Glimpsing the Iceberg: Parent-Child Physical Aggression and Abuse

Abstract

Despite evidence that parents’ physical aggression abuse has long-lasting negative consequences, information about the true population prevalence of aggression and physical abuse is limited. We have even less information about how parental aggression and abuse vary by child age, parent gender, and how that aggression and abuse might be clustered within families. To address these gaps, an anonymous, computer-based assessment was administered to nearly 40,000 parents of more than 60,000 children in the United States Air Force, which included a detailed assessment on up to four minor children of aggression and its impact. The survey was the largest of its type ever conducted in the United States, allowing for stable, crossvalidated estimation of rates of both corporal punishment and physical abuse. Approximately 39% of children experienced corporal punishment, peaking at three years of age, and 7% experienced physical abuse, peaking at age six. About 45% of parents reported perpetrating corporal punishment and 8% abuse; these rates were higher in multi-child families and most often involved more than one child. Parent gender was not associated with physical aggression or abuse.

Keywords

parent-child aggression child abuse physical abuse prevalence

Glimpsing the Iceberg: Parent-Child Physical Aggression and Abuse

Physical child abuse (i.e., physical aggression with measurable, or an inherently high probability of, harm to the child) and physical discipline that is less likely to cause physical harm (e.g., corporal punishment) (Slep et al., 2013) are widespread and pressing public health issues in the United States. There is consensus regarding detrimental effects of coporal punishment on children’s health and development (Gershoff; 2010) and acute and lifelong effects of child physical abuse including elevated rates of medical problems, cognitive and socioemotional deficits, and behavioral problems (Carr et al., 2020). There are over 70,000 substantiated cases of child physical abuse in the U.S. annually (U.S. Department of Health & Human Services, 2019). Yet, substantiated cases tremendously underrepresent the true number of affected children. National surveys suggest that approximately 5% of children in the United States are physically abused annually (Finkelhor et al., 2015), with lifetime prevalence for 14-to-17-year-olds estimated at 18.1%. Rates of corporal punishment are much higher: 49% in the past year for children ages 0–9; and 23% for children ages 10–17 (Finkelhor et al., 2019; parent report for children ages 0–9 years and youth report for children ages 10–17 years). These annual rates of self-reported child physical abuse are approximately 40 times higher than those in official substantiated estimates (i.e., the National Child Abuse and Neglect Data System [NCANDS]). A series of meta-analyses of research using official informants (i.e., social services or community sentinels) indicates global rates of physical abuse of 0.3%, whereas self-report data reveals a much higher lifetime rate of 22.6% (Stoltenborgh et al., 2011). Thus, official rates of child maltreatment are likely vast underestimates of the actual prevalence.

Like other public health concerns, there is recognition of the importance of the problem despite our continued lack of information about its true scope. On the one hand, the need to reduce physical abuse rates is widely accepted. On the other hand, fundamental issues hamper our progress toward this goal and contribute to a disconnect between the high rates of abuse and the scope of prevention efforts. Most critically, despite several important efforts to move toward a definitional consensus regarding when parents’ aggression toward their children constitutes abuse (e.g., CDC definitions), gaps and variability remain between abusive acts that would be substantiated if referred to child welfare and those that are identified by researchers’ attempts to understand the scope of undetected child physical abuse. Many child protective service agencies substantiate child physical abuse only if there is a visible injury or a high risk of injury. In contrast, the National Survey of Children’s Exposure to Violence (Finkelhor et al., 2015), asks parents, “Not including spanking on your bottom, at any time in your child’s life, did a grown-up in your child’s life hit, beat, kick, or physically hurt your child in any way?” (Hamby et al., 2011). Thus, the operationalizations differ in their explicit consideration of the impact of the abusive act. In addition, multiple-item scales are psychometrically superior to single-item ones in terms of both reliability and validity (Diamantopoulos et al., 2012). No matter how well-constructed an item is, the inherent limitations of a single item provide cover by which child abuse policymakers can create distance from the population-estimate findings and instead focus on “caught cases” as the sole instances of “real abuse.” Establishing population rates based on anonymous reports using the same definition of child physical abuse used by child protection systems is the best way to understand the true size of the iceberg.

Additionally, because most child physical abuse goes unreported (Sedlak et al., 2010), we are reliant on population surveys for information about epidemiology, including rates of child physical abuse and non-abusive aggression by child age, and the extent to which abuse and aggression cluster for children in the same family. However, sample sizes in population surveys are necessarily limited, and, as the sample is subdivided into smaller bands, the precision with which meaningful differences can be detected is reduced. Keeping these limitations in mind, population surveys indicate that younger children are significantly less likely to experience physical abuse than older children (Finkelhor et al., 2015, 2019) or suggest no significant age differences (Theodore et al., 2005). Populations surveys using mothers’ reports have found the highest rates of corporal punishment for children aged 5–8 years (Theodore et al., 2005). Such surveys have not found significant child gender differences in rates of child physical abuse (Finkelhor et al., 2015; Theodore et al., 2005). Mothers report that they engage in more physically abusive acts than their partners (Theodore et al., 2005). Unfortunately, it is difficult to compare these differences in age and gender distributions to those seen in substantiated cases due to published reports’ aggregating across all maltreatment types (U.S. Department of Health and Human Services, 2019). Other studies make determining rates of child physical aggression and abuse difficult due to methodological decisions. For instance, the Fragile Families and Child Wellbeing Study (FFCWS) did not administer a full corporal punishment measure to parents of children under three; rates for children over three may be attenuated due to lack of anonymity, not allowing participants to justify for their reported socially undesirable behaviors, coverage of different forms of corporal punishment, and a short reporting window (e.g., past month).

