Overview
Project goals
The goals of this project are to establish:
if children and adults generalize from a sample to a social group
from a sample that is, unbeknownst to them, structurally skewed,
resulting in inaccurate beliefs about the group
if children and adults can adjust their generalization from a
sample to a social group to account for the fact that the sample was
skewed by a structural process
This study focuses on question (2) in adults.
Study goals
The primary goal of this study was to see if, given evidence of that
a sample was skewed, adults adjust their inferences about a social
population to account for the skew.
Adults were shown the exact same sample of novel group members
(Zarpies), but the sample was either not skewed (Zarpies were
sampled without any being turned away) or skewed (many
additional Zarpies were turned away during the sampling process). Adults
were then asked to estimate the average height of the same and the
average height of the population.
Adults in the critical occluded conditions did not observe
the heights of Zarpies in the population, but were able to hear/see the
success/failure of the sampling process. As controls for a potential
null result, separate groups of adults in visible conditions
observed the heights of Zarpies during the sampling process (i.e., that
they were the same height, or that they were much taller).
Results
This study confirmed our pre-registered hypothesis that
adults are capable of adjusting their inferences about a social
population against structural skew, although this might be
weakened by some caveats from exploratory findings.
Pre-registered: As expected if adults are able to
adjust, adults made different population inferences when the sample was
skewed versus not skewed, in both occluded and visible sets of
conditions. (see population
inference).
- Exploratory: However, this adjustment was counteracted in
the critical occluded skewed condition by the fact that adults also made
inflated estimates of the sample in this condition (and only this
condition), even though the sample was the same in both conditions. (see
sample representation).
- Exploratory: As a result, in the critical occluded skewed
condition, adults did not respond significantly differently when asked
about the population compared to the sample; both were inflated relative
to the true sample mean. (see sample vs
population).
Pre-registered: As expected if adults are able to
adjust, adults were more likely to report that the population is taller
than the sample and less likely to report that the population is the
same in height as the sample in the skewed conditions compared to the
not skewed conditions, in both occluded and visible sets of
conditions.
- Exploratory: However, even in the skewed conditions, the
population is “the same” as the sample was a very common response.
Alternative hypotheses we can rule out:
Adults fail to adjust their generalization from
sample to population against structural skew, instead just generalizing
directly off the sample, unless they have direct population
information.
- Inconsistent with the facts that both population inferences and
explicit reports varied in occluded skewed vs not skewed conditions
(pre-registered results).
- Consistent with the fact that adults didn’t make significantly
different responses for sample vs population in the critical occluded
skewed condition (an exploratory null result).
- Left unexplained is the fact that sample estimates were
significantly higher in the occluded skewed condition only.
Adults are guessing and don’t understand the
paradigm.
- Inconsistent with the skewed vs not skewed effects in both visible
and occluded sets of conditions.
Alternative hypotheses/twists on the main hypothesis that could still
be in play:
Adults fail to adjust their generalization from
sample to population against structural skew, instead generalizing in a
way weighted by visual salience/attention (e.g., the
scrunching/unscrunching Zarpies in the shorter boat condition).
- Consistent with the skewed vs not skewed effects in the occluded
conditions: adults adjusted their population estimates upward when they
heard/saw the sampled Zarpies scrunch/unscrunch.
- Would need to run a follow-up with a not skewed condition involving
a short boat, where the same sample boards, 2 scrunch, but none are
turned away.
- Left unexplained is the fact that sample estimates were
significantly higher in the occluded skewed condition only.
Adults are able to make adjustments against structural skew, but
adjust too much, adjusting both their sample and
population estimates. This would require adults’ representation
of the sample to be contaminated by their representation of the
population (e.g., by an expectation that samples should be
representative).
Consistent with the fact that sample estimates were significantly
higher in the occluded skewed condition only: adults adjusted their
sample estimates to correspond with what they expected from the
population/sampling information.
However, inconsistent with the fact that adults were more likely
to explicitly report that the population is taller than the sample in
the skewed condition than the not skewed condition.
Methods
The study was preregistered on
OSF.
Participants
Data was collected from 399 adults recruited via Prolific on Mon
8/18/2025. Participants were required to be in the United States, fluent
in English, and have not participated in any pilots of this study.
Participants were paid $2.75 for an estimated 10-12 minute task. In
fact, the study generally took about 10 minutes for participants.
