Structural skew
Study 1b children
Marianna Zhang
2025-12-21
Design
This study investigated whether 4-year-olds and 7-year-olds are sensitive to sampling information in making inferences about a social group, i.e., whether they can adjust their inferences after seeing a skewed sample of group members.
We did not preregister directional predictions about 4-year-olds, but suspected they might fail based on exploratory results from Exp 1a.
We preregistered that 7-year-olds would be sensitive, i.e., be more likely to report that a novel group population is taller than the sample observed, after seeing a sample selected for being short, based on exploratory results from Exp 1a.
Compared to Exp 1a, this experiment is intended to power the age by condition interaction, and uses a different control condition to make sure that children are not just generalizing directly off the sample by more heavily weighting the taller scrunching Zarpies, since the scrunching Zarpies only appear in the skewed condition in Exp 1a.
We have also used a different “the same” warmup (white vs brown chicken), added correct responses to the warmup, and changed exclusion criteria to include on warmups, comprehension check, and memory check.
Results summary
- We found that 4-year-olds failed to adjust in this task, as demonstrated by consistent non-significant/Bayesian results in favor of the null in our preregistered non-directional analyses:
4yo showed no difference in overall responses
4yo showed no difference in choices of “Zarpies on Zarpie island” as taller across the two conditions
Note that 4yo’s difficulty could be due to a variety of reasons, including adjusting rather than suspending inference, or structural reasoning about the boat. There could also be task-specific factors for 4yo’s failure, for example, having to do with the cognitive or verbal complexity of the DV (requiring 4yo to compare a distribution of heights seen a moment ago, to a different distribution constructed through adjustment). However, 4yo have been shown in past work to be capable of comparing two ensemble representations of continuous variables (e.g., which of two trees grows larger oranges on average, even when there are many oranges and the trees are flashed on screen too quickly for serial attention to individual oranges: Sweeny et al., 2015).
- We also found suggestive evidence that 7-year-olds are adjusting in this task, by confirming 2 of our 3 preregistered hypotheses:
7yo showed marginal difference in overall responses
7yo chose “Zarpies on Zarpie island” as taller significantly more frequently in the skewed condition, compared to the not skewed condition
7yo chose “Zarpies on Zarpie island” as taller significantly more frequently than chance in the skewed condition.
However, note that this study did not rule out the possibility that 7yo succeed on this task by tracking revealed population information in the boarding scene. (See Study 1c with adults.)
- Comparing across our age groups, we found suggestive evidence of developmental change, as suggested by 1 marginal test out of our 2 preregistered hypotheses:
There was no evidence of an interaction between age (4yo vs 7yo) and condition on overall responses. An exploratory analysis failed to find a similar interaction with age (continuous).
There was a marginal interaction between age (4yo vs 7yo) and condition on population responses. An exploratory analysis found a similar marginal interaction with age (continuous).
Methods
The study was preregistered on OSF.
Power analysis
See 1b_children_power_analysis.html.
Participants
690 children participated via PANDA in December 2, 2025 - June 29, 2026.
Participants’ families were paid $10 for an estimated 10-15 minute task. Children’s parent/guardian provided consent and children provided assent.
sample_age_cond <- data %>%
group_by(age_cat, boarding) %>%
summarize(n = length(unique(ID)))
sample_age_condAfter applying exclusion criteria, the final sample included 589 children (n = 145-148 in each of the 4 conditions).
sample_to_replace <- sample_age_cond %>%
filter(boarding == "not skewed old")
sample_to_replaceFour-year-old and seven-year-old participants were recruited by mass emails to all eligible participants in the PANDA database, excluding participants from the earlier study (Study 1a). Due to PANDA recruitment setting limitations, participants in an earlier pilot study will be manually excluded at the data analysis stage.
Due to experimenter error, the following errors affected the initial participants participating: - Participants assigned to the “not skewed” condition were assigned to the “not skewed” condition from the earlier study (Exp. 1a), and viewed videos of the sample and DV questions corresponding to the previous “not skewed” condition (featuring a tall boat), rather than the new “not skewed” condition (featuring a short boat). - In addition, all participants saw the same counterbalance version of the critical question (i.e., “Who is taller? The Zarpies on Zarpie island, the Zarpies who visited, or are they the same?”), rather than evenly viewing different counterbalance versions across participants.