Furthermore, because standard methods sample one child within a household, we have no population-level information regarding how corporal punishment and physical abuse might cluster in families. Population surveys demonstrate that rates of corporal punishment increase as family size increases, with rates for younger children of 43% in single-child homes and 56% in homes with four or more children; rates for older children show a similar pattern with rates of 17% in single-child homes and 37% in homes with four or more children (Finkelhor et al., 2019). Population surveys of child physical abuse have not examined rates as a function of family size (e.g., Finkelhor et al., 2015). Although the corporal punishment findings above indicate that risk increases as family size increases, we are left without information about whether all children within those families are at greater risk or if risk is centered around a single child.

To address these gaps, we have analyzed data from the U.S. Air Force’s (USAF) Community Assessment (CA), which included a detailed assessment of parents’ aggression toward up to four minor children and the impact of that aggression in a sample of approximately 40,000 active duty and civilian parents. This sample size of parents is 10 times larger than the most comprehensive population data on child abuse and non-abusive parental aggression toward children (Finkelhor et al., 2015; 2019) and allows for the examination of clustering of abuse and aggression within families and subgroup analyses by age and gender. In addition, the abuse measure was designed to map precisely onto the USAF’s substantiation criteria (Heyman et al., 2020), thus reducing concerns stemming from single-item assessments of physical abuse and lack of correspondence between survey- and agency-criteria for considering a child as abused.

There are several reasons why it is reasonable to assume that rates of child physical abuse and non-abusive aggression would be similar across USAF service member/civilian spouse and U.S. population samples. First, the USAF comprises volunteers from all 57 states/territories and members born in 207 countries. There are some differences demographically between the USAF and the U.S. population. The USAF is more heavily male than the U.S. population (US [adults 18–59 years of age] vs. USAF — men: 49.9% vs. 80%, women: 51.1% vs. 20%); however, because this survey is administered to spouses as well, the gender distribution is less of an issue. Educationally, the USAF is close to the US population, except that volunteer requirements exclude those with less than a high school (H.S.) education (US [adults 18–59 years of age, weighted to USAF gender distribution] vs. USAF — No H.S. diploma: 14.5% vs. 0.04%, H.S. graduate [or GED; includes AA and/or some college]: 60.1% vs. 62.7%; BA/BS: 17.9% vs. 14.4%; MA/MS: 5.9% vs. 8.6%; professional degree (e.g., PhD, JD, MD): 1.6% versus 1.9%. The USAF is younger than the general population, but this may be advantageous as it provides a natural oversample of the age groups at highest risk for family maltreatment (US [adults 18–59 years of age, weighted to USAF gender distribution] vs. USAF — 18–24: 17% vs. 33%; 25–34: 25% vs. 38%; 35–44: 28% vs. 24%; 45–59 31% vs. 4%). Finally, the USAF slightly overrepresents Whites and Blacks and underrepresents Hispanics (US [18–44 years old] vs. USAF —White 68.4% vs. 74.5%; Black: 12.6% vs. 16.2%; Hispanic 13.9% vs. 5.5%; other: 5.1% vs. 3.9%). Most service members report joining the USAF for prosaic reasons such as educational and travel opportunities (Defense Manpower Data Center, 2000). Notably, USAF volunteers and their families deviate from the general population in being lower on various problems. Volunteers are initially screened for substance abuse, criminal history, and mental and physical health problems. Legal and personality problems can lead to expulsion from the subpopulation. At least one family member is full-time employed (by the service), and all are provided with housing and health care. Given these differences, all data were weighted before analyses to make the sample as comparable to the relevant U.S. population as possible. Note that the alternative (weighting the active duty members to the USAF) would require us to omit all civilian spouse data, which seemed more problematic.

This study aimed to determine the prevalence of substantiatable child physical abuse in a large sample and (a) test the relations of child physical abuse and corporal punishment with child age, number of children in the home, and parent gender, and (b) determine whether these relations differed for corporal punishment and child physical abuse. We hypothesized that child age would be curvilinearly linked with both parental aggression forms but that corporal punishment’s peak age would be younger than that of physical abuse. We hypothesized that both forms would cluster within families. Finally, we did not have directional hypotheses about parent gender but conducted those analyses in an exploratory manner.

Method

Participants

A random sample of USAF active duty (AD) members (N = 118,393) and the population of spouses (N = 145,836) were invited to complete the 2006 CA, a biennial, anonymous survey conducted at 82 USAF bases worldwide. AD member sampling occurred via stratification procedures, with technical details of the sample selection process available from the RAND Corporation (Bigelow, 2007). The response rate was 45.7% (n = 54,543) among AD members and 13.5% among spouses (n = 19,722). The methods and instruments described here were approved by both a university and a military institutional review board. Participants were presented with a consent document that they clicked to indicate consent.

