The theory is applicable when there is sufficient agreement across people to assume that a single set of answers exists.
The problem addressed by cultural consensus theory is how to estimate beliefs when there is some degree of heterogeneity present in responses.
Although there are statistical methods to evaluate whether agreement among raters is greater than chance (Binomial test, Friedman test, or Kendall's coefficient of concordance), these methods do not provide a best estimate of the “true” answers nor do they estimate competence of the raters.
[6][8] The formal model has direct parallels in signal detection theory and latent class analysis.
Simple match or covariance measures are then corrected for guessing and the proportion of positive responses, respectively.
To determine whether the solution meets cultural consensus criteria, that only a single factor is present, a goodness of fit rule is used.
Individual competence values are used to weight the responses and estimate the culturally correct answers.
In the formal model, a confidence level (Bayesian adjusted probabilities) is obtained for each answer from the pattern of responses and the individual competence scores.
Also, note that factor scores are usually provided as standardized variables (mean of zero), but may be transformed back to your original data collection units.
Similarly, sample size can be estimated with reliability theory and the Spearman–Brown prophecy formula (applied to people instead of items).
For a relatively low level of agreement (an average correlation of .25 between people, comparable to an average competence of .50) and a high degree of desired validity (.95 correlation between the estimated answers and the true answers), a study would require a minimum sample size of 30 subjects.
The model proceeds from axioms and uses mathematical proofs to arrive at estