher and are more likely to compare their children to children from the same class. Nesting in data violates the assumption of independence of observations (Geiser, 2011). Therefore, it should be accounted for when investigating parents' judgment accuracy. Finally, regression analysis allows testing the functional form of the relation between parents' judgments and children's test scores (i.e., linearity vs. quadratic relation; Hox & van de Schoot, 2017). Quadratic relations would indicate that judgment accuracy varies for children of different ability levels (e.g., less accurate judgments for children with more extreme ability levels than children of average ability). The regression approach therefore appears to be the most appropriate here.

Possible moderators

Various factors beyond the cognitive ability of children influence parents' judgments. Studies on such factors are rare and typically have not considered their moderating effects on judgment accuracy (last column of Table 1). Nonetheless, studies indicate potential influences on parents' judgment accuracy.

Characteristics of the child

Gender

Parents' gender role‐stereotyped perceptions of their children's competencies can influence their cognitive ability judgments (Eccles et al., 1990). Most people perceive psychometric intelligence as more of a masculine trait (Petrides et al., 2004) and parents have been found to judge their sons' cognitive ability higher than their daughters' (Furnham & Valgeirsson, 2007). Additionally, girls' high achievement tends to be attributed to their effort and motivation whereas boys' achievement tends to be attributed to their cognitive ability (Tiedemann, 2000). As a result, girls' cognitive potential may be overlooked. However, several studies found no influence of gender on judgment accuracy (e.g., Glascoe & Sandler, 1995; Kirkcaldy et al., 2007; Waschbusch et al., 2000).

Birth order

The birth order effect describes that those born earlier have higher cognitive ability test scores, better school achievement, and higher educational attainment (Black et al., 2005; Hotz & Pantano, 2015). Parents judge their first‐born's ability significantly higher than their later‐born's ability (Furnham et al., 2002; Furnham & Petrides, 2004). However, most empirical studies have not found an effect of birth order on parental judgment accuracy (e.g., Malhi et al., 2005; Willinger & Eisenwort, 2005).

Characteristics of the parents

Gender

Mothers frequently spend more time with their children than fathers (Miller & Davis, 1992; Voß, 1994) and invest more time in the upbringing of their children (primary caretaker hypothesis; Babchuk et al., 1985). Consequently, they have more opportunities to observe their children and accurately recognize their abilities. Consistent with this, Chamorro‐Premuzic et al. (2009) found that fathers overestimated their children's cognitive ability more than mothers. However, most differences in accuracy between fathers and mothers were small or not significant (e.g., Chamorro‐Premuzic et al., 2009; Glascoe & Sandler, 1995). Further, many of these findings are relatively old, and parenting roles have changed significantly in recent years, with fathers increasingly involved in parenting (BMFSFJ, 2016).

Socioeconomic background

Parents with higher educational levels and socioeconomic status are assumed to have greater knowledge about the development and parenting of children (Bornstein et al., 2010). They spend more time with their children (Guryan et al., 2008) and have more access to social and professional support (Bornstein et al., 2010). Consequently, they might provide more stimulating learning environments where children's potential can be observed. However, the majority of studies have not found an influence of educational level or socioeconomic status on parents' judgment accuracy regarding their children's cognitive ability (e.g., Malhi et al., 2005; Miller & Davis, 1992; Willinger & Eisenwort, 2005).

To summarize, empirical studies have suggested that parents show moderate to high judgment accuracy with a tendency to overestimate their children's abilities. Most studies used correlational analyses and did not investigate moderator variables. Therefore, empirical evidence on possible moderators is scarce; the available findings point to no or only small influences on judgment accuracy. Rather than reflecting a true small or null effect, this could be because of not using an optimal method to examine moderator variables. For example, some studies compared the accuracy of different groups through t‐tests or correlations (e.g., Chamorro‐Premuzic et al., 2009). Correlations only show whether there is a relationship between the accuracy and the moderator variable, but not how the moderator affects accuracy. Therefore, using regression analyses for moderator analyses (i.e., by including an interaction term between the possible moderator and children's cognitive ability) may reveal different relationships than previously found. Regression analysis also has the advantage that more than two groups can be compared.

To conclude, the existing research should be complemented with investigations using larger samples of children and their parents and more appropriate methods of analysis (i.e., moderator analyses in regression analysis, latent variable modeling, modeling nested data structures, tests for quadratic relation) to better understand parents' judgment accuracy and possible moderators.

The present study

The present study investigates parents' judgment accuracy in a large sample of elementary school children in Grades 1 to 4 (M = 8.93 years). Previous studies reported considerable variability in parents' judgment accuracy. We therefore examined potential moderators selected based on both literature and availability in the dataset, which originates from the norming of an intelligence test. We replicated and extended previous findings by conducting latent variable regression analyses while considering the nested data structure. We tested different functional forms of the relationship between parents' judgments and children's test scores (i.e., linear vs. quadratic relation) to explore whether judgment accuracy is comparable for children with different cognitive ability levels.

Based on the state of research on parents' judgment accuracy, we formulated the following research questions and hypotheses:

1. How accurate are parents' judgments of their children's cognitive ability?

• In line with previous findings (e.g., Schrader & Praetorius, 2018), we expected moderate accuracy (i.e., moderately high and positive regression coefficients).

