heaviness {eba}

Weights Judging Data

Description

Beaver and Gokhale (1975) presented fifty subjects with all 20 ordered pairs of bottles filled with lead shot and asked them to choose the bottle that felt heavier. The mass of the bottles was 90, 95, 100, 105, and 110 grams, respectively. Choice frequencies were aggregated across subjects for the two within-pair presentation orders.

Usage

data(heaviness)

Format

A 3d array consisting of two square matrices:

heaviness[, , order = 1]

holds the choices where the row stimulus was presented first for each pair (in the upper triangle, and vice versa in the lower triangle).

heaviness[, , order = 2]

holds the choices where the column stimulus was presented first for each pair (in the upper triangle, and vice versa in the lower triangle).

Source

Beaver, R.J., & Gokhale, D.V. (1975). A model to incorporate within-pair order effects in paired comparisons. Communications in Statistics, 4, 923–939. doi: 10.1080/03610927308827302

See Also

eba.order for a model that includes a within-pair order effect.

Examples

data(heaviness)
## 6 subjects chose 90g over 100g, when 90g was presented first.
heaviness["90g", "100g", order=1]

## 44 subjects chose 100g over 90g, when 90g was presented first.
heaviness["100g", "90g", order=1]

## 14 subjects chose 90g over 100g, when 90g was presented second.
heaviness["90g", "100g", order=2]

## 36 subjects chose 100g over 90g, when 90g was presented second.
heaviness["100g", "90g", order=2]

## Bradley-Terry-Luce (BTL) model for each within-pair order
btl1 <- eba(heaviness[, , 1])
btl2 <- eba(heaviness[, , 2])

xval <- seq(90, 110, 5)
plot(uscale(btl1) ~ xval, type="n", log="y",
     xlab="Mass of lead shot filled bottle (in g)",
     ylab="Perceived heaviness (BTL model)",
     main="Weights judging experiment")
mtext("(Beaver and Gokhale, 1975)", line=.5)

arrows(xval, uscale(btl1) - 1.96*sqrt(diag(cov.u(btl1))),
       xval, uscale(btl1) + 1.96*sqrt(diag(cov.u(btl1))), .05, 90, 3, "gray")
arrows(xval, uscale(btl2) - 1.96*sqrt(diag(cov.u(btl2))),
       xval, uscale(btl2) + 1.96*sqrt(diag(cov.u(btl2))), .05, 90, 3, "gray")

points(uscale(btl1) ~ xval, type="b", pch=16)
points(uscale(btl2) ~ xval, type="b", lty=2, pch=21, bg="white")

text(90.3, .01,  "Lower weight judged first", adj=0)
text(90.3, .08, "Higher weight judged first", adj=0)