The sample comprised 39,629 parents (n = 27,021 AD members and n = 12,608 spouses) of at least one minor (≤17 years old) child (n = 74,982), who reported that at least 80% of their answers on the survey were accurate (n = 414 removed), and who did not exhibit evidence of malingering (n = 46 removed for endorsing every possible act of family maltreatment). We used several variables (gender, length of marriage, number and ages of children in the home) to match cases in which both members of a given couple participated (n = 1597 couples). To avoid problems of nonindependence, one member of each matched couple (n = 833 active duty members, n = 764 spouses) was then randomly selected and removed from the dataset. Unweighted sample demographic information is presented in Table 1.

Table 1.

Unweighted Sample Demographics.

Variable	Assessed in the Whole Sample	Assessed in Active Duty Members Only, %
Male parent	57.4%
Number of minor children
1	37.0%
2	41.7%
3	15.8%
4 or more	5.5%
Currently deployed (either parent)		4.5%
Paygrade
E1 - E4		9.9%
E5 - E6		46.4%
E7 - E9		20.6%
O1 - O3		9.5%
O4 or higher		13.6%
Marital status
Married to active duty military member		12.9%
Married to reserve military member		1.5%
Married to civilian		76.4%
Single, never married, and not living with significant other		1.6%
Single and living with significant other		1.1%
Legally separated or filed for divorce		1.3%
Divorced or widowed		5.2%
Race/ethnicity
Black or African American		14.6%
Hispanic or Latino		7.2%
Other		2.9%
Unknown		2.1%
White		73.2%
Mean (SD) child age in years	8.4141 (4.96)

Procedure

The CA was administered online by Caliber Associates for an 8-week window in 2006. AD members were e-mailed an invitation containing the Web link to the survey; civilian spouses were sent postcard invitations in the mail. Weekly e-mails were sent reminding the selected AD members to participate; civilian spouses received two reminder postcards (at two and 4 weeks post-launch). Each base also conducted its own community-wide campaign encouraging participation from anyone who had been invited to do so. The survey took approximately 45–60 min to complete.

Measures

The CA assessed individual, family, organizational, and community functioning, as well as demographics, response accuracy, and parent-child aggression, which are of focus herein.

Parent-child aggression

Participants who were parents of minor children completed the Family Maltreatment (FM) measure, which assesses the presence of clinically significant and subclinical forms of emotional and physical aggression in the family (Heyman et al., 2020). Parents completed the FM separately for each child, up to four minor children. Parents of more than four minor children completed the FM for their youngest four children. We focus on the parent-child physical aggression module here given the scope of the present paper. Using diagnostic criteria from the Diagnostic and Statistical Manual of Mental Disorders-Fifth Edition (DSM-5; American Psychiatric Association, 2013) and International Classification of Diseases-11th Edition (ICD-11; World Health Organization, 2022) criteria, the FM distinguishes physically abusive from subthreshold forms of physical parent-child aggression and exhibits content and response process validity, as well as convergent validity with the Parent-Child Conflict Tactics Scale (Straus et al., 1998) per Heyman et al. (2020).

Parents were first asked to indicate their 12-month use of 18 different acts of physical aggression on a child-by-child basis. The first seven acts were lower intensity: (1) shook child, (2) spanked child on the bottom with a bare hand, (3) slapped child’s hand, (4) pushed or shoved child, (5) slapped child’s arm, leg, or torso, (6) grabbed child, and (7) hit or spanked child using a belt, electrical cord, switch, or some similar object. Parents who endorsed having (a) shaken a 2-year-old (or younger) child or (b) engaged in any of other acts with any of their children were further asked about 11 higher intensity acts: (1) pinched child, (2) hit or spanked child using a stick, hairbrush, or some other hard object, (3) slapped child on the face, head, or ears, (4) kicked child hard, (5) hit child with a fist, (6) threw or knocked child down, (7) grabbed child around the neck and choked child, (8) slammed child against a wall, fence, furniture, car, etc., (9) twisted child’s arm or leg, (10) burned or scalded child on purpose, and (11) beat up child—that is, hit child over and over as hard as [the parent] could.

To discourage underreporting due to social undesirability, parents were not asked to report the frequencies of acts. Instead, they indicated the reason(s) for using each of the 18 behaviors: (a) “I did this to teach,” (b) “I did this to punish,” (c) “I did this because I was frustrated/lost my cool,” and (d) “I never did this.” Each behavior was scored as present (responses 1, 2, or 3 are endorsed) versus absent (response 4 is endorsed).

Participants were then presented with a list of all acts they endorsed, if any, and asked about the presence/absence of eight associated injuries to the child: pain at least 4 hours later, bruise, welt, cut that required stitches, sprain, unconsciousness, broken bone, and/or loosened or chipped tooth.

Scores for analysis

Physical abuse per DSM–5/ICD-11 criteria was scored as present if the parent reported (a) any physical act in combination with any injury to that child or (b) any physical act with a high potential for injury (i.e., burned or scalded child, beat up child, choked child around the neck, struck child with an object, hit child with a fist, kicked child hard, shook a 2-year-old or younger child). Corporal punishment was scored as present if any physical act was endorsed (excluding those with high injury potential) and the parent reported an absence of all injuries. Aggression was scored as undetermined if a parent endorsed any physical act but failed to complete the injury items.

Two versions of these scores were created. The first version was calculated for each child. The second version, used for parent-level analyses, was scored at the level of the parent and indicates the most severe form reported across all children. For example, if a parent reported physical abuse against one child and corporal punishment against another child, the parent was scored as reporting physical abuse.