• 2Do characteristics of children (ability level, gender, and birth order) and parents (gender, socioeconomic background) moderate judgment accuracy?

• Given the lack of previous findings, we examined possible moderating influences of children's and parents' characteristics exploratively.

Controlling for academic achievement and self‐concept

We conducted our regression analyses with and without controlling for children's academic achievement and academic self‐concept (i.e., children's self‐evaluation regarding their academic ability), which are both positively related to children's cognitive ability (Chen et al., 2012; Roth et al., 2015; Zaboski et al., 2018). According to the Realistic Accuracy Model (Funder, 2012), indicators of cognitive ability must be available to and recognized by the judge to make an accurate judgment. Grades are provided to parents by teachers in reports or tests, and parents are usually required to sign reports or tests to ensure that they receive this information. Moreover, research on people's perceptions of intelligence shows that most lay people—including most parents—assume a positive relationship between cognitive ability and achievement (Niu, 2020). That is, for parents, school grades are a very salient indicator of their children's cognitive ability, and it is therefore possible that parents rely heavily on grades when judging children's cognitive ability (e.g., Fisicaro & Lance, 1990). Students in different grade levels received different kinds of school grades (see Method). We therefore conducted our analyses with the overall sample and by grade level. Furthermore, children's academic self‐concept influences how children respond to new challenges (Rutter, 1985), which can be observed by parents. In addition, children's academic self‐concept has been found to be strongly related to parents' judgments (Steinmayr et al., 2019). By including children's academic achievement and self‐concept, we controlled for their possible influence on parents' judgments of children's cognitive ability.

METHOD

Design and sample

The sample stems from the standardization of the THINK 1–4, an intelligence test for elementary school children (Baudson et al., 2016). The data were collected between September 2012 and February 2014. The standardization sample included 2850 students (15.8% of Grade 1, 19.7% of Grade 2, 25.8% of Grade 3, and 35.4% of Grade 4) from 209 classrooms in 70 elementary schools in Germany (1 to 28 students participated per class, M = 12.22, SD = 4.54). Females made up 48.5% of the sample and the average age was M = 8.93 years (SD = 1.20). The sample originates from six different federal states (out of a total of 16) from northern, southern, western, and eastern regions of Germany. Schools were contacted by letter or phone and selected so that different sizes and locations (rural or urban areas) were represented in the data (no random selection of schools). If there was a school known to us, it was always contacted to increase the likelihood of participation. In most cases, the entire school participated. Parental consent was obtained in advance and was a requirement for child participation. Participation was voluntary for students and their parents and could be discontinued at any time. The gender and rural/urban distribution of the sample is comparable to the national population of elementary school students in Germany. The proportion of elementary school children with a migration background (22.4%) was lower than in the general population (32%; Federal Statistical Office, 2012), whereas the proportion of children from families with lower school education was comparable between both groups (12.3% in the norm sample compared to 13.3% in the general population; Federal Statistical Office, 2013).

The parents of all students were invited to participate in the study. They were given a questionnaire and were free to choose which of them completed the questionnaire or whether they completed it together. Thus, there was one parent questionnaire for each child (either mother/father/both or other). The participation rate was 82.32% and parental cognitive ability judgments were available for 2346 of the students (48.3% female); this comprised the final analysis sample with 15.5% of children in Grade 1, 19.9% in Grade 2, 26.9% in Grade 3, and 37.7% in Grade 4. The average age of the students was M = 8.94 years (SD = 1.19) and 75.9% spoke only German as their native language. In total, 1283 (54.7%) judgments were made by mothers, 426 (18.2%) by fathers, and 637 (27.2%) by both parents together. This distribution of responses is comparable to other studies in which both parents or only one parent participated (Rothenbusch et al., 2018).

Measures

Cognitive ability

Children's general cognitive ability was assessed with the THINK 1–4 (Baudson et al., 2016). The test consists of 36 items covering figural, verbal, and numerical content. It is structured into eight subscales (2 from the verbal and 3 each from the figural and numerical content areas), seven of which measure logical and deductive reasoning, and one that measures vocabulary as an important predictor of school success. The THINK 1–4 has adequate validity and reliability (for detailed information see Baudson et al., 2016). It shows high correlations with other intelligence tests (e.g., Grundintelligenztest (CFT) tests, Kognitiver Fähigkeitstest (KFT) 4–12+, e.g., Heller & Perleth, 2000; Weiß & Osterland, 2013; r = .55–.88, p < .001) and with external judgments of cognitive ability by teachers (r = .52–.63, p < .001). Internal consistency ranges from α = .77 to .82, split‐half reliability from r _tt = .79 to .85, and test–retest reliability from r _tt = .71 to .77.