These bugs was caught and the following changes made on Tuesday, December 16, 2025 at 4:43pm Eastern Time.
Changes: - We will replace participants mistakenly assigned to the “not skewed old” condition ( 4-year-olds, 7-year-olds). Specifically, we will recruit the same number of additional participants after the current sample is completed, to ease the condition assignment process in Qualtrics. - The counterbalance variable controlling the order of options in the critical question was reweighted to reflect the fact that all participants until that point had seen one order; Qualtrics will automatically assign the next batch of participants to the alternate order of options until the numbers balance out, at which point it will automatically return to even counterbalancing.
No data from the dependent measures have been analyzed yet, and data analysis of the dependent measures will not begin until all data collection, including replacement participants, is completed.
Exclusion criteria
A total of 101 participants (14.6% of all participants) were excluded for meeting at least 1 of the following exclusion criteria:
- not passing video validation, e.g., no parent or child in frame for entire duration of video (n = NA)
Demographics
Of included participants.
| age | ||
| mean | sd | n |
|---|---|---|
| 5.93 | 1.48 | 589 |
| age groups | |
| age_cat | n |
|---|---|
| 4 | 296 |
| 7 | 293 |
| age groups by condition | |
| not skewed | skewed |
|---|---|
| 4 | |
| 148 | 148 |
| 7 | |
| 145 | 148 |
| gender | n | prop |
|---|---|---|
| female | 312 | 53.0% |
| male | 277 | 47.0% |
| race | n | prop |
|---|---|---|
| Caucasian | 323 | 54.8% |
| Asian | 82 | 13.9% |
| Asian, Caucasian | 36 | 6.1% |
| Caucasian, Hispanic | 29 | 4.9% |
| Hispanic | 28 | 4.8% |
| African American | 25 | 4.2% |
| African American, Caucasian | 18 | 3.1% |
| NA | 13 | 2.2% |
| Asian, Hispanic | 6 | 1.0% |
| African American, Asian | 3 | 0.5% |
| African American, Caucasian, Hispanic | 3 | 0.5% |
| Caucasian, Native American | 3 | 0.5% |
| African American, Asian, Caucasian | 2 | 0.3% |
| African American, Caucasian, Native American | 2 | 0.3% |
| African American, Asian, Hispanic | 1 | 0.2% |
| African American, Hispanic | 1 | 0.2% |
| Asian, Caucasian, Arab | 1 | 0.2% |
| Asian, Caucasian, Hispanic | 1 | 0.2% |
| Asian, Native American | 1 | 0.2% |
| Asian, South Asian | 1 | 0.2% |
| Asian/white | 1 | 0.2% |
| Caucasian, Ashkenazi Jewish | 1 | 0.2% |
| Caucasian, Cajun | 1 | 0.2% |
| Caucasian, Hispanic, Guatemalan/Albanian | 1 | 0.2% |
| Caucasian, Middle eastern | 1 | 0.2% |
| Middle Eastern | 1 | 0.2% |
| Mixed (white and Trinidadian) | 1 | 0.2% |
| Multiple races | 1 | 0.2% |
| Native American | 1 | 0.2% |
| White & Asian | 1 | 0.2% |
| education | n | prop |
|---|---|---|
| Less than high school | 1 | 0.2% |
| High school/GED | 22 | 3.7% |
| Some college | 64 | 10.9% |
| Bachelor's (B.A., B.S.) | 182 | 30.9% |
| Master's (M.A., M.S.) | 227 | 38.5% |
| Doctoral (Ph.D., J.D., M.D.) | 80 | 13.6% |
| Prefer not to specify | 2 | 0.3% |
| NA | 11 | 1.9% |
| country | n |
|---|---|
| Canada | 2 |
| UK | 1 |
| US | 585 |
| NA | 1 |
| state | n |
|---|---|
| AL | 4 |
| AR | 3 |
| AZ | 10 |
| CA | 50 |
| CO | 8 |
| CT | 6 |
| DC | 3 |
| DE | 1 |
| FL | 23 |
| GA | 18 |
| HI | 3 |
| IA | 4 |
| ID | 4 |
| IL | 21 |
| IN | 13 |
| KS | 3 |
| KY | 7 |
| LA | 4 |
| MA | 20 |
| MD | 9 |
| MI | 16 |
| MN | 12 |
| MO | 13 |
| MT | 1 |
| NC | 20 |
| ND | 1 |
| NE | 4 |
| NH | 3 |
| NJ | 32 |
| NM | 2 |
| NY | 85 |
| OH | 14 |
| OK | 4 |
| OR | 6 |
| PA | 34 |
| RI | 4 |
| SC | 8 |
| SD | 1 |
| TN | 14 |
| TX | 40 |
| UT | 12 |
| VA | 19 |
| VT | 2 |
| WA | 16 |
| WI | 6 |
| NA | 6 |
Almost all participants (n = 585) were based in the United States, from across 45 states. We also had a few international participants (n = 1 from UK, n = 2 from Canada).