Demographic variables

Parent-level predictors included gender (coded 1 = female, 2 = male) and number of minor children in the household (1–4 [or more]). The sole child-level predictor was age, measured in years (1–19), except for the youngest two age categories (<6 months [coded as .25 years] and 6–11 months [coded as .75 years]). Additional demographic variables were assessed for descriptive purposes in the AD subsample: current deployment status of either partner, paygrade, marital status, and race/ethnicity.

Response accuracy

Participants were asked the following question: “For what percentage of questions were your answers accurate?” There were 11 response options, ranging from 0% to 100%, in 10% increments.

Analytic Strategy

Overview

Analyses were conducted with Mplus version 8 software (Muthén & Muthén, 1998–2017), using full information maximum likelihood (FIML) estimation of all available data. Analyses at the parent level used the robust maximum likelihood estimator. Because children were nested within families, analyses at the child level used the robust pseudo maximum likelihood estimation method (type = complex in the Mplus analysis specifications); this method uses a sandwich estimator to adjust parameters’ standard errors for the non-independence of clustered observations (Asparouhov & Muthén, 2005).

To allow for cross-validation (i.e., the reproduction of study results), parents were randomly assigned at a ∼1:1 ratio into two subsamples, ns = 19,815 (Development) 19,814 (Replication). Child ns by subsample were ns = 37,532 (Development) and 37,450 (Replication). The samples did not significantly differ on demographic characteristics (Table 2). Using multigroup analysis, each model was estimated twice, with regression parameters (intercepts [i.e., categorical “means”] in prevalence models; regression weights [i.e., predictor-aggression associations] in prediction models) freely estimated versus equated in the Development versus Replication samples. Comparative model fit was compared by computing the −2*LL difference, adjusted for the MLR scaling factor. All comparative fit models were significant (i.e., had different results by subsample) (Table 3). Thus, we report prevalences and regression parameters separately by subsample in Tables 4 –6. Online Figure 1 plots were based on a parallel set of analyses combining the Development and Replication samples.

Table 2.

Demographic Comparisons for Development versus Replication Samples.

	Subsample
Variable	Development	Replication	p
Male parent	46.2%	45.8%	.421
Number of minor children			.177
1	39.8%	39.7%
2	39.4%	40.1%
3	15.4%	14.7%
4 or more	5.4%	5.4%
Currently deployed (either parent)	4.1%	4.6%	.060
Paygrade			.578
E1 - E4	7.0%	6.6%
E5 - E6	39.8%	39.7%
E7 - E9	27.4%	27.7%
O1 - O3	7.5%	7.9%
O4 or higher	18.2%	18.0%
Marital status			.967
Married to active duty military member	13.2%	13.3%
Married to reserve military member	1.5%	1.4%
Married to civilian	75.1%	74.8%
Single, never married, and not living with significant other	1.6%	1.7%
Single and living with significant other	0.9%	0.9%
Legally separated or filed for divorce	1.2%	1.4%
Divorced or widowed	6.5%	6.6%
Race/ethnicity
Black or African American	10.4%	10.8%	.087
Hispanic or Latino	16.0%	16.2%
Other	6.6%	6.1%
Unknown	2.0%	2.4%
White	64.9%	64.5%
Mean (SD) child age in years	8.40 (4.99)	8.42 (4.94)	.698

Note. p-values correspond to Pearson χ² tests of independence for all variables except child age, for which they correspond to independent samples t-tests.

Table 3.

Model Fit Comparisons for the Development.

Criterion Variable/Model	# Free Parameters	MLR LL	Scaling	Adjusted LL	Adjusted-2*LL Difference	df-2*LL Difference
Prevalences of parent perpetration
Free	7	−54,231.43	1.53	−83,212.71
Constrained	4	−54,232.44	1.54	−83,463.72	502.01	3
Prevalences of child victimization
Free	7	−101,385.89	2.49	−252,805.71
Constrained	4	−101,389.77	2.63	−267,141.78	28,672.12	3
Prevalences of aggression by parent in multi-child families
Physical abuse
Free	5	−22,899.76	1.43	−32,641.31
Constrained	3	−22,899.87	1.45	−33,097.19	911.75	2
Corporal punishment
Free	5	−35,750.53	1.51	−53,994.03
Constrained	3	−35,752.85	1.52	−54,197.75	407.43	2
Undetermined
Free	5	−15,493.00	1.51	−23,337.11
Constrained	3	−15,495.64	1.52	−23,609.16	544.11	2
Child victimization by age
Free	19	−53,243.96	1.49^a	−79,272.27
Constrained	13	−53,262.44	1.49^a	−79,299.79	55.03	6
Parent perpetration in relation to parent gender
Free	13	−54,224.33	1.52	−82,502.32
Constrained	10	−54,226.07	1.53	−82,738.13	471.63	3

Note. All p-values < .001; MLR = robust maximum likelihood; LL = loglikelihood; Free = regression parameters allowed to differ for Development and Replication samples; Constrained = regression parameters equated for Development and Replication samples; ^a The mean scaling factor for the two models was used in place of the original scaling factors for the Free (1.50) and Constrained (1.48) models, because the original adjusted −2*LL difference (−2682.18) was negative, thus its p-value undefined; judged by the original adjusted −2*LL difference, model fit actually improved when adding constraints.

Table 4.

Prevalences of Parent Perpetration and Child Victimization.