Parents' judgments of children's cognitive ability

Parents judged their children's cognitive ability on a scale with six items developed within the THINK project. It includes indicators of general cognitive ability (i.e., fluid intelligence and reasoning, short‐term memory, crystallized intelligence, and verbal ability). The items are translated from the original German wording: “understands new content very quickly,” “can remember most things the first time,” “recognizes connections very quickly,” “can express him‐/herself in a verbally differentiated way,” “generalizes newly acquired knowledge to other appropriate areas,” and “knows a lot.” Internal consistency for the rating scale is α = .89 (with part‐whole corrected item‐total correlations between .59 and .77). Ratings were made on a six‐point Likert scale (0 = does not apply at all to 5 = applies fully). The convergent validity of the scale is supported by correlations with teachers' ratings of students' cognitive ability using a teacher version of the scale (r = .54, p < .001, N = 1795).

Children's academic achievement

Students' academic achievement was measured by their average grades in mathematics and the German language, as reported by their parents. Students in our sample either received verbal grades (written descriptions of students' achievements without assigning a number; students in Grades 1 and 2) or numeric grades (with 1 being the best and 6 being the worst grade; students in Grades 3 and 4). For students in Grades 1 and 2, parents estimated students' numeric grades based on the last report card that described students' achievements. For students in Grades 3 and 4, parents reported teacher‐assigned numeric grades from the last report card. For analyses, numeric grades were inverted so that higher grades indicate better performance.

Children's academic self‐concept

Academic self‐concept was measured with three items from the FEESS‐K (Rauer & Schuck, 2003), a self‐report questionnaire for the assessment of emotional and social school experiences of elementary school children. Items were as follows: “I am good at school,” “I can learn quite well,” and “I do most things right at school.” Ratings were made on a three‐point Likert scale (0 = no, that is not quite true, 1 = sometimes this is true, sometimes not, 2 = yes, that is actually always true). The internal consistency is α = .72 (part‐whole corrected item‐total correlations between .52 and .59).

Demographic variables

Parents reported their children's and their own gender. To measure their socioeconomic background, parents reported their highest educational level (1 = no educational degree, 2 = degree from the lowest secondary level, 3 = degree from intermediate secondary level, 4 = degree from at least the highest secondary level) and approximately how many books they possess in their household (see also Avvisati, 2020). Parents further reported the number and age of siblings. To determine children's birth order, a new variable was created based on this information (0 = single child, 1 = first‐born, 2 = middle child, and 3 = last‐born). Note that the number of siblings and birth order are strongly interrelated (e.g., r = .87 between being a middle child and having three or more siblings compared to the references being a first‐born or single child). To avoid multicollinearity, only birth order was used as a moderator in subsequent analyses.

Statistical analyses

Data preparation and handling of missing data

We used SPSS Version 29 (IBM Corp, 2022) to prepare our data and compute descriptive statistics. No variable had more than 6.2% missing values except for possession of books (29.4% missing). Analyses were conducted with Mplus Version 8.3 (Muthén & Muthén, 1998–2019) using maximum likelihood estimation with robust standard errors. Missing data were handled using the full information maximum likelihood approach. We used confirmatory factor analysis (one‐factor models) to estimate latent variables for children's cognitive ability (3 indicators: verbal, numerical, and figural subtest scores), academic achievement (2 indicators: grade in math and German), academic self‐concept (3 indicators: 3 academic self‐concept items), and parents' judgment of children's cognitive ability (6 indicators: 6 items of the parent judgment scale).

Because of the nested data structure (e.g., 2346 students nested in 193 classrooms), we used the “type is complex” option to correct for biased standard error estimations. For this purpose, we used students' class membership as a cluster variable. The intra‐class correlation of parental judgments was .015, indicating that 1.5% of the variability in parental judgments could be attributed to between‐class differences.

Analytic procedure

Five latent regression models were specified with parental judgments as outcome. In Model 1, children's cognitive ability served as a (linear) predictor. To investigate if the relation between children's cognitive ability and parents' judgments was comparable over cognitive ability levels (i.e., linear relation) or not (i.e., quadratic relation), in Model 2, a quadratic term for children's cognitive ability was added as a predictor. In Model 3, children's academic achievement and self‐concept were added as control variables. In Model 4, the characteristics of the child (i.e., gender and birth order) and the parents (i.e., gender, educational level, and possession of books) were added as moderator variables. For this purpose, interaction terms between the child's cognitive ability and the moderator variable were included (e.g., CA × gender) in addition to including the variable as a predictor. Otherwise, the interaction term would not be interpretable as it confounds main effects and interaction effects. Children's birth order was dummy coded with first‐born serving as the reference category. Parents' educational level was dummy coded, with the highest secondary degree as reference category. In Model 5, both the control variables and the moderator variables were included. The analyses were run for the overall sample and for two subsamples (Grades 1 and 2; Grades 3 and 4) to account for differences in grade assignment (i.e., verbal grades vs. numeric grades). Results are reported with a focus on the overall group compared to the subsamples.

RESULTS

Data preparation and descriptive statistics

Confirmatory analyses of the four latent factors (children's cognitive ability, academic achievement, academic self‐concept, and parents' judgments) yielded a sufficient model fit (χ ² = 590.220, df = 71, p < .001; comparative fit index = .951, root mean square error of approximation = .056, 90% CI: .052, .060). All item loadings were significant with p < .001 and ranged between .57 and .83 (standardized values). McDonald's omega (ω) values indicated sufficient reliability with .89, .70, .79, and .72 for the four latent factors parents' judgments, children's cognitive ability, academic achievement, and academic self‐concept. Descriptive statistics are presented in Table 3. The overall sample was comparable to the norm sample of the THINK 1–4.

