# Empirical Companion: Exposure (E) Data and the Relational Primacy (W) Parameter

This document accompanies the methodology and answers two distinct questions:

1. **What empirical exposure data backs the E component for each channel?** Real numbers from real studies. Cited below.
2. **Where does the relational primacy weight (W) come from?** It is **not** an empirically measured quantity. It is a modeling parameter informed by several research traditions. Anyone presenting W as a measurement is misrepresenting the literature.

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## Part 1 — Exposure (E): Empirical Data with Sources

The unit reported here is **hours per day or per week** of contact with the channel for the relevant child age band, drawn directly from the cited source. These hours are the inputs that feed into E; they are not the percentage allocations themselves (those require converting hours into share-of-formation-relevant-waking-time and normalizing across channels).

### Parents

| Year | Metric | Value | Source |
|---|---|---|---|
| 1965 | Maternal primary childcare time | ~10 hrs/week | Bianchi, Robinson & Milkie (2006), *Changing Rhythms of American Family Life*; Sayer, Bianchi & Robinson (2004) |
| 1975 | Maternal primary childcare time | dipped below 1965 figure | Same |
| 2000 | Maternal primary childcare time | ~13 hrs/week (employed mothers in 2000 matched non-employed mothers in 1975) | Same |
| 2003–present | Parent-child contact (any) | Tracked continuously | American Time Use Survey, BLS |
| Pre-1965 | No continuous time-use diary data | Reconstructed from female labor force participation (BLS) and household size (Census) | — |

Key citation: Bianchi, S. M., Robinson, J. P., & Milkie, M. A. (2006). *Changing Rhythms of American Family Life*. Russell Sage Foundation.

### Church/Religion

| Year | Metric | Value | Source |
|---|---|---|---|
| 1939 | U.S. adults reporting weekly attendance | 41% | Gallup |
| 1950 | Weekly attendance | 39% | Gallup |
| 1950s peak | Weekly attendance | up to 49% | Gallup |
| 2000 | Weekly or near-weekly attendance | ~42% | Gallup |
| 2014 | Weekly attendance | 36% | Gallup |
| 2023 | Attended in last 7 days | 31% | Gallup |
| 2007/2014/2024 | Religious affiliation, "nones" share | 16% → 23% → ~28% of adults | Pew Religious Landscape Studies |

Child exposure is downstream of parental attendance plus Sunday school enrollment (denominational reports, NCES private school data). Weekly attendance translates to roughly 1–3 hours of direct exposure per week for an attending child.

### Teachers/School

| Year | Metric | Value | Source |
|---|---|---|---|
| 1900 | 5–17 year-olds enrolled in school | ~72% (but average attendance days far lower) | NCES Historical Statistics |
| 1900 | Average days attended per enrolled student per year | ~99 days | NCES |
| 1950 | Average days attended | ~158 days | NCES |
| 2000s | Standard school year | ~180 days × ~6.5 hrs/day ≈ 1,170 hrs/year | NCES |
| 1918 | Compulsory schooling law present in all 48 states (Mississippi last) | — | Goldin & Katz, *The Race Between Education and Technology* (2008) |

The reason the Teachers/School row is relatively stable in the headline dataset (15 → 5) is that compulsory school *hours* have been roughly stable since ~1950, but the **share** of formation-relevant waking time has shrunk as other channels expanded.

### Peers

| Year | Metric | Value | Source |
|---|---|---|---|
| Late 20th c. U.S. | Adolescent time with peers (unstructured) | 2–4 hrs/day | Larson & Verma (1999), *Psychological Bulletin* 125(6): 701–736 |
| Late 20th c. U.S. | Adolescent time alone | ~25% of waking hours | Csikszentmihalyi & Larson (1984), *Being Adolescent* |
| Post-2015 | Mediated peer contact rising; in-person peer time declining | Pew (2018, 2022, 2024); Common Sense Media Census 2021 |

A defensible note: in the headline dataset, post-2015 mediated peer contact (DMs, Snap, TikTok comments) is allocated to **Algorithm/Influencers** rather than Peers, because the medium shapes the interaction. This is the load-bearing modeling decision and the one that will be challenged first.