	Development Sample			Replication Sample
		95% CI			95% CI
	Prevalence (%)	Low	High	Prevalence (%)	Low	High
All families
Aggression (parent)
None	46.00	45.02	46.96	46.73	45.77	47.70
Corporal punishment	45.39	44.46	46.33	44.80	43.87	45.74
Physical abuse	8.02	7.54	8.52	7.85	7.37	8.32
Undetermined	0.61	0.45	0.76	0.62	0.46	0.78
Victimization (by child)
None	53.69	52.82	54.56	54.62	53.75	55.49
Corporal punishment	39.13	38.30	39.97	38.19	37.37	39.02
Physical abuse	6.72	6.29	7.16	6.65	6.23	7.08
Undetermined	0.47	0.37	0.58	0.54	0.42	0.66
Aggression by parent in multi-child families
Physical abuse
0 children abused	89.60	88.91	90.29	89.50	88.81	90.20
1 child abused	4.37	3.91	4.84	4.50	4.02	4.98
>1 child abused	6.04	5.50	6.5858	5.99	5.47	6.52
Corporal punishment
0 children punished	47.87	46.67	49.06	48.58	47.39	49.78
1 child punished	17.08	16.19	17.98	17.73	16.83	18.63
>1 child punished	35.06	33.96	36.17	33.69	32.60	34.78
Undetermined
0 children victimized	99.14	98.93	99.37	99.29	99.08	99.50
1 child victimized	0.65	0.44	0.86	0.43	0.26	0.60
>1 child victimized	0.21	0.13	0.30	0.28	0.16	0.40

Table 5.

Parent Perpetration in Relation to Number of Children and Parent Gender.

				95% CI
Sample/Criterion^a/Predictor	OR	SE	p	Low	High
Development sample
Corporal punishment
Number of children	2.71	0.30	<.001	2.16	3.37
Number of children²	0.90	0.02	<.001	0.86	0.95
Physical abuse
Number of children	3.73	0.73	<.001	2.54	5.44
Number of children²	0.90	0.04	<.001	0.83	0.97
Undetermined aggression
Number of children	30.35	24.01	.206	6.44	143.10
Number of children²	0.58	0.09	<.001	0.43	0.78
Replication sample
Corporal punishment
Number of children	2.78	0.32	<.001	2.23	3.47
Number of children²	0.88	0.02	<.001	0.84	0.93
Physical abuse
Number of children	5.54	1.10	<.001	3.76	8.17
Number of children²	0.83	0.03	<.001	0.76	0.89
Undetermined aggression
Number of children	2.74	1.80	.128	0.76	9.90
Number of children²	0.90	0.12	<.001	0.70	1.16
Development sample
Corporal punishment
Parent gender^b	1.08	0.04	.070	1.00	1.17
Physical abuse
Parent gender^b	0.97	0.07	.543	0.85	1.10
Undetermined aggression
Parent gender^b	1.08	0.27	.774	0.67	1.77
Replication sample
Corporal punishment
Parent gender^b	1.03	0.04	.430	0.95	1.12
Physical abuse
Parent gender^b	0.95	0.07	.406	0.82	1.08
Undetermined aggression
Parent gender^b	0.67	0.18	.068	0.39	1.14

Note. ^a Reference category is no aggression; ^b parent gender coded 1=female, 2=male; number of children variable is z-scored.

Table 6.

Child Victimization by Age.

				95% CI
Sample/Criterion^a/Predictor	OR	SE	p	Low	High
Development sample
Corporal punishment	1.02	0.01	.298	0.99	1.04
Child age
Physical abuse	0.99	0.00	<.001	0.99	0.99
Child age
Child age²
Undetermined aggression	1.02	0.01	.298	0.99	1.04
Child age	0.9999	0.0000	<.001	0.9999	1.0000
Child age²
Replication sample
Corporal punishment	1.03	0.01	.021	1.01	1.06
Child age	0.99	0.00	<.001	0.99	1.00
Child age²
Physical abuse
Child age	1.12	0.03	<.001	1.06	1.18
Child age²	0.99	0.00	<.001	0.99	0.99
Undetermined aggression
Child age
Child age²	1.03	0.09	.758	0.86	1.23

Note. ^a Reference category is no aggression; ^b child age variables are z-scored.

Figure 1.

The associations of parent perpetration with the number of household children in the full sample (top panel), and of child victimization with child age (bottom panel). Note. Estimates are based on models combining the Development and Replication subsamples.

Missing data handling

FIML drops cases with missing data on categorical outcomes but not predictors. Since statistical models for prevalences did not include predictors, parents who did not provide aggression data were dropped from the estimation models. However, in the association models, cases with missing aggression were included if they had data on predictors.

Prevalence models

To obtain prevalence estimates and 95% CIs, intercept-only models were specified, with parent-child aggression treated as a parent-level nominal variable with four categories (no aggression, corporal punishment, physical abuse, and undetermined aggression).

All available data were included in each model. All parent perpetration estimates for the full sample of parents are based on n = 33,052 because n = 6577 did not provide aggression data. For multi-child family prevalence models, n = 20,832 for parent-level analyses; we excluded n =14,673 parents with only one child and n = 4124 of the remaining parents of more than one child who had missing perpetration data. The child victimization prevalence models treated parent-child aggression as a child-level variable and were based on n = 62,642 children (i.e., excluding n = 12,496 children missing victimization data).