The final sample included 381 adults (n = 85-107 in each of the 4
conditions).
| boarding |
participants |
| visible |
| not skewed |
85 |
| skewed |
107 |
| occluded |
| not skewed |
103 |
| skewed |
86 |
Exclusion criteria
18 participants (4.5% of all participants) were excluded for meeting
at least 1 of the following exclusion criteria:
failing the sound check (n = 0 participants)
failing to select the correct task description (i.e., did not
select “Watching videos about fictional people from an island”) (n = 4
participants)
failing the memory check (n = 10
participants)
failing the comprehension
check (n = 5 participants)
Note that participants who did not respond to the comprehension check
were included in the final sample. Excluding them does not change the
below results.
Memory check
Participants overwhelmingly passed the memory check for the Quaffa
boarding sequence, i.e., “no”, not all the Quaffas made it onto the
boat.
Participants who made incorrect responses were excluded.
Comprehension check
Participants overwhelmingly passed the comprehension check for 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.
Note that there are some non-responses (NAs), because I forgot to
require a response on this question in Qualtrics. These participants
were included below, but excluding them does not change anything.
Demographics
This study recruited a sample representative of the US on sex, age,
and ethnicity (simplified US Census categories), using the
representative sample feature on Prolific.
| age |
| mean |
sd |
n |
| 46.10 |
15.76 |
381 |
- The sample was largely young and middle-aged.
| gender |
n |
prop |
| Female |
190 |
49.9% |
| Male |
184 |
48.3% |
| Non-binary |
5 |
1.3% |
| Prefer not to specify |
2 |
0.5% |
- The sample was diverse in terms of gender identities in the US.
| race |
n |
prop |
| White, Caucasian, or European American |
233 |
61.2% |
| Black or African American |
42 |
11.0% |
| Hispanic or Latino/a |
24 |
6.3% |
| White, Caucasian, or European American,Hispanic or Latino/a |
20 |
5.2% |
| South or Southeast Asian |
12 |
3.1% |
| East Asian |
9 |
2.4% |
| White, Caucasian, or European American,Black or African American |
8 |
2.1% |
| Native American, American Indian, or Alaska Native |
4 |
1.0% |
| Prefer not to specify |
4 |
1.0% |
| Middle Eastern or North African |
3 |
0.8% |
| White, Caucasian, or European American,East Asian |
3 |
0.8% |
| White, Caucasian, or European American,Native American, American Indian, or Alaska Native |
3 |
0.8% |
| South or Southeast Asian,East Asian |
2 |
0.5% |
| White, Caucasian, or European American,Black or African American,Native American, American Indian, or Alaska Native |
2 |
0.5% |
| White, Caucasian, or European American,Middle Eastern or North African |
2 |
0.5% |
| American Citizen |
1 |
0.3% |
| Black or African American,Native American, American Indian, or Alaska Native |
1 |
0.3% |
| Hispanic or Latino/a,Black or African American |
1 |
0.3% |
| Hispanic or Latino/a,South or Southeast Asian |
1 |
0.3% |
| Indigenous American |
1 |
0.3% |
| White, Caucasian, or European American,East Asian,Native Hawaiian or other Pacific Islander |
1 |
0.3% |
| White, Caucasian, or European American,Native Hawaiian or other Pacific Islander |
1 |
0.3% |
| White, Caucasian, or European American,South or Southeast Asian |
1 |
0.3% |
| White, Caucasian, or European American,South or Southeast Asian,Native Hawaiian or other Pacific Islander,Prefer not to specify |
1 |
0.3% |
| White, Caucasian, or West Asian American (Iranian/Persian) |
1 |
0.3% |
- The sample was also racially diverse.
| education |
n |
prop |
| Less than high school |
3 |
0.8% |
| High school/GED |
56 |
14.7% |
| Some college |
115 |
30.2% |
| Bachelor's (B.A., B.S.) |
151 |
39.6% |
| Master's (M.A., M.S.) |
40 |
10.5% |
| Doctoral (Ph.D., J.D., M.D.) |
15 |
3.9% |
| Prefer not to specify |
1 |
0.3% |
- The sample was about evenly split in whether they had attained a
college degree or not.
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 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.
Prior setting and familiarization.
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 the skewed condition, the boat was 6
units tall. In the not skewed condiiton, the boat was 10 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 height of animals were scaled to the height of the boat, such
that 10 animals were always shorter than the boat (these animals boarded
successfully) and 10 animals were always taller than the boat (all but
one were unable to board; the third quaffa successfully boards by
bending its head).
Quaffas in the skewed condition. Note the
Quaffas are short, since the skewed condition involves a short
boat.