| median household income of zipcode | |
| in dollars, US participants only | |
| avg | sd |
|---|---|
| 101263.1 | 39967.74 |
Procedure
This study was administered as a Qualtrics survey, and approved by the NYU IRB (IRB-FY2024-9169).
After providing their consent, participants completed a captcha and sound check, and were asked to watch videos sound on. Participants then watched the following videos in order:
In the warmup phase, participants were familiarized with answering questions about height in terms of who is taller or whether they are the same height. Participants saw a duck and a chicken appear on screen against a grid, who were the same in height, and were asked who is taller: the duck, the chicken, or are they the same. A same question was asked about a giraffe and a bunny, where the giraffe is in fact taller. The order of these two questions was counterbalanced.
In the prior setting and familiarization phase, participants saw a photorealistic picture of 5 human adults and then another picture of a different 5 adults appear on screen against a grid. These adults were all 10 gridline units tall.
In the boat training phase, participants were shown a parade of fictional animals attempting to board the boat, to illustrate how the boat works. In both conditions condition, the boat was 6 units tall.
The boat height was specified to be accidental (“When the boat builders were building the boat, they started building the boat from the bottom, but ran out of the special wood they needed for the boat! So the boat ended up being this tall. It might be hard for anyone who is taller than the boat to get on the boat.”), to avoid any justificatory reasoning about the height of the boat being informative about the height of Zarpies or vice versa.
To communicate how the boat functions to exclude those shorter than the boat, participants then watched a parade of 20 fictional animals (Quaffas, taken from Foster-Hanson et al., 2019) attempt to board the boat, one at a time, from shortest to tallest.
The Quaffa parade was identical for both skewed and not skewed conditions, as the boat height was the same.
Participants were asked a boat check: “Which Quaffa can get on the boat for sure?” (short Quaffa or tall Quaffa), and heard the correct answer (short Quaffa).
In the boat boarding phase, participants learned that Zarpies live on Zarpie island, and saw an island with many Zarpies overhead. Participants learned that all the grownup Zarpies’ names were put into a hat, and some of their names “were drawn out of a hat to try and visit us”. Participants saw then saw a parade of Zarpies attempt to board the boat to visit us, one at a time. Participants were told that they were all grown-up Zarpies. The boarding phase was occluded: i.e., the heights of Zarpies were hidden behind a curtain that showed only their feet.
In the skewed condition, 20 Zarpies attempt to board, 6 of whom successfully make it on (6 out of 16 successful = 30% successful). Of the 6 who make it on, 2 had to stoop to board.
In the not skewed condition, 6 Zarpies attempt to board, all of whom successfully make it on (6 out of 6 successful = 100% successful). Of the 6 who make it on, 2 had to stoop to board.
After the boat boarding phase, participants were asked a comprehension check: “Did all of the Zarpies board the boat?” (yes/no), and received either an affirmation (if they said “no” in the skewed condition, or “yes” in the not skewed condition) or correction (if they said “yes” in the skewed condition, or “no” in the not skewed condition).
In the sample observation phase, all participants saw the Zarpies who successfully boarded the boat get off the boat to visit us. The Zarpies got off one at a time, and each waved/descrunched if relevant. The height of this observed sample (4, 5, 6, 6, 7, 8) was held constant across conditions.
- To emphasize the height of the Zarpies relative to the boat, participants watched Zarpies deboard the boat, wave, reboard the boat (with any Zarpies taller than the boat stooping down again to board again), and deboard again (with any Zarpies taller than the boat straightening up again).