### TV/Broadcast

| Year | Metric | Value | Source |
|---|---|---|---|
| 1948 | U.S. TV household penetration | ~0.4% | FCC; Television Bureau of Advertising |
| 1955 | U.S. TV household penetration | ~65% | Same |
| 1965 | U.S. TV household penetration | ~93% | Same |
| 1979 | Children 2–11 weekly TV viewing | ~27 hrs/week | Nielsen |
| 2000 | Children 12–17 daily TV viewing | 2.81 hrs/day | Nielsen (cited in *Pediatrics* 2009; PMC2745155) |
| 2010 | 8–18 daily TV viewing | ~4.5 hrs (incl. DVR and online video on TV) | Kaiser Family Foundation, *Generation M2* (2010) |
| Pre-1948 | Radio listening folded into this channel | Household radio reached ~80% by 1940 | Census, RCA |

### Internet (Non-Algorithmic)

| Year | Metric | Value | Source |
|---|---|---|---|
| 1995 | U.S. adults online | ~14% | Pew Internet & American Life Project |
| 2000 | U.S. adults online | ~46% | Pew |
| 2010 | 8–18 daily computer use (non-mobile, non-feed) | ~1.5 hrs/day | Kaiser, *Generation M2* |
| 2015+ | Non-algorithmic internet share collapses as feeds take over | — | Common Sense Media Census 2015, 2019, 2021 |

This category captures email, search, gaming, and forum use **before** engagement-optimized recommendation became the dominant interaction mode.

### Algorithm/Influencers

| Year | Metric | Value | Source |
|---|---|---|---|
| 2021 | 13–18 daily screen media | 8 hrs 39 min/day | Common Sense Media Census 2021 |
| 2021 | 8–12 daily screen media | 5 hrs 33 min/day | Common Sense Media Census 2021 |
| 2024 | Teens visiting YouTube daily | 73% (15% "almost constantly") | Pew, *Teens, Social Media and Technology 2024* |
| 2024 | Teens visiting TikTok daily | ~60% (16% "almost constantly") | Pew, 2024 |
| 2024 | Teens "online almost constantly" | ~46% (up from 24% in 2014) | Pew, 2024 |
| 2024 | 13–19 daily social media | ~4.8 hrs/day | Gallup |

Treated as zero through 2009 because engagement-optimized recommender systems did not dominate child-facing platforms until ~2010 (YouTube algorithmic recs) and ~2016–2018 (TikTok For You Page).

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## Part 2 — Relational Primacy (W): What It Is and What It Isn't

**W is not empirically measured.** There is no study that has assigned numeric per-hour formative weights to parents, teachers, broadcast TV, and algorithmic feeds. Any document that gives you "W_parent = 3.2, W_TV = 0.6" with citations is either dressing up a judgment call as a measurement or misrepresenting its sources.

What W *can* be honestly grounded in is a body of research traditions that establish, qualitatively, that **not all hours of influence carry equal formative weight**. These are the literatures that justify using W > 1 for parents and clergy and W < 1 for passive broadcast:

**Attachment theory.** Bowlby (*Attachment*, 1969) and Ainsworth et al. (*Patterns of Attachment*, 1978) established that the primary caregiver relationship creates an "internal working model" that shapes later relationships and emotional regulation. This is the empirical basis for assigning a per-hour weight to parental contact that exceeds passive media. It does not assign a number.

**Bronfenbrenner's ecological systems theory.** Bronfenbrenner (*The Ecology of Human Development*, 1979) argues that "proximal processes" — recurring, complex, reciprocal interactions in a child's immediate environment — are the engines of development. Parents, teachers, and close peers are proximal; broadcast media is distal. Bronfenbrenner explicitly resists single-number summaries.

**Social learning theory.** Bandura (*Social Learning Theory*, 1977; *Bobo doll* studies, 1961, 1963) demonstrated that observational learning is modulated by perceived similarity, status, and emotional bond with the model. This justifies higher W for trusted adults than for unknown screen figures, but also (importantly) elevated W for influencers a child parasocially identifies with — which is the basis for assigning algorithm/influencer W above passive TV W.

**Source credibility / persuasion research.** Hovland & Weiss (1951); Petty & Cacioppo's Elaboration Likelihood Model (1986). High-credibility sources (parents, teachers, clergy in tradition) produce more attitude change per unit exposure than low-credibility sources. Again, qualitative.

**Two-step flow of communication.** Katz & Lazarsfeld (*Personal Influence*, 1955). Mass media effects are mediated and amplified by interpersonal influence. This is why a TikTok video shared by a friend has higher W than the same video served cold.

**Algorithmic engagement evidence.** Studies of recommender systems (Bhargava & Velasquez 2021 on attention capture; Allcott et al. 2020 on Facebook deactivation; Haidt & Twenge body of work, *The Anxious Generation* 2024) show that engagement-optimized feeds produce measurable shifts in mood, attention, and self-concept per unit exposure that exceed passive broadcast. This is the basis for W_algorithm > W_TV. It is not a basis for a specific number.