Parents who did (n = 33,052) versus did not (n = 6577) provide aggression data were compared on the eight demographic variables listed in Table 1 via χ² tests for independence (categorical variables) or independent samples t-tests (continuous variables). Small, but significant, differences were obtained in five comparisons. Compared with parents who did not provide aggression data, those that did were disproportionately female (p < .001); more likely to have two, compared with more or fewer, children (p = .019); at higher enlisted or officer paygrades (p < .001); more likely to be a married AD member compared with other marital statuses (p < .001); were identified in records as white or of unknown race (p < .001); and have children of younger mean ages (p < .001). These differences can potentially affect the prevalences we report.

Association models

To test the association of parent-child aggression with the number of children living in the household (n = 39,629), multinomial regression models were estimated at the parent level in which the nominal parent-child aggression variable was first regressed on the number of children. To investigate curvilinearity in this association, models were also estimated by adding terms for the squared and cubed number of children. Given the absence of a significant cubed number of children effects, the final model included only the number of children and the number of children squared; each predictor was z-scored. The reference category of parent-child aggression was the absence of aggression. For ease of interpretation, predicted probabilities based on this model were plotted by number of children. The associations of parent-child aggression with parent gender (coded 1 = female, 2 = male; n = 39,629) and child age (z-scored; n = 74,982) were evaluated in a parallel manner.

Data weighting

To make the sample more representative of the relevant U.S. population, we obtained the 2005 American Community Survey Public Use Microdata Sample (PUMS) dataset (U.S. Census Bureau, 2006), retaining households with (a) at least one minor child and (b) at least one adult employed full-time between 17 and 50 years of age. Using weighted marginals obtained from the PUMS data, gender-specific CA sample weights were then created and raked, using WesVar Version 4.2 (WestatWesVar 4.0, 2000), on ethnicity (Black, non-Hispanic White, Hispanic/Latinx, or other), age (assessed in spouses; estimated by rank in AD members), ages and number of children in the home, and household dual-versus single-income status. Raking uses iterative proportional fitting to match marginal distributions of a sample to known population distributions. Extreme weights (four times greater than or less than the mean weight) were trimmed so that extreme weights did not overly influence results (Potter, 1988). Weights were applied in all analyses, other than the sample demographics presented in Table 1.

Results

Prevalence of Parent Perpetration and Child Victimization

The prevalences of parent perpetration and child victimization among all parents, as well as of parent perpetration of single versus multiple children in multi-child families, are reported in Table 4, separately by subsample. Across the samples, mean prevalences of parent perpetration were 45.1% for corporal punishment, 7.9% for physical abuse, and 0.6% for undetermined aggression. Mean prevalences of child victimization were 38.7% for corporal punishment, 6.7% for physical abuse, and 0.5% for undetermined aggression.

In multi-child families, across samples, the mean rate of corporal punishment was 2.0 times as high against multiple (34.4%) versus single (17.4%) children. The mean rate of physical abuse was 1.4 times as high against multiple (6.0%) versus single (4.4%) children.

Parent Perpetration in Relation to Number of Children and Parent Gender

The number of children in the household exhibited significant associations with physical abuse, corporal punishment, and undetermined parent-child aggression (Table 5; Online Figure 1, top panel). Although principally linear, the quadratic coefficients were also significant, indicating some curvilinearity of these associations. To illustrate, the rate of physical abuse was 4.2 times as great among parents with four or more children (17.5%) versus one child (4.2%). For corporal punishment, the ratio was 1.5 (55.5% vs. 36.3%, respectively). Parent gender was not significantly associated with parent-child aggression.

Child Victimization in Relation to Child Age

Child age exhibited curvilinear associations with physical abuse, corporal punishment, and undetermined parent-child aggression (Table 6; Online Figure 1, bottom panel). The curvilinear pattern was most pronounced for corporal punishment, which was experienced by 41.9% of children under 6 months, rising to 54.2% at 3 years, then dropping to 20.4% at age 17. Physical abuse followed a similar pattern but peaked somewhat later; its rate was 6.0% at <6 months, 8.7% at 6 years, and 2.8% at 17 years.

Discussion

This study is the first to use a validated measure of parent-reported, child-directed aggression that allows for the distinction of physical abuse from corporal punishment in a sufficiently large sample to reliably estimate their relations with parent sex, child age, and number of children. Physical abuse was reported by 8% of parents, affecting nearly 7% of children. This suggests that less granular ways of measuring physical abuse in the population underestimate the prevalence of child physical abuse, both in scope and in severity, given that our best anonymously self-reported national estimates were approximately 3.4%, 4.4%, and 5% in surveys conducted in 2003, 2008, and 2013 respectively (Finkelhor et al., 2015).

Findings regarding clustering in families confirm the importance of parent-level (compared with child-level) risk for maltreatment and expands its empirical base. In multi-child families, parents who engaged in corporal punishment were twice as likely to aggress against multiple children (66.4%) versus one child (33.6%). The same pattern held for physical abuse, but the difference was less pronounced (57.6% multiple children vs. 42% one child). These findings suggest that risk for corporal punishment and physical abuse is somewhat clustered in families. Although parent-level and family-level risk factors have consistently been seen as superseding child risk factors in the literature (e.g., Stith et al., 2009), we believe these results are the first to indicate degree of clustered risk within families and indicate that if one child in the family comes to the attention of formal systems for possible child physical abuse, the risk to all children in the family should be assessed.