Participants were asked a single DV:
- Participants were asked an explicit comparison question asking them to who is taller: Zarpies who visited, Zarpies on Zarpie island, or are they the same (see [explicit comparison]). The order of the first two options were counterbalanced (“the same” always came last).
Finally, participants’ parent or guardian were asked for any problems or confusion they had and demographic information.
Results
Interference
Interference was (fixme: rare). Interference was defined as a parent, guardian, sibling, or other agent verbally overriding the participant’s verbally expressed response, pointing to the screen to indicate a particular response when the participant was uncertain, restating the question in a leading way, or otherwise encouraging the participant to respond in a particular way.
Checks
Warmup questions
We asked participants questions designed to elicit a “taller” and a “the same” response to get participants comfortable with answering either option.
The order of these two questions was counterbalanced. The order of options within each question was fixed, and not counterbalanced.
Taller warmup
Participants almost all answered the taller warmup correctly.
Participants who made an incorrect response were still included.
The same warmup
Performance was a bit more mixed on “the same” question, although most participants still answered correctly.
Participants who made an incorrect response were still included.
Boat check
Most participants passed the comprehension check assessing their understanding of how the boat works, although younger children were more likely to fail.
Participants who selected an incorrect response were still included.
# did boat check performance vary by age
boat_check_age <-
glm(boat_check_pass ~ age_cat,
family = "binomial",
data = data_all)
boat_check_age %>%
Anova()Unexpectedly, there was a significant effect of age (exact) on boat check performance: younger children were more likely to fail (likelihood ratio test: \(\chi^2\)(1) = 16.44, p < .001).
Comprehension check
Participants mostly passed the comprehension check for understanding what happened during the Zarpie boarding sequence. Note the correct answer to this question depends on condition:
In the skewed condition, the correct answer is “no”, not all of the Zarpies made it onto the boat.
In the not skewed condition, the correct answer is “yes”, all of the Zarpies made it onto the boat.
Those who responded incorrectly were still included.
Condition differences within age groups
Participants were explicitly asked to compare the population and the sample: “Who is taller? The Zarpies on Zarpie island, the Zarpies who visited, or are they the same?” The order of the first two options was counterbalanced across participants.
## # A tibble: 12 × 5
## # Groups: age_cat, boarding [4]
## age_cat boarding dv_comp n prop
## <dbl> <fct> <fct> <int> <dbl>
## 1 4 not skewed Zarpies who visited 26 0.176
## 2 4 not skewed the same 61 0.412
## 3 4 not skewed Zarpies on Zarpie island 61 0.412
## 4 4 skewed Zarpies who visited 25 0.169
## 5 4 skewed the same 62 0.419
## 6 4 skewed Zarpies on Zarpie island 61 0.412
## 7 7 not skewed Zarpies who visited 32 0.221
## 8 7 not skewed the same 55 0.379
## 9 7 not skewed Zarpies on Zarpie island 58 0.4
## 10 7 skewed Zarpies who visited 19 0.128
## 11 7 skewed the same 50 0.338
## 12 7 skewed Zarpies on Zarpie island 79 0.5344yo
# condition diff in overall responses?
dv_comp_4yo_cond <-
multinom(dv_comp ~ boarding,
data = data %>%
filter(age_cat == "4"))
dv_comp_4yo_cond %>%
Anova()# condition diff in overall responses?
