Primary results
Sample representation
As a check for their representation of the observed sample (fixed across conditions: 6 Zarpies of heights 4, 5, 6, 6, 7, 8), participants were asked: “Which picture shows how tall most of the Zarpies who visited are?” Response options were a Zarpie of height 4, 6, or 8.
The expected answer to this question is 6 (indicated by the dashed line on the below plot), since 6 is the mode of the observed sample (fixed across conditions: 6 Zarpies of heights 4, 5, 6, 6, 7, 8).
As expected, there was no main effect of boat height on sample representations (in a simple linear regression), since all participants observed the same sample (6 Zarpies: 4, 5, 6, 6, 7, 8).
lm(dv_sample ~ boatheight,
data = data) %>%
summary()##
## Call:
## lm(formula = dv_sample ~ boatheight, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1545 -0.2454 -0.2150 -0.1545 1.8456
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.97263 0.39964 14.945 <0.0000000000000002 ***
## boatheight 0.03030 0.04914 0.617 0.539
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6915 on 91 degrees of freedom
## Multiple R-squared: 0.004161, Adjusted R-squared: -0.006783
## F-statistic: 0.3802 on 1 and 91 DF, p-value: 0.539Slightly surprisingly, participants overall reported the sample to be slightly taller than 6, the true mode.
t.test(data %>%
select(dv_sample),
mu = 6) # true mean of observed sample##
## One Sample t-test
##
## data: data %>% select(dv_sample)
## t = 3.0092, df = 92, p-value = 0.00338
## alternative hypothesis: true mean is not equal to 6
## 95 percent confidence interval:
## 6.073116 6.356992
## sample estimates:
## mean of x
## 6.215054Population inferences
To assess their inferences about the population, participants were asked: “Which picture shows how tall most Zarpies are on Zarpie island?” Response options were a Zarpie of height 4, 6, or 8.
The use of “most” was intended to be a child-friendly version of eliciting the mean/average of a distribution.
Unexpectedly, there was a significant positive effect of boat height on inferences of population height (in a simple linear regression). That is, participants who saw a taller boat thought Zarpies in general were also slightly taller. This effect, however, is pretty small.
lm(dv_pop ~ boatheight,
data = data) %>%
summary()##
## Call:
## lm(formula = dv_pop ~ boatheight, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.15836 -0.40078 -0.15836 -0.03715 1.96285
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.30987 0.46067 11.53 <0.0000000000000002 ***
## boatheight 0.12121 0.05665 2.14 0.0351 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7971 on 91 degrees of freedom
## Multiple R-squared: 0.0479, Adjusted R-squared: 0.03744
## F-statistic: 4.578 on 1 and 91 DF, p-value: 0.03506Some speculation about why there is a small but positive effect:
participants could be engaging in just-world/justificatory reasoning, where the boat is designed to be optimal for Zarpies, and thus signals something about Zarpie height.
participants could be engaging in perceptual scaling of stimuli to everything else on screen, including the boat. The boat is on-screen during the population inference DV, as a visual reminder of the boat height. Perceptually, a taller boat may make a taller Zarpie look more “proportional”?