TABLE 3.

Descriptive statistics for the overall sample and the subsamples.

	Overall sample					Grades 1 and 2 samples					Grades 3 and 4 samples
	n	M (SD)	Range	Skew (SE)	Kurtosis (SE)	n	M (SD)	Range	Skew (SE)	Kurtosis (SE)	n	M (SD)	Range	Skew (SE)	Kurtosis (SE)
Children
CA	2346	102.11 (14.89)	70–145 a	−0.03 (.05)	−0.48 (.10)	831	102.04 (14.98)	70–145 a	0.00 (.09)	−0.50 (.17)	1515	102.15 (14.85)	70–145 a	−0.04 (.06)	−0.46 (.13)
Acad. achievement b	2200	4.86	1.5–6.0	−0.84 (.05)	0.68 (.10)	734	5.03 (0.65)	2–6	−1.12 (.09)	2.10 (.18)	1466	4.77 (0.74)	1.5–6	−0.72 (.06)	0.29 (.13)
Acad. self‐concept	1993	1.61 (0.43)	0–2	−0.85 (.06)	0.03 (.11)	688	1.71 (0.39)	0–2	−1.30 (.09)	1.19 (.19)	1305	1.56 (0.44)	0–2	−0.66 (.07)	−0.26 (.14)
Birth order c	n	%				n	%				n	%
Single child	306	13.0				107	13.4				199	13.7
First‐born	776	33.1				285	33.6				491	33.8
Middle child	295	12.6				100	12.5				195	13.4
Last‐born	877	37.4				308	38.5				569	39.1
Gender (female)	2346	48.3				831	47.1				1515	48.9
Parents
Judgments CA	2293	4.03 (0.68)	0.8–5.0	−0.92 (.05)	1.19 (.10)	813	4.10 (0.61)	1.67–5.0	−0.82 (.09)	0.83 (.17)	1480	3.99 (0.71)	.83–5.0	−0.91 (.06)	1.14 (.13)
Number of books	1656	326.18 (469.20)	0–7000	4.89 (.06)	41.369 (.12)	577	331.44 (462.15)	0–5000	4.20 (.10)	28.01 (.20)	1079	323.37 (473.12)	3–7000	5.24 (.07)	48.03 (.15)
Educat. level	n	%				n	%				n	%
No degree	20	0.9				10	1.3				10	0.7
Lowest degree	254	11.1				80	10.3				174	11.5
Intermediate	750	32.9				230	29.7				520	34.5
Highest degree	1259	55.1				454	58.7				805	53.3
Gender (female)	1709	75.1				609	73.3				1100	76.2

Abbreviation: CA, children's cognitive ability.

^a Values correspond to the minimal and maximal values achievable in the THINK 1–4.

^b Academic achievement: higher grades indicate better performance.

^c On average, children had M = 1.3 (SD = 0.94) siblings.

Latent correlations for the study variables in the overall sample are reported in Table 4 (the latent correlations for the subsamples are reported in Tables S1 and S2, and the manifest correlations for all samples are reported in Tables S3–S5). Significant correlations were found between parents' judgments and children's academic achievement, cognitive ability, academic self‐concept, and parental possession of books and educational level. The correlation with children's cognitive ability indicates a moderately high level of parental judgment accuracy (Cohen, 1988). Parents' judgments showed a higher relation with academic achievement than with cognitive ability. Academic achievement was more strongly related to parents' judgments than to cognitive ability.

TABLE 4.

Bivariate correlations of study variables in the overall sample (n = 2346).

Variable	1	2	3	4	5	6	7
1. Parental judgments of CA	–
2. CA	.46***	–
3. Academic achievement a	.74***	.65***	–
4. Academic self‐concept	.38***	.34***	.54***	–
5. Gender b (reference ‘female’)	−.02	.04	−.02	−.03	–
6. Parental gender b	.02	−.01	.01	.02	.01	–
7. Parental possession of books	.10***	.22***	.17***	.09***	.01	.00	–
Dichotomous dummy variables
6. Birth order (reference ‘first‐born’)
6a. Single child	−.02	−.05	−.09*	−.06	−.01	.04	−.06
6b. Middle child	−.05	.01	−.04	.01	.03	.04	.03
6c. Last‐born	−.04	−.05	.03	−.03	.03	−.09*	.04
8. Educational level (reference ‘highest secondary degree’)
8a. No secondary degree	−.08	−.13***	−.04	.02	−.05*	.02	−.04***
8b. Lowest secondary degree	−.13***	−.28***	−.33***	−.12**	.00	.02	−.16***
8c. Intermediate secondary degree	−.14***	−.17***	−.20***	−.07*	−.02	.01	−.23***

Note: Correlations were estimated based on latent factor scores of parental judgments of CA, CA, academic achievement, and academic self‐concept. Type is a complex option in Mplus that was applied to control for the nested data structure (i.e., students in classes). Correlations between dichotomous dummy variables were not estimated because of convergence issues.

Abbreviation: CA, children's cognitive ability.

^a Higher grades indicate better performance.

