Trend target: 20, Cluster target: 11 
Lineups consist of \(M\) plots (usually 20) which are evaluated by \(K\) individuals.
We can examine visual statistics (plots) and conduct tests using participant plot evaluations.
If most participants select a single plot, we conclude there's a visually significant difference.
Andrew Gelman proposed a lessformalized method of posterior predictive model checking in a [JCGS discussion article](http://www.stat.columbia.edu/~gelman/research/published/p755.pdf) in 2004
We reject \(H_0\) if the calculated pvalue is less than 0.05
vinference
R package calculates pvalues accounting for this scenario (using simulation)V3
reference distribution are used for comparison purposes in this studyThis model accounts for all panels in a lineup
The marginal distributions of the Multinomial model reduce to BetaBinomials, each representing one panel of the lineup.
We will mostly work with the betabinomial/marginal models
Allow the evaluation data to dominate any prior beliefs
We strongly believe all plots are equal
But perhaps some plots are more equal than other plots?
We compare Model 1 to Model 2 using Bayes Factors



100
iterations of:
20
evaluations20
V3
pvalue for each scenario