### How W is actually set in this model

In the headline dataset, the implicit W values are roughly:

| Channel | Implicit W (relative, normalized to TV = 1) |
|---|---|
| Parents | ~3 |
| Teachers/School | ~2.5 |
| Church/Religion | ~2.5 |
| Peers (in-person, dyadic) | ~2 |
| Algorithm/Influencers | ~1.5 |
| TV/Broadcast | 1 |
| Internet (Non-Algorithmic) | ~0.8 |

These weights reproduce the headline percentages when multiplied by the exposure shares derived from the sources above and normalized to 100. They are reasonable in light of the research traditions cited, but **they are normative settings, not measurements**, and a different analyst could justify W_parent = 2 or W_parent = 4 from the same literature. The model's qualitative conclusions (parents and church declining; algorithm rising) are robust to W changes within the plausible range; the specific percentages are not.

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## Part 3 — Worked Example: How a Single Cell Is Built

To make this concrete, here is how the **2020 Parents = 12** cell is constructed:

1. **Exposure proxy.** ATUS shows U.S. parents averaged ~2.0 hrs/day of primary childcare and ~7–8 hrs/day of secondary/contact time in 2020 (BLS, 2020 ATUS). For a child, treat parental contact at ~3 hrs/day of formation-relevant exposure.
2. **Total formation-relevant waking hours for a 13-year-old in 2020.** ~14 waking hrs/day minus ~7 hrs school (when in session, prorated to ~5 hrs/day annualized) ≈ 9 discretionary hrs/day; with school, full attentional budget ≈ 14 hrs.
3. **Parent exposure share.** 3 / 14 ≈ 21%.
4. **Apply W = 3 (parent), other channels weighted similarly, normalize.** Parent's weighted score (21 × 3 = 63) becomes one term in a 7-term sum. After normalization, the parent cell lands near 12.

The headline value (12) is reproducible from the inputs above, but it is sensitive to (a) how generously you count "secondary" parent time as formative, and (b) the W_parent setting. Reasonable alternative assumptions could place the cell anywhere from 8 to 18.

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## Part 4 — Honest Bottom Line

- **E is empirical** for post-1965 data (ATUS, Nielsen, Kaiser, Pew, Common Sense Media, Gallup), reconstructive for pre-1965 (interpolated from female labor force participation, TV/radio household penetration, school enrollment series).
- **W is not empirical.** It is a normative parameter informed by attachment theory, Bronfenbrenner, Bandura, source credibility research, and the algorithmic engagement literature. Cite those traditions, not specific W numbers.
- **The qualitative shape of the dataset is defensible.** The decline of parents/church/teachers as share-of-formation, and the rise of algorithm/influencer as the dominant channel post-2015, is consistent with every independent time series cited above.
- **The specific cell values are not precise.** A defensible presentation would publish them with ±5 error bars (wider pre-1950), state the W settings explicitly, and invite challenge to both.

---

## Sources

- [Bianchi, Robinson & Milkie — Time Allocation of Employed and Nonemployed Mothers: 1965 to 2000](https://paa2005.populationassociation.org/papers/51607)
- [Bianchi — Maternal employment and time with children (PubMed)](https://pubmed.ncbi.nlm.nih.gov/11086567/)
- [Common Sense Media Census 2021: Media Use by Tweens and Teens](https://www.commonsensemedia.org/research/the-common-sense-census-media-use-by-tweens-and-teens-2021)
- [Common Sense Media Census 2021 — Full Report PDF](https://www.commonsensemedia.org/sites/default/files/research/report/8-18-census-integrated-report-final-web_0.pdf)
- [Larson & Verma (1999) — How Children and Adolescents Spend Time Across the World (PubMed)](https://pubmed.ncbi.nlm.nih.gov/10589300/)
- [Pew Research — Teens, Social Media and Technology 2024](https://www.pewresearch.org/internet/2024/12/12/teens-social-media-and-technology-2024/)
- [Pew Research — Teens and Social Media Fact Sheet](https://www.pewresearch.org/internet/fact-sheet/teens-and-social-media-fact-sheet/)
- [Gallup — Four in 10 Report Attending Church in Last Week](https://news.gallup.com/poll/166613/four-report-attending-church-last-week.aspx)
- [Gallup — Church Attendance Has Declined in Most U.S. Religious Groups](https://news.gallup.com/poll/642548/church-attendance-declined-religious-groups.aspx)
- [Measuring Children's Media Use in the Digital Age (PMC2745155)](https://pmc.ncbi.nlm.nih.gov/articles/PMC2745155/)
- [Nielsen 2000 Report on Television (historical archive)](https://www.worldradiohistory.com/Archive-Ratings-Documents/Nielsen-2000-Report-on-Television.pdf)