^b 0 = female, 1 = male.

^* p < .05;

^** p < .01;

^*** p < .001.

Main analyses

How accurate are parents' judgments of their children's cognitive ability?

The results for the overall sample are presented in Table 5. In Model 1, children's cognitive ability significantly predicted parents' judgments (β = .47, SE = .03, p < .001) and explained 22% of their variance (p < .001; 95% CI = .17, .27). In Model 2, the additional quadratic predictor was significant (β = −.18, SE = .03, p < .001) increasing the explained variance to 34% (p < .001; 95% CI = .24, .44). The negative quadratic prediction indicated that the relation between parents' judgments and children's cognitive ability was weaker for more intelligent children (see Figure 2).

TABLE 5.

Regression models with predictors of parents' judgments of children's cognitive ability (overall sample, n = 2346).

Parameter	Model 1		Model 2		Model 3		Model 4		Model 5
	β (SE)	p	β (SE)	p	β (SE)	p	β (SE)	p	β (SE)	p
Characteristics of the child
CA linear effect	.47 (.03)	<.001	.52 (.04)	<.001	.00 (.07)	.949	.70 (.09)	<.001	.15 (.20)	.147
CA quadratic effect			−.18 (.03)	<.001	−.06 (.04)	.142	−.24 (.04)	<.001	−.14 (.04)	<.001
Academic achievement a					.74 (.07)	<.001			.83 (.08)	<.001
Academic self‐concept					−.02 (.04)	.556			−.09 (.04)	.042
Gender b (reference ‘girls’)							−.04 (.03)	.140	−.01 (.03)	.832
Birth order (reference ‘first‐born’)
Single child							−.02 (.03)	.439	−.00 (.03)	.887
Middle child							−.05 (.03)	.138	−.03 (.03)	.268
Last‐born							−.04 (.03)	.302	−.05 (.03)	.118
Interactions
CA × gender b (reference ‘girls’)							.07 (.03)	.017	.07 (.03)	.006
CA × birth order (reference ‘first‐born’)
Single child							−.01 (.04)	.762	−.03 (.03)	.269
Middle child							−.02 (.03)	.626	−.02 (.02)	.447
Last‐born							−.09 (.04)	.017	−.07 (.03)	.034
Characteristics of the parents
Gender b (reference ‘mothers’)							−.05 (.03)	.140	−.01 (.02)	.834
Educational level (reference ‘highest secondary degree’)
No secondary degree							−.05 (.04)	.171	−.07 (.04)	.053
Lowest secondary degree							.00 (.04)	.937	.09 (.04)	.019
Intermediate secondary degree							−.02 (.04)	.591	.07 (.03)	.015
Possession of books							−.03 (.05)	.485	−.02 (.04)	.641
Interactions
CA × gender a (reference ‘mothers’)							−.05 (.04)	.257	−.05 (.03)	.106
CA × educational level (reference ‘highest secondary degree’)
No secondary degree							−.09 (.03)	.003	−.07 (.03)	.004
Lowest secondary degree							−.08 (.06)	.169	−.11 (.05)	.028
Intermediate secondary degree							−.08 (.05)	.080	−.06 (.04)	.117
CA × possession of books							.04 (.03)	.167	.03 (.03)	.464
Variance components
Residual variance	.78 (.03)	<.001	.67 (.05)	<.001	.45 (.03)	<.001	.56 (.07)	<.001	.34 (.04)	<.001
R 2 (explained variance)	.22 (.03)	<.001	.34 (.05)	<.001	.55 (.03)	<.001	.44 (.07)	<.001	.66 (.04)	<.001
Model fit
df	28		29		49		110		148
Loglikelihood	−25,188.031		−25,154.955		−37,796.018		−17,592.863		−24,972.520
Scaling factor	1.549		1.590		1.598		2.411		2.113
Akaike information criterion	50,432.061		50,367.910		75,690.035		35,405.727		50,241.040
BIC	50,593.354		50,534.963		75,972.298		35,971.785		51,002.646
Adjusted BIC	50,504.393		50,442.824		75,816.615		35,622.372		50,532.527

Note: Standardized regression coefficients with standard errors in parentheses. Bold values are significant with at least p < .05.

Abbreviations: BIC, Bayesian information criterion; CA, children's cognitive ability.

^a Higher grades indicate better performance.

^b 0 = female, 1 = male.

FIGURE 2.

Graphical depiction of the quadratic relation between children's cognitive ability level and parents' judgments.

Accuracy after controlling for academic achievement and self‐concept

After including children's academic achievement and self‐concept in Model 3, academic achievement was the only significant predictor of parental judgments (β = .74, SE = .07, p < .001). The variables in Model 3 explained 55% of the variance in parental judgments (p < .001; 95% CI = .49, .60).

Do characteristics of children and parents moderate judgment accuracy?

