Perception of points in a swarm

Five raters were asked to guess the number of points in a swarm for 10 different figures (which - unknown to the raters - were each repeated three times).

Format

A data frame with 30 observations on the following 6 variables.

SAND

The true number of points in the swarm. Each picture is replicated thrice

ME

Ratings from judge 1

TM

Ratings from judge 2

AJ

Ratings from judge 3

BM

Ratings from judge 4

LO

Ratings from judge 5

Source

Collected by Claus Ekstrom.

Details

The raters har approximately 10 seconds to judge each picture, and the thought it was 30 different pictures. Before starting the experiment they were shown 6 (unrelated) pictures and were told the number of points in each of those pictures. The SAND column contains the picture id and the true number of points in the swarm.

Examples

data(rainman)
long <- data.frame(stack(rainman[,2:6]), figure=factor(rep(rainman$SAND,5)))
figind <- interaction(long$figure,long$ind)
# Use a linear random effect model from the
# lme4 package if available
if(require(lme4)) {
  model <- lmer(values ~ (1|ind) + (1|figure) + (1|figind), data=long)
}

#
# Point swarms were generated by the following program
#

set.seed(2) # Original
npoints <- sample(4:30)*4
nplots <- 10
pdf(file="swarms.pdf", onefile=TRUE)

s1 <- sample(npoints[1:nplots])
print(s1)
#>  [1] 120  48  88  32  24 100  52  80  72  96
for (i in 1:nplots) {
  n <- s1[i]
  set.seed(n)
  x <- runif(n)
  y <- runif(n)
  plot(x,y, xlim=c(-.15, 1.15), ylim=c(-.15, 1.15), pch=20, axes=FALSE,
       xlab="", ylab="")
}
s1 <- sample(npoints[1:nplots])
print(s1)
#>  [1]  48  24  96 100  52  80  88  72 120  32
for (i in 1:nplots) {
  n <- s1[i]
  set.seed(n)
  x <- runif(n)
  y <- runif(n)
  plot(y,x, xlim=c(-.15, 1.15), ylim=c(-.15, 1.15), pch=20, axes=FALSE,
       xlab="", ylab="")
}
s1 <- sample(npoints[1:nplots])
print(s1)
#>  [1]  72  48  24  32  96  52 120  80 100  88
for (i in 1:nplots) {
  n <- s1[i]
  set.seed(n)
  x <- runif(n)
  y <- runif(n)
  plot(-x,y, xlim=c(-1.15, .15), ylim=c(-.15, 1.15), pch=20, axes=FALSE,
       xlab="", ylab="")
}
dev.off()
#> quartz 
#>      2