dv_comp_4yo_cond_brm <-
brm(dv_comp ~ boarding,
family = categorical,
prior = c(set_prior("normal(0,1)", class = "Intercept",
dpar = "muthesame"),
set_prior("normal(0,1)", class = "Intercept",
dpar = "muZarpiesonZarpieisland"),
set_prior("normal(0,1)", class = "b",
dpar = "muthesame"),
set_prior("normal(0,1)", class = "b",
dpar = "muZarpiesonZarpieisland")),
data = data %>%
filter(age_cat == "4"))
dv_comp_4yo_cond_brm %>%
hypothesis(c("muthesame_boardingskewed = 0",
"muZarpiesonZarpieisland_boardingskewed = 0"))
dv_comp_4yo_null_brm <-
brm(dv_comp ~ 1,
family = categorical,
prior = c(set_prior("normal(0,1)", class = "Intercept",
dpar = "muthesame"),
set_prior("normal(0,1)", class = "Intercept",
dpar = "muZarpiesonZarpieisland")),
data = data %>%
filter(age_cat == "4"))
bayes_factor(dv_comp_4yo_cond_brm, dv_comp_4yo_null_brm)## Analysis of Deviance Table (Type II tests)
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## Iteration: 4## Estimated Bayes factor in favor of dv_comp_pop_4yo_cond_brm over dv_comp_pop_4yo_null_brm: 0.230197yo
## # weights: 12 (6 variable)
## initial value 321.893401
## final value 297.669369
## converged## # weights: 6 (2 variable)
## initial value 321.893401
## final value 301.064244
## converged## Analysis of Deviance Table (Type II tests)
##
## Response: dv_comp
## LR Chisq Df Pr(>Chisq)
## boarding 6.7897 4 0.1474##
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## Iteration: 4## Estimated Bayes factor in favor of dv_comp_7yo_cond_brm over dv_comp_7yo_null_brm: 1.48621## Analysis of Deviance Table (Type II tests)
##
## Response: dv_comp_pop
## LR Chisq Df Pr(>Chisq)
## boarding 5.2825 1 0.02154 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
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## Iteration: 4## Estimated Bayes factor in favor of dv_comp_pop_7yo_cond_brm over dv_comp_pop_7yo_null_brm: 2.83489Age by condition interaction
Overall responses
## # weights: 21 (12 variable)
## initial value 647.082638
## iter 10 value 603.494915
## final value 603.489548
## converged## Analysis of Deviance Table (Type II tests)
##
## Response: dv_comp
## LR Chisq Df Pr(>Chisq)
## age_cat 2.2647 2 0.3223
## boarding 3.6754 4 0.4517
## age_cat:boarding 3.1421 4 0.5343## # weights: 21 (12 variable)
## initial value 647.082638
## iter 10 value 603.651094
## final value 603.639051
## converged## Analysis of Deviance Table (Type II tests)
##
## Response: dv_comp
## LR Chisq Df Pr(>Chisq)
## age_exact 2.5086 2 0.2853
## boarding 3.6481 4 0.4557
## age_exact:boarding 2.5992 4 0.6270There was no interaction of age (4yo vs 7yo) or age (exact) with condition on overall responses.
Population responses
##
## Call:
## glm(formula = dv_comp_pop ~ age_cat * boarding, family = "binomial",
## data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.28779 0.45046 -0.639 0.523
## age_cat -0.01681 0.07932 -0.212 0.832
## boardingskewed -0.72108 0.63484 -1.136 0.256
## age_cat:boardingskewed 0.18027 0.11139 1.618 0.106
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 807.95 on 588 degrees of freedom
## Residual deviance: 800.83 on 585 degrees of freedom
## AIC: 808.83
##
## Number of Fisher Scoring iterations: 4There was a marginal interaction between age group (4yo vs 7yo) and condition (\(z\) = 1.62, p = 0.106).
##
## Call:
## glm(formula = dv_comp_pop ~ age_exact * boarding, family = "binomial",
## data = data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.339685 0.492849 -0.689 0.491
## age_exact -0.006814 0.080989 -0.084 0.933
## boardingskewed -0.762223 0.689909 -1.105 0.269
## age_exact:boardingskewed 0.173728 0.112811 1.540 0.124
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 807.95 on 588 degrees of freedom
## Residual deviance: 800.71 on 585 degrees of freedom
## AIC: 808.71
##
## Number of Fisher Scoring iterations: 4There was a marginal interaction between age (exact) and condition (\(z\) = 1.54, p = 0.124).
Vs chance within condition
For each age group, within each condition, are responses different from chance?
# chi sq: not skewed condition, vs chance
dv_comp_4yo_not_skewed_counts <- data %>%
filter(age_cat == 4 &
boarding == "not skewed") %>%
count(dv_comp)
dv_comp_4yo_not_skewed_chisq <-
chisq.test(
dv_comp_4yo_not_skewed_counts$n,
p = rep(1/3, 3) # chance
)
dv_comp_4yo_not_skewed_chisqYes, 4yo’s responses in the not skewed condition are significantly different from chance (\(\chi^2\)(2) = 16.55, p < .001).