- Participants were asked a memory check: “Did all of
the animals board the boat?” (yes/no), and received an affirmation (if
they said “no”) or correction (if they said “yes”).
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.
In the occluded condition, the heights of Zarpies were hidden
behind a curtain that showed only their feet. 
In the visible condition, the heights of Zarpies were
visible.
In the not skewed condition, the boat is 10 units tall. 6 Zarpies
attempt to board, all of whom successfully make it on (6 out of 6
successful = 100% successful). Of the 6 who board, none had to stoop to
board.
Boarding in visible not skewed condition.
- In the skewed condition, the boat is 6 units tall. 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.
Boarding in visible skewed condition.
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).
- Note: I forgot to turn on validation to force a response, so there
are quite a few non-responses to this question. These people were
retained in the following analyses.
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).
Observed sample in skewed condition. Note the
observed sample is the same, but the height of the boat is short in the
skewed condition, vs tall in the not skewed condition.
Participants were asked the following DVs in the
following order:
Participants were asked the average height of the Zarpies who
visited (Sample representation) and
the average height of Zarpies on Zarpie island (Population inference), in
counterbalanced order.
Participants were then asked an explicit comparison question
asking them to compare the heights of Zarpies on Zarpie island to that
of Zarpies who visited: shorter, about the same, or taller (see explicit comparison).
Finally, participants were asked for any problems or confusion they
had, what they thought the task was about (see [Participant feedback]),
and demographic information.
Primary results
Sample representation
As a check that they could retrieve the mean of the sample they
observed, participants were asked, “Which picture shows the average
height of the Zarpies who visited?”, and had to choose between a Zarpie
of height 4, 5, 6, 7, or 8.
We did not preregister any results on this measure.
Sample representation question in the skewed
condition, with the response options in red boxes.
Since all participants saw the same sample, participants should
provide the same response, regardless of condition. The sample was (4,
5, 6, 6, 7, 8), so the the response is expected to be the mean of the
sample, which is 6 (indicated with red dots below).
Unexpectedly, there was an interaction between the population
occluded/visible and boarding skewed/not skewed conditions,
such that in the occluded condition only, such that those in the skewed
sample condition reported taller estimates of the sample than those in
the not skewed sample condition. (t = 2.95, p =
0.004). This was unexpected, since both conditions observed the same
sample.
In the occluded skewed condition, participants on average reported
taller heights than the true mean of the sample, which is 6
(t(85) = 4.3, p < .001), while participants were
accurate and not significantly different from the true mean in all of
the other three conditions.
Population inference
To assess how tall participants thought Zarpies in general are,
participants were asked: “Which picture shows the average height of
Zarpies on Zarpie island?” Response options were a Zarpie of height 4,
5, 6, 7, or 8.
Population representation question in the skewed
condition, with the response options in red boxes.
We pre-registered that if participants adjust their inferences about
the population based on biases in the sampling process:
- Participants in the not skewed condition should infer that the
population is like the sample, since everyone was able to
board, so they should respond with something similar to sample mean,
i.e., 6.
- Participants in the skewed condition should infer the population is
taller than the sample, since Zarpies taller than the boat were
unable to board, so they should report significantly taller height than
those in the unrestricted condition.
In the occluded condition, participants reported the
population was taller in the skewed condition than the not
skewed condition (t = 3.97, p < .001),
consistent with adjustment against skew. In the visible condition,
participants reported the population was taller in the skewed
condition than the not skewed condition (t = 5.18,
p < .001), consistent with the actual height difference
between the populations they each saw.
In the visible not skewed condition, participants’ population
inferences were no different from 6, the actual population mean
(t(84) = 1.3, p = 0.198).
In contrast, in the visible skewed condition, participants’
population inferences were significantly shorter than 8, the actual
population mean (t(106) = -21.39, p < .001).
Explicit comparison
Participants were explicitly asked to compare the population to the
sample: “Do you think the Zarpies on Zarpie island are shorter,
the same, or taller in height than the Zarpies who
visited?”
We pre-registered that if adults do adjust, they should be more
likely to say “taller” in the skewed condition than the not skewed
condition for both the visible and occluded sets of conditions.
Notably, “the same” is an extremely common response across all
conditions.
| population |
boarding |
shorter |
the same |
taller |
| visible |
not skewed |
4% |
86% |
11% |
| visible |
skewed |
9% |
43% |
48% |
| occluded |
not skewed |
3% |
89% |
8% |
| occluded |
skewed |
6% |
55% |
40% |
Participants’ explicit comparisons were significantly different
between conditions (p < .001, Fisher’s exact).