We found family size to be linked with parental aggression, especially physical abuse. Approximately 4% of parents with one child reported physical abuse in the past year; over four times that many (17.5%) parents with four or more children did. A similar but less pronounced pattern was apparent for corporal punishment. Parents with four or more children were 1.5 times as likely to report corporal punishment as parents with one child. Factors such as household chaos (Coldwell et al., 2006) and parenting stress (Wilson et al., 2018) may be implicated; furthermore, this finding may also suggest that parenting does not always improve from mere experience. Although the literature on family size and child maltreatment clearly establishes multiple children as a risk factor for neglect (e.g., Mulder et al., 2018), results regarding physical abuse are more mixed. Initial survey findings suggested a positive relationship (e.g., Connelly & Straus, 1992), the second National Incidence Study found that singletons were at highest risk for physical abuse (Sedlak, 1997), whereas the fourth National Incidence Study again found the highest risk among the largest families (Sedlak et al., 2010). These results highlight the importance of considering the number of children being parented when working clinically with at-risk families. It is likely that larger families operate near or at parents’ capacities a high proportion of the time and may benefit more from supports that lessen competing demands.

Alarmingly, parents reported that over 40% of infants under 6 months of age were victims of corporal punishment, and approximately 6% were victims of physical abuse. This is especially concerning because young infants are highly vulnerable and more likely than older children to experience severe injury and death when abused (Davies et al., 2015). These rates are considerably higher than even those from at-risk samples, which is likely due to methodological differences. For example, the Fragile Families and Child Wellbeing Study (FFCWS) did not administer a full corporal punishment measure to parents of children under 3 years of age. Instead, an assessment included a telephone interview with a single item reflecting spanking in the past month, with MacKenzie and colleagues (2011) finding that approximately 15% of 1-year-olds are spanked. There are at least four potential prevalence-attenuating factors in the FFCWS’s methods compared with the CA’s. First, the FFCWS’s telephone interview was not anonymous, which may attenuate reporting due to social desirability bias. Second, the FFCWS measure did not allow parents to give justifications for these socially undesirable behaviors, which focus groups preceding the 2006 CA indicated may promote reporting acts. Third, FFCWS’s construct coverage of corporal punishment was poor, notably excluding the second most common act of corporal punishment (slapping the hand, arm, or leg; (Lorber & Slep, 2018) and others (e.g., slapping the face). Fourth, FFCWS parents were asked only about spanking in the last month.

In contrast, parents in this study completed truly anonymous online surveys, were able to justify their behaviors, reported on 18 physically aggressive acts (6 of which are typically classified as corporal punishment), and reported on behavior over the preceding 12 months. Each of these design choices likely resulted in a more accurate estimate of yearly prevalence. Furthermore, for infants, the striking contrast in previously published rates and those obtained here suggest that prevention and response systems are inadequately sensitized to their risk of victimization. Clearly, widespread education efforts to prevent shaken-baby syndrome (e.g., Morrill et al., 2015) are critical, but they do not address the scope of parental aggression and abuse to infants reported by parents in this sample. The more widespread abuse of infants often goes undetected by any formal systems. The USAF, where these data were collected, has (a) universal child maltreatment risk screening of all pregnant women receiving healthcare through military-provided obstetrical care via the Family Needs Screener and (b) a nurse home-visitation program to reduce risk for child abuse (Travis et al., 2015). That these rates were obtained despite that screening and support, and in a population with at least one employed parent, should provide a clarion call for improved responses in both military and civilian populations.

We found that rates of corporal punishment peaked when children were 3 years old; physical abuse peaked when children were 6 years old. Our peak age for child physical abuse is strikingly lower than that found in the National Incidence Surveys (NIS; see Sedlak et al., 2010; Zolotor & Shanahan; 2010), where the peak risk for child physical abuse occurs among 12–14-year-olds. This likely is due to the NIS using sentinels and mandated reporters and our study using parental self-reports. Given parents’ admissions, stakeholders need to heighten detection of abuse among younger children, who may be less likely to disclose the abuse. In contrast, consistent with the NIS, adolescents were at lower risk for both physical child aggression and abuse. Twenty percent of parents of 17-year-olds reported using physical aggression; 3% reported committing physical abuse. These rates differ, however, from those found in national surveys of youth, wherein 14–17-year-olds report the highest rates of physical abuse victimization (Finkelhor et al., 2015). This is possibly a function of our study holding reporters constant regardless of the age of the child, whereas national surveys often rely on (a) sentinels for information regarding younger children and (b) adolescents themselves.