# not skewed condition: same vs chance
dv_comp_4yo_not_skewed_same <- data %>%
filter(age_cat == 4 &
boarding == "not skewed") %>%
pull(dv_comp_same)
dv_comp_4yo_not_skewed_same_ttest <-
t.test(
dv_comp_4yo_not_skewed_same,
mu = 1/3) # chance
dv_comp_4yo_not_skewed_same_ttestFor 4yo’s responses in the not skewed condition, 4yo were not any more likely to say “the same” compared to chance (\(t\)(147) = 1.94, p = 0.054).
# chi sq: skewed condition, vs chance
dv_comp_4yo_skewed_counts <- data %>%
filter(age_cat == 4 &
boarding == "skewed") %>%
count(dv_comp)
dv_comp_4yo_skewed_chisq <-
chisq.test(
dv_comp_4yo_skewed_counts$n,
p = rep(1/3, 3) # chance
)
dv_comp_4yo_skewed_chisqIn the skewed condition, 4yo’s overall responses are significantly different from chance (\(\chi^2\)(2) = 18.01, p < .001).
# skewed condition: pop vs chance
dv_comp_4yo_skewed_pop <- data %>%
filter(age_cat == 4 &
boarding == "skewed") %>%
pull(dv_comp_pop)
dv_comp_4yo_skewed_pop_ttest <-
t.test(
dv_comp_4yo_skewed_pop,
mu = 1/3) # chance
dv_comp_4yo_skewed_pop_ttestIn the skewed condition, 4yo respond with “population” responses significantly more than chance (\(t\)(147) = 1.94, p = 0.054).
# chi sq: not skewed condition, vs chance
dv_comp_7yo_not_skewed_counts <- data %>%
filter(age_cat == 7 &
boarding == "not skewed") %>%
count(dv_comp)
dv_comp_7yo_not_skewed_chisq <-
chisq.test(
dv_comp_7yo_not_skewed_counts$n,
p = rep(1/3, 3) # chance
)
dv_comp_7yo_not_skewed_chisqIn the not skewed condition, 7yo’s overall responses were different from chance (\(\chi^2\)(2) = 8.37, p = 0.015).
# not skewed condition: same vs chance
dv_comp_7yo_not_skewed_same <- data %>%
filter(age_cat == 7 &
boarding == "not skewed") %>%
pull(dv_comp_same)
dv_comp_7yo_not_skewed_same_ttest <-
t.test(
dv_comp_7yo_not_skewed_same,
mu = 1/3) # chance
dv_comp_7yo_not_skewed_same_ttestIn the not skewed condition, 7yo did not respond with “the same” any more frequently than chance (\(t\)(144) = 1.14, p = 0.257).
# chi sq: skewed condition, vs chance
dv_comp_7yo_skewed_counts <- data %>%
filter(age_cat == 7 &
boarding == "skewed") %>%
count(dv_comp)
dv_comp_7yo_skewed_chisq <-
chisq.test(
dv_comp_7yo_skewed_counts$n,
p = rep(1/3, 3) # chance
)
dv_comp_7yo_skewed_chisqIn the skewed condition, 7yo’s overall responses are significantly different from chance (\(\chi^2\)(2) = 36.5, p < .001).
# skewed condition: pop vs chance
dv_comp_7yo_skewed_pop <- data %>%
filter(age_cat == 7 &
boarding == "skewed") %>%
pull(dv_comp_pop)
dv_comp_7yo_skewed_pop_ttest <-
t.test(
dv_comp_7yo_skewed_pop,
mu = 1/3) # chance
dv_comp_7yo_skewed_pop_ttestIn the skewed condition, 7yo responded with “population” responses significantly more frequently than chance (\(t\)(147) = 4.87, p < .001).