##
## Call:
## glm(formula = dv_comp_taller ~ boarding, family = binomial, data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.4744 0.3681 -6.721 0.000000000018 ***
## boardingskewed 2.0496 0.4291 4.776 0.000001789462 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 200.23 on 188 degrees of freedom
## Residual deviance: 171.67 on 187 degrees of freedom
## AIC: 175.67
##
## Number of Fisher Scoring iterations: 5
##
## Call:
## glm(formula = dv_comp_same ~ boarding, family = binomial, data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.1239 0.3190 6.658 0.0000000000278 ***
## boardingskewed -1.9373 0.3856 -5.024 0.0000005057386 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 218.39 on 188 degrees of freedom
## Residual deviance: 188.47 on 187 degrees of freedom
## AIC: 192.47
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = dv_comp_shorter ~ boarding, family = binomial,
## data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.5066 0.5859 -5.984 0.00000000217 ***
## boardingskewed 0.7215 0.7454 0.968 0.333
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 66.253 on 188 degrees of freedom
## Residual deviance: 65.281 on 187 degrees of freedom
## AIC: 69.281
##
## Number of Fisher Scoring iterations: 6
In the occluded condition, participants were more likely to say that
Zarpies on Zarpie island are “taller” and less likely to say “the same”
compared to Zarpies who visited, in the skewed condition compared to the
not skewed condition. Responses that they are “shorter” were rare and
did not differ across conditions.
##
## Call:
## glm(formula = dv_comp_taller ~ boarding, family = binomial, data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.1335 0.3525 -6.052 0.00000000143 ***
## boardingskewed 2.0400 0.4021 5.073 0.00000039218 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 238.50 on 191 degrees of freedom
## Residual deviance: 205.53 on 190 degrees of freedom
## AIC: 209.53
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = dv_comp_same ~ boarding, family = binomial, data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.8056 0.3115 5.796 0.00000000678 ***
## boardingskewed -2.0878 0.3676 -5.679 0.00000001357 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 255.04 on 191 degrees of freedom
## Residual deviance: 215.43 on 190 degrees of freedom
## AIC: 219.43
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = dv_comp_shorter ~ boarding, family = binomial,
## data = .)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.3081 0.5878 -5.628 0.0000000183 ***
## boardingskewed 1.0360 0.6752 1.534 0.125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 95.105 on 191 degrees of freedom
## Residual deviance: 92.397 on 190 degrees of freedom
## AIC: 96.397
##
## Number of Fisher Scoring iterations: 6
In the visible condition, same results.
Secondary results
Sample vs population
As an implicit comparison, we can compare each participant’s sample
representation and population inference to each other.
##
## Call:
## lm(formula = response ~ boarding * dv, data = data_tidy %>% filter(population ==
## "occluded"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.38372 -0.23256 -0.04854 -0.03883 1.96117
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.048544 0.051023 118.544 <0.0000000000000002 ***
## boardingskewed 0.184014 0.075640 2.433 0.0155 *
## dvdv_pop -0.009709 0.072158 -0.135 0.8930
## boardingskewed:dvdv_pop 0.160872 0.106971 1.504 0.1335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5178 on 374 degrees of freedom
## Multiple R-squared: 0.06995, Adjusted R-squared: 0.06249
## F-statistic: 9.376 on 3 and 374 DF, p-value: 0.000005457
Within the occluded condition, there is no interaction
between the boarding condition (skewed vs not skewed) and the DV (sample
vs pop), suggesting participants in the skewed condition did
not generalize from sample to population differently than participants
in the not skewed condition.
In each of the not skewed conditions, participants did not
give different responses to sample and population questions (occluded
not skewed: t(102) = 0.3, p = 0.765, visible not
skewed: t(84) = 0.35, p = 0.726). This is expected
since in the not skewed conditions, the sample and the population are
identical.
In the visible skewed condition, participants gave taller
responses to the population than to the sample question (t(106)
= -6.83, p < .001). This is expected since in the visible
skewed condition, the population is observed to be taller than the
sample.
In the occluded skewed condition, participants did
not give different responses to the population versus sample
questions (t(85) = -1.58, p = 0.118). This
suggests that participants may not have adjusted their generalization
from the sample based on the sampling process they observed.
Sample vs population by explicit comparison
Order effects
Participants saw the two DVs in counterbalanced order:
pop_sample = population DV first, then sample DVsample_pop = sample DV first, then population DV
There were no order effects on any of the three DVs.
Sample representation order effects
The interaction between conditions on the sample representation was
consistent, regardless of DV order.