In Model 4, including all moderator variables (interaction terms), last‐born children were judged less accurately than first‐born children (β = −.09, SE = .04, p = .017) and parents with no secondary degree showed lower judgment accuracy than parents with the highest secondary degree (β = −.09, SE = .03, p = .003). Children's cognitive ability significantly predicted parents' judgments (linear term: β = .70, SE = .09, p < .001; quadratic term; β = −.24, SE = .04, p < .001). The explained variance was 44% (p < .001; 95% CI = .30, .58). In Model 5, including both the moderator variables and the control variables, children's cognitive ability (only quadratic term; β = −.14, SE = .04, p < .001), academic achievement (β = .83, SE = .08, p < .001), and academic self‐concept (β = −.09, SE = .04, p = .042) were significantly associated with parents' judgments. Boys were judged more accurately than girls (β = .07, SE = .03, p = .006). Last‐born children were judged less accurately than first‐born children (β = −.07, SE = .03, p = .034) and parents with no or an intermediate secondary degree showed lower judgment accuracy than parents with the highest secondary degree (no degree: β = −.07, SE = .03, p = .004; intermediate: β = −.11, SE = .05, p = .028). The explained variance was 66% (p < .001; 95% CI = .58, .73).

Subsamples

Findings of the regression analyses for the subsamples are reported in Tables S6 and S7. In Grades 3 and 4, more variability in parents' judgments could be explained by children's cognitive ability and academic achievement than in Grades 1 and 2 or the overall sample (Model 1: 26% vs. 16% vs. 22%; Model 2: 37% vs. 25% vs. 34%; Model 3: 58% vs. 49% vs. 55%). Of note, in Grades 1 and 2, parents estimated numerical grades from written report cards while in Grades 3 and 4, they reported the numerical grades assigned by teachers. In Model 4, including all moderator variables (interaction terms), other than in the overall sample, birth order did not significantly moderate parents' judgment accuracy in both subsamples. The explained variance was 43% (Grades 1 and 2) and 46% (Grades 3 and 4). In Model 5, including all control and moderator variables, there were some differences in findings for both subsamples. The quadratic term of children's cognitive ability was not a significant predictor in Grades 1 and 2 and academic self‐concept was not a significant predictor in Grades 3 and 4. Other than in the overall sample, there was no significant difference in judgment accuracy between last‐born and first‐born children in both subsamples. Number of books at home significantly moderated parents' judgment accuracy in both subsamples but in different directions. In Grades 1 and 2, a higher number of books was related to less accurate judgments (β = −.13, SE = .03, p < .001) while in Grades 3 and 4 a higher number of books was related to more accurate judgments (β = .07, SE = .03, p = .029). The explained variance was 69% (Grades 1 and 2) and 67% (Grades 3 and 4).

DISCUSSION

We investigated the accuracy of parents' judgments of their children's cognitive ability in a large sample of elementary school children and their parents using regression analyses with latent variables. Based on previous findings, we expected parents' judgment accuracy to be moderately high. We further examined the moderating role of different characteristics of the children and parents and controlled for children's academic achievement and self‐concept.

Parents' judgment accuracy for children's cognitive ability

In line with our hypothesis, we found a moderate accuracy of parents' judgments of their children's cognitive ability. This finding is well aligned with other studies using correlation or regression analyses (e.g., Furnham & Valgeirsson, 2007; Rothenbusch et al., 2018). The relation between parents' judgments and children's cognitive ability was weaker for more intelligent children indicating less accurate parents' judgments for these children.

Cognitive ability is not directly observable, and according to the Realistic Accuracy Model (Funder, 2012), parents must infer information about their children's cognitive ability from their children's behavior and other sources of information. Stimuli that are available, recognized, and interpreted by parents as indicative of cognitive ability are more likely to influence their judgments than stimuli that are unavailable, difficult to recognize, or interpreted as irrelevant. Academic achievement is highly available and easy to recognize because parents receive feedback through their children's grades and teachers (Fisicaro & Lance, 1990). In addition, most people assume a positive relationship between cognitive ability and achievement (Niu, 2020). Accordingly, school grades are very salient for parents when judging their children's cognitive ability. In fact, parents' judgments of children's cognitive ability were more strongly related to school grades than to children's cognitive ability. In their meta‐analysis of the accuracy of teachers' judgments of students' cognitive ability, Machts et al. (2016) reported a similar finding (teachers' judgments of students' intelligence correlated with students' intelligence by r = .43 and with students' academic achievement by r = .61), which the authors termed “academic achievement bias.” Even when teachers were instructed to distinguish between academic achievement and cognitive ability in their judgments, their judgments of students' cognitive ability depended more on everyday academic performance than on cognitive ability per se (Lavrijsen & Verschueren, 2020). Our findings suggest a similar “academic achievement bias” among parents. When we controlled for students' school grades, we found no significant relationship between parents' judgments and children's cognitive ability. Parents may assume that academic achievement is more indicative of children's cognitive ability than it is. Or they may have difficulty recognizing other behaviors that indicate their children's cognitive ability, such as how quickly they process information and how easily they learn new material or solve problems. This is problematic because parents are likely to misperceive children whose academic performance does not match their cognitive abilities. While a slight overestimation of children's cognitive abilities can be beneficial for their development, underestimation can lead to a loss of confidence, motivation, and cognitive ability in children (Helmke et al., 2004; Niklas & Schneider, 2017). Notably, the relationship between parents' ratings and children's cognitive ability was weaker for more intelligent children. This finding may be explained by a ceiling effect in the parent rating scale, which makes it difficult to distinguish between above‐average and high ability levels. The ceiling effect, which is indicated by a negative skewness value of the parent rating scale in our data (Skew = −.92, SE = .05), could be enhanced by the fact that parents tend to overestimate their child, which is not possible for highly intelligent children due to the upper limit of the parent rating scale, thus suppressing the strength of the correlation. The weaker relationship between parents' judgments and children's cognitive ability for more intelligent children could also be explained by a ceiling effect in school grades, which is indicated by a negative skewness value in our data (Skew = −.84, SE = .05). For example, ceiling effects in school grades prevent highly intelligent children, who are also likely to perform better academically, from receiving better grades than children with above‐average ability. These relatively poorer school grades, in turn, could lead to an underestimation of highly intelligent children by their parents.