It is noteworthy that mothers and fathers report similar rates of physical aggression or abuse in this large sample. This is consistent with findings, including a review by Nobes and Smith (2000), that mothers and fathers engage in similar rates of corporal punishment and physical abuse when assessed with comparable methods (Ferrari, 2002; Mahoney et al., 2000; Nobes et al., 1999). Most published studies have found similar corporal punishment prevalence for mothers compared to fathers; some studies report higher corporal punishment frequency for mothers (Maxwell, 1993; Strassberg et al., 1994). Although some published studies report higher rates for mothers’ versus fathers’ corporal punishment and physical abuse (e.g., Creighton & Noyes, 1989; Stattin et al., 1995), most such studies rely on a) substantiated cases that suffer from reporting biases; b) studies that do not account for father absence, which artificially inflate mother versus father perpetration; and c) studies of self- and partner-reported perpetration which typically include more mother than father participants and suffer from reporting bias wherein parents tend to underestimate their partners’ use of physical punishment (Nobes & Smith, 2000). In contrast, studies tend to report higher rates of severe physical punishment and physical abuse for fathers compared to mothers when retrospective victim reports are used, when official reports account for father absence, or when only severe acts of physical abuse are assessed (e.g., Andrews, 1994; Malkin & Lamb, 1994; Sariola & Utela, 1992). Such methods are also problematic; they may suffer from recall biases or rely on official reports of physical abuse.

There are several implications of these findings. First, from a public health perspective, child physical abuse, especially among infants, is vastly underdetected by community stakeholders. Of note, observed rates of child physical abuse in the USAF for the year in which these data were collected was 0.14% (personal communication from USAF Family Advocacy Headquarters). Comparing this rate to our parent-reported prevalence rate of 8% for parent perpetration and 7% for child victimization, it is clear that a significant proportion of physical abuse goes unreported and is unknown to sentinels. Parental reports provide the best picture of what’s going on in the privacy of homes but are, no doubt, lower than the true prevalence of abuse. Given the sequelae of abuse, even this truncated prevalence estimate is sobering. Relatedly, our findings imply that given anonymity and the opportunity to contextualize the motives behind their actions, parents will report perpetrating child physical abuse. Second, because our sample was from the U.S. Air Force and the data are several years old, replicating these results using similar methods in a large, nationally representative population sample is imperative. Third, using a policy lens, screening for risk for child physical abuse should be considered more important; perhaps tools such as the USAF’s Family Needs Screener (McCarthy et al., 2020) could be applied in a wider range of settings, helping identify at-risk parents and provide preventative services. Finally, our findings regarding family clustering of physical abuse suggest that (a) comprehensive assessment of all children is needed if any child comes to the community’s attention for possible maltreatment, and (b) parenting interventions should focus on parenting overall, not solely on parenting the child who was an identified victim.

No study is without limitations. First, this study employed parental reports of their own perpetration in a study sponsored by their employer, likely tempering reports. There were no independent sentinels to offer contrasting data if parents denied impacts. Second, the computer-based assessment employed sensible, empirically derived skip patterns to minimize response burden, but this may have also resulted in missing some parental aggression and abuse. Second, this sample does not include families with several known risk factors (i.e., no employed parent, parental substance or significant mental health problems), which could lead to higher rates in the general population. Third, this sample comprised parents who were active duty military members or spouses. We weighted the sample to civilian demographics, which seemed preferable to omitting all the civilian spouse data, but weighting is unlikely to make the sample fully comparable with civilians of the same age range who are employed or married to someone employed. Additionally, this sample, even when weighted, cannot represent those living in poverty and families with no employed parent. Missing aggression reports may have also influenced our findings; the predictorless prevalence models drop all cases with missing data. Fourth, the proportion of spouses who participated is lower than the proportion of Air Force members. It is possible that participating spouses differ from those who did not participate in ways that we cannot account for through weighting. Finally, this is a secondary analysis of archival data collected in 2006. Studies of child maltreatment have shown declining rates of physical abuse since the early 1990s (Child Trends; 2015; Finkelhor et al., 2015), with most of the decline occurring in the 1990s (Runyan et al., 2018); U.S. surveys since 2000 suggest that the prevalence of child physical abuse may be continuing to decline slightly, or may be stabilizing (Finkelhor et al., 2010, 2015, 2019). Thus, this study’s prevalences could be higher than if the data were collected today. The possibility of slight attenuations in prevalence estimates do not negate our findings that child physical abuse, operationalized using clinical-significance criteria adopted by DSM-5/ICD-11, is more pervasive than typically believed.

Despite these limitations, the thorough measurement of physical aggression and abuse for multiple children in families within this large sample has allowed us to answer important and previously unaddressed research questions. The rates of physical abuse found are concerningly high, especially for infants. Families with infants — especially those with multiple children — may require more support than current systems provide. Education about shaken baby syndrome should be expanded to include the dangers of any physical discipline with infants. It can be argued that more support is available to military families (e.g., accessible, affordable, high-quality childcare; home visitation programs; parenting classes) than to civilian families. Even in these circumstances, rates of aggression and abuse are concerningly high. Given the clear importance of early childhood trauma, we must become sensitive to the true prevalence of child physical abuse and improve surveillance and intervention for families in need.

Footnotes

Acknowledgments

We would like the thank the personnel at the local Air Force sites who were responsible for promoting the survey, to Caliber Associates (especially Dr Chris Spera) for administering the web survey, and to the active-duty members who took time to complete it. Correspondence concerning this article should be addressed to Amy M. Smith Slep, Family Translational Research Group, New York University, 137 E. 25^th St, New York, NY, 10010; Amy.slep@nyu.edu.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by U.S. Department of Defense grant W81XWH0710328 and U.S. Centers for Disease Control grant 5R49CE00091902. The opinions expressed in this article are solely those of the authors and do not necessarily represent the official views of the U.S. Government, the Department of Defense, the Department of the Air Force, or the Centers for Disease Control.

ORCID iDs

Amy M. Smith Slep

Kimberly A. Rhoades

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