Session info
## R version 4.5.2 (2025-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS Tahoe 26.5
##
## Matrix products: default
## BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: America/New_York
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] brms_2.23.0 Rcpp_1.1.1 effectsize_1.0.1 emmeans_2.0.1
## [5] nnet_7.3-20 lmerTest_3.2-0 lme4_1.1-38 Matrix_1.7-4
## [9] car_3.1-3 carData_3.0-5 tidycensus_1.7.3 zipcodeR_0.3.5
## [13] viridis_0.6.5 viridisLite_0.4.2 ggtext_0.1.2 lubridate_1.9.4
## [17] forcats_1.0.1 stringr_1.6.0 dplyr_1.1.4 purrr_1.2.1
## [21] readr_2.1.6 tidyr_1.3.2 tibble_3.3.1 ggplot2_4.0.1
## [25] tidyverse_2.0.0 gt_1.3.0 scales_1.4.0 janitor_2.2.1
## [29] here_1.0.2
##
## loaded via a namespace (and not attached):
## [1] RColorBrewer_1.1-3 tensorA_0.36.2.1 rstudioapi_0.18.0
## [4] jsonlite_2.0.0 datawizard_1.3.0 magrittr_2.0.4
## [7] TH.data_1.1-5 estimability_1.5.1 farver_2.1.2
## [10] nloptr_2.2.1 rmarkdown_2.30 ragg_1.5.0
## [13] fs_1.6.6 vctrs_0.7.1 memoise_2.0.1
## [16] minqa_1.2.8 terra_1.8-93 htmltools_0.5.9
## [19] distributional_0.6.0 curl_7.0.0 raster_3.6-32
## [22] Formula_1.2-5 StanHeaders_2.32.10 sass_0.4.10
## [25] KernSmooth_2.23-26 bslib_0.10.0 sandwich_3.1-1
## [28] zoo_1.8-15 cachem_1.1.0 uuid_1.2-2
## [31] lifecycle_1.0.5 pkgconfig_2.0.3 R6_2.6.1
## [34] fastmap_1.2.0 rbibutils_2.4.1 snakecase_0.11.1
## [37] digest_0.6.39 numDeriv_2016.8-1.1 colorspace_2.1-2
## [40] ps_1.9.1 rprojroot_2.1.1 textshaping_1.0.4
## [43] RSQLite_2.4.5 labeling_0.4.3 timechange_0.3.0
## [46] httr_1.4.7 abind_1.4-8 compiler_4.5.2
## [49] proxy_0.4-29 bit64_4.6.0-1 withr_3.0.2
## [52] inline_0.3.21 backports_1.5.0 S7_0.2.1
## [55] DBI_1.2.3 QuickJSR_1.9.0 pkgbuild_1.4.8
## [58] MASS_7.3-65 rappdirs_0.3.4 classInt_0.4-11
## [61] loo_2.9.0 tools_4.5.2 units_1.0-0
## [64] otel_0.2.0 glue_1.8.0 callr_3.7.6
## [67] nlme_3.1-168 gridtext_0.1.5 grid_4.5.2
## [70] sf_1.0-24 checkmate_2.3.3 generics_0.1.4
## [73] gtable_0.3.6 tzdb_0.5.0 class_7.3-23
## [76] hms_1.1.4 utf8_1.2.6 sp_2.2-0
## [79] xml2_1.5.2 pillar_1.11.1 vroom_1.6.7
## [82] posterior_1.6.1 splines_4.5.2 lattice_0.22-7
## [85] survival_3.8-6 bit_4.6.0 tidyselect_1.2.1
## [88] knitr_1.51 reformulas_0.4.3.1 gridExtra_2.3
## [91] V8_8.0.1 stats4_4.5.2 xfun_0.56
## [94] bridgesampling_1.2-1 matrixStats_1.5.0 rstan_2.32.7
## [97] stringi_1.8.7 yaml_2.3.12 boot_1.3-32
## [100] evaluate_1.0.5 codetools_0.2-20 cli_3.6.5
## [103] RcppParallel_5.1.11-1 systemfonts_1.3.1 xtable_1.8-4
## [106] parameters_0.28.3 Rdpack_2.6.5 processx_3.8.6
## [109] jquerylib_0.1.4 coda_0.19-4.1 parallel_4.5.2
## [112] rstantools_2.6.0 blob_1.3.0 bayestestR_0.17.0
## [115] bayesplot_1.15.0 Brobdingnag_1.2-9 ggthemes_5.2.0
## [118] mvtnorm_1.3-3 tigris_2.2.1 e1071_1.7-17
## [121] insight_1.4.5 crayon_1.5.3 rlang_1.1.7
## [124] rvest_1.0.5 multcomp_1.4-29