Possible moderators of parent's judgment accuracy

Parents' judgment accuracy was significantly lower for girls compared to boys, for last‐born children compared to first‐born children, and for parents with no or the lowest secondary degree compared to parents with the highest secondary degree. Our finding that parents are more successful in assessing their sons' cognitive ability could be due to a tendency for parents to attribute boys' achievement to their cognitive ability rather than to motivation or effort, as is the case with girls (Tiedemann, 2000). Within the realistic accuracy model, this would indicate that parents primarily regard achievement as a valid indicator of cognitive ability for boys, but less so for girls. Since achievement and cognitive ability are positively correlated and parents rely mainly on achievement in their judgments, this could increase judgment accuracy for boys. However, we conducted an exploratory analysis to compare the latent correlations between parental judgments of cognitive ability and school grades across gender and this analysis revealed comparable correlations for girls and boys (r _girls = .75, r _boys = .72). Another explanation would be that parents pay more attention to their son's cognitive abilities than to their daughter's, which may lead to more observations and information searches and thus to more accurate judgments. However, this assumption is rather speculative and requires further testing.

Parents also had higher accuracy in judging first‐born children compared to last‐born children. Parents have known their first‐born child longer than their last‐born child, giving them more time to form a more accurate picture of their first‐born child. Alternatively, one could speculate that as the number of children increases, parents have less time to focus on individual children and observe their abilities, which would lead to less accurate judgments for later‐born children. Since in most studies, only one child is judged by their parents, there is still a lack of reliable evidence on how accurately siblings or only children are judged in comparison.

In line with previous research (Hunt & Paraskevopoulos, 1980) we found that higher educated parents were better at judging their children's cognitive ability than lower‐educated parents. In relation to the realistic accuracy model, they may recognize indicators of cognitive ability better or be more likely to use the information correctly to arrive at an accurate judgment. Further, parents with a higher level of education have more resources to offer their children a stimulating learning environment which increases the development of potential in their children. This also gives them more opportunities to show their potential and increase their visibility and thereby might support the recognition of potential. Children of less educated parents, on the other hand, are judged less accurately by their parents. This might hinder their further cognitive development if parents over‐ or underchallenge their children. Therefore, it would be important to investigate the causes behind this relation, such as parents' knowledge about cognitive indicators, the actual time spent with their children, the involvement in their children's education, or the frequency of their exchange with teachers. As another indicator of socioeconomic background, parents' possession of books was investigated and proved to be a negative moderator of judgment accuracy in Grades 1 and 2 and a positive moderator in Grades 3 and 4. Since the number of books in Grades 1 and 2 correlates only with cognitive ability but not with parental judgments, this could represent a suppression of the effect. At the same time, there were many missing values for this variable making the findings less reliable.

Interesting additional findings not included in our research questions showed that judgment accuracy was higher for Grades 3 and 4 than for Grades 1 and 2. Students in Grades 3 and 4 were given numerical grades, while students in Grades 1 and 2 were given verbal grades that parents had to translate into numerical grades. Therefore, the grade information was more uncertain for students in Grades 1 and 2, which may explain the higher accuracy in Grades 3 and 4. In addition, over time, parents may get to know their children better and become more adept at assessing their potential. In Grades 1 and 2, academic self‐concept was negatively related to parental judgments possibly because children's self‐perceptions of their academic ability might not be as accurate as those of older children. However, the effect was only found in Grades 1 and 2 and was relatively small. Further, fathers judged children's cognitive ability lower than mothers did, but judgment accuracy did not differ between fathers and mothers. Of note, the number of fathers in the Grades 1 and 2 subsample was rather small and findings need to be interpreted with caution. Another side finding was that, compared to parents with the highest secondary degree, those with no secondary degree tended to judge their children's cognitive ability lower, and those with the lowest and intermediate degree tended to judge them higher. However, the samples of some subgroups (e.g., no secondary degree and fathers) were comparatively small, resulting in reduced statistical power. Therefore, findings must be interpreted with caution and subsequent studies should examine moderators with similarly sized groups.

