gkwreg (version 2.1.6)

WeatherTask: Weather Task with Priming and Precise and Imprecise Probabilities

Description

Data from a cognitive psychology experiment on probabilistic learning and probability judgments. Participants estimated probabilities for weather events under different priming and precision conditions.

Usage

WeatherTask

Format

A data frame with 345 observations on 4 variables:

agreement

numeric. Probability indicated by participants, or the average between minimum and maximum estimates in the imprecise condition. Response variable scaled to (0, 1).

priming

factor with levels two-fold (case prime) and seven-fold (class prime). Indicates the partition priming condition.

eliciting

factor with levels precise and imprecise (lower and upper limit). Indicates whether participants gave point estimates or interval estimates.

Details

All participants in the study were either first- or second-year undergraduate students in psychology, none of whom had a strong background in probability or were familiar with imprecise probability theories.

Task description: Participants were asked: "What is the probability that the temperature at Canberra airport on Sunday will be higher than 'specified temperature'?"

Experimental manipulations:

• Priming: Two-fold (simple binary: above/below) vs. seven-fold (multiple temperature categories)

• Eliciting: Precise (single probability estimate) vs. imprecise (lower and upper bounds)

The study examines how partition priming (number of response categories) and elicitation format affect probability judgments. Classical findings suggest that more categories (seven-fold) lead to different probability assessments than binary categories (two-fold).

References

Smithson, M., Merkle, E.C., and Verkuilen, J. (2011). Beta Regression Finite Mixture Models of Polarization and Priming. Journal of Educational and Behavioral Statistics, 36(6), 804--831. tools:::Rd_expr_doi("10.3102/1076998610396893")

Smithson, M., and Segale, C. (2009). Partition Priming in Judgments of Imprecise Probabilities. Journal of Statistical Theory and Practice, 3(1), 169--181.

Examples

# \donttest{
require(gkwreg)
require(gkwdist)

data(WeatherTask)

# Example 1: Main effects model
# Probability judgments affected by priming and elicitation format
fit_kw <- gkwreg(
  agreement ~ priming + eliciting,
  data = WeatherTask,
  family = "kw"
)
summary(fit_kw)

# Interpretation:
# - Alpha: Seven-fold priming may shift probability estimates
#   Imprecise elicitation may produce different mean estimates

# Example 2: Interaction model with heteroscedasticity
# Priming effects may differ by elicitation format
# Variability may also depend on conditions
fit_kw_interact <- gkwreg(
  agreement ~ priming * eliciting |
    priming + eliciting,
  data = WeatherTask,
  family = "kw"
)
summary(fit_kw_interact)

# Interpretation:
# - Alpha: Interaction tests if partition priming works differently
#   for precise vs. imprecise probability judgments
# - Beta: Precision varies by experimental condition

# Test interaction
anova(fit_kw, fit_kw_interact)

# Example 3: McDonald distribution for polarized responses
# Probability judgments often show polarization (clustering at extremes)
# particularly under certain priming conditions
fit_mc <- gkwreg(
  agreement ~ priming * eliciting | # gamma
    priming * eliciting | # delta
    priming, # lambda: priming affects polarization
  data = WeatherTask,
  family = "mc",
  control = gkw_control(method = "BFGS", maxit = 1500)
)
summary(fit_mc)

# Interpretation:
# - Lambda varies by priming: Seven-fold priming may produce more
#   extreme/polarized probability judgments
# }