## Anova Table (Type II tests)
##
## Response: dv_sample
## Sum Sq Df F value Pr(>F)
## population 0.930 1 4.1661 0.041945 *
## boarding 0.227 1 1.0162 0.314068
## cb_dvorder 0.068 1 0.3058 0.580585
## population:boarding 1.637 1 7.3349 0.007074 **
## population:cb_dvorder 0.021 1 0.0926 0.761078
## boarding:cb_dvorder 0.015 1 0.0672 0.795566
## population:boarding:cb_dvorder 0.176 1 0.7898 0.374728
## Residuals 83.237 373
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Population inference order effects
There is no effect of DV order or interaction with DV order on
population representations.
##
## Call:
## lm(formula = dv_pop ~ population * boarding * cb_dvorder, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.26829 -0.26829 -0.04839 -0.02273 1.97727
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 6.022727 0.090233
## populationoccluded 0.001663 0.129922
## boardingskewed 0.426548 0.115472
## cb_dvordersample_pop 0.074834 0.129922
## populationoccluded:boardingskewed -0.182646 0.175526
## populationoccluded:cb_dvordersample_pop -0.050837 0.177188
## boardingskewed:cb_dvordersample_pop 0.107470 0.177480
## populationoccluded:boardingskewed:cb_dvordersample_pop 0.089129 0.250427
## t value
## (Intercept) 66.747
## populationoccluded 0.013
## boardingskewed 3.694
## cb_dvordersample_pop 0.576
## populationoccluded:boardingskewed -1.041
## populationoccluded:cb_dvordersample_pop -0.287
## boardingskewed:cb_dvordersample_pop 0.606
## populationoccluded:boardingskewed:cb_dvordersample_pop 0.356
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## populationoccluded 0.989794
## boardingskewed 0.000254 ***
## cb_dvordersample_pop 0.564968
## populationoccluded:boardingskewed 0.298752
## populationoccluded:cb_dvordersample_pop 0.774341
## boardingskewed:cb_dvordersample_pop 0.545193
## populationoccluded:boardingskewed:cb_dvordersample_pop 0.722109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5985 on 373 degrees of freedom
## Multiple R-squared: 0.1226, Adjusted R-squared: 0.1062
## F-statistic: 7.449 on 7 and 373 DF, p-value: 0.00000002143
Explicit comparison order effects
## # weights: 27 (16 variable)
## initial value 418.571282
## iter 10 value 247.873414
## iter 20 value 245.154477
## iter 30 value 245.036208
## final value 245.035637
## converged
## Call:
## multinom(formula = dv_comp ~ population * boarding * cb_dvorder,
## data = data)
##
## Coefficients:
## (Intercept) populationoccluded boardingskewed cb_dvordersample_pop
## the same 3.610184 -1.242676 -2.3737962 -0.7200521
## taller 1.790456 -1.096115 -0.6205841 -1.3845531
## populationoccluded:boardingskewed
## the same 1.441669
## taller 1.024843
## populationoccluded:cb_dvordersample_pop
## the same 12.43378
## taller 11.36994
## boardingskewed:cb_dvordersample_pop
## the same 2.192665
## taller 3.306657
## populationoccluded:boardingskewed:cb_dvordersample_pop
## the same -0.4801181
## taller 0.1574901
##
## Std. Errors:
## (Intercept) populationoccluded boardingskewed cb_dvordersample_pop
## the same 1.013025 1.179388 1.081463 1.246554
## taller 1.079789 1.290726 1.145210 1.413848
## populationoccluded:boardingskewed
## the same 1.334891
## taller 1.441608
## populationoccluded:cb_dvordersample_pop
## the same 130.2371
## taller 130.2403
## boardingskewed:cb_dvordersample_pop
## the same 1.662764
## taller 1.786296
## populationoccluded:boardingskewed:cb_dvordersample_pop
## the same 24.92392
## taller 24.92074
##
## Residual Deviance: 490.0713
## AIC: 522.0713
## Analysis of Deviance Table (Type II tests)
##
## Response: dv_comp
## LR Chisq Df Pr(>Chisq)
## population 2.456 2 0.292913
## boarding 69.809 2 0.0000000000000006938 ***
## cb_dvorder 9.985 2 0.006787 **
## population:boarding 1.241 2 0.537708
## population:cb_dvorder 7.498 2 0.023543 *
## boarding:cb_dvorder 7.726 2 0.021003 *
## population:boarding:cb_dvorder 0.248 2 0.883589
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1