Practical implications

The scientific literature has increased our knowledge of teachers' judgment accuracy considerably in recent years (e.g., Urhahne & Wijnia, 2021). In comparison, findings for parents' judgment accuracy are scarce. Our results show that there is room for improvement in parents' judgment accuracy. Compared to parents, teachers have more sources of comparison than parents do and access to formal comparison data. Lack of comparison information or objective criteria can make it difficult for parents to improve their own diagnostic skills (Wahl et al., 2005). But especially in elementary school, accurately judging children's academic potential (i.e., cognitive ability) is important, as elementary school students have had comparatively little opportunity to acquire knowledge and skills. Therefore, parents should be made aware of possible biases in judging their children's potential, such as relying on academic achievement or on gender role stereotyped perceptions of their children's competencies. Particular attention needs to be paid to children with lower‐educated parents. Diagnostic competencies of parents could be included in parenting training. Teachers could be trained to talk with parents about their judgments of their children's cognitive ability and exchange their perceptions. To compensate for any undetected support needs, teachers and parents should cooperate in providing support and offer adequate learning opportunities (Tabeling et al., 2022).

Limitations

Our study has a cross‐sectional design; therefore, no causal statements can be made. Longitudinal studies are needed to investigate possible reciprocal effects between parents' judgment accuracy and students' development. Moreover, study participation was voluntary. This could have led to a selected sample of parents with higher self‐concepts of their diagnostic abilities or higher educational levels. However, the educational level of parents was comparable to that of the norm sample. Another limitation is that we used grades reported by the parents. In German elementary school, first and second graders do not receive numerical grades, but a written summary of their progress and observations during the first school year. In this case, parents translated the written feedback into grades. It is unclear how well the parents succeeded in translating the feedback into grades. Further, in our study, we used different scales to measure parents' judgments and children's cognitive abilities. Therefore, we could not compare the two measures in terms of over‐ or underestimation of children by their parents. In addition, we only controlled for nesting of data with respect to classrooms, but not with respect to families (e.g., birth order effects within families) because we did not have the data to account for. Relatedly, we were not able to compare the judgment accuracy of mothers and fathers of the same child. Furthermore, in the case of joint answers from both parents, it cannot be concluded how they decided on an answer. Finally, while we were only able to examine two‐way interactions between the linear cognitive ability effect and the moderators, the nonlinear relationship between cognitive ability and parent judgments may indicate three‐way interactions between the quadratic cognitive ability effect and the moderators. However, it was not possible to implement this within our latent modeling approach in Mplus.

Future research directions

Our comprehensive review and study raise many questions for future research. These relate to the assessment, description, explanation, consequences, and improvement of parents' diagnostic competence in judging their children's cognitive abilities.

Regarding assessment, measures without ceiling effects are needed that allow for a more nuanced assessment of parents' judgments of children's cognitive abilities (e.g., in relation to different cognitive abilities). Assessments should take into account parents' prior knowledge, what parents base their judgments on, and what indicators they actually use to make judgments. Furthermore, individual accuracies should be investigated. Future studies could use standardized residuals or measure parents' judgments for different test items. However, tests of cognitive ability often include tasks that children do not encounter in their everyday lives and that parents cannot observe. This could lead to a misrepresentation of the accuracy of parents' judgments. Furthermore, a research design that combines differently generated information (e.g., test scores and parental judgments) is consistent with common practice in the counseling field (Frischknecht et al., 2014). Using different operationalizations of accuracy could help to improve comparability across studies and shed light on different aspects of accuracy (e.g., over‐ vs. underestimation or relative vs. absolute accuracy; Urhahne & Wijnia, 2021).

In terms of description and consequences, we need longitudinal studies that show how parents' judgments and diagnostic competencies develop across conditions and over time (e.g., how they are influenced by the amount of time parents spend with their children or the development of children's cognitive abilities) along with their children's development. Including teachers' diagnostic competencies in such a longitudinal study would be challenging, but necessary to understand the complex interplay of the co‐development of others' judgments and children's abilities, competencies, or self‐perceptions. This already tackles the point of explanation. A considerable amount of variance in judgment accuracy remained unexplained in our study and most of the studies in our review. Future studies should examine other moderators, such as parents' gender with sufficiently large samples of comparable size, parents' knowledge of cognitive indicators, their theories about the stability of competence (Pomerantz & Dong, 2006), their own cognitive ability (Kirkcaldy et al., 2007), or their diagnostic self‐concept, to further explore the variance in judgment accuracy and better understand the deductive process of parents' judgment formation. Another variable that should be examined in this context is parents' educational aspirations as they are positively related to children's cognitive ability (e.g., Murayama et al., 2016), which in turn, is positively related to parents' judgments of children's cognitive ability (e.g., Rothenbusch et al., 2018). Models such as the Realistic Accuracy Model (Funder, 2012) could serve as a framework to integrate findings from different studies. Last but not least, the question of the trainability of parents' judgment accuracy and intervention effects on children's development needs more attention. We hope that our findings will stimulate further research in this direction.

CONFLICT OF INTEREST STATEMENT

The authors have no competing financial interests or conflicts of interest to disclose.

Supporting information

Appendix S1.

Mack, E. , Scherrer, V. , & Preckel, F. (2025). How smart is my child? The judgment accuracy of parents regarding their children's cognitive ability. Child Development, 96, 122–140. 10.1111/cdev.14156

DATA AVAILABILITY STATEMENT

The data, analytic code, and materials necessary to reproduce the analyses presented here are not publicly accessible. The analyses presented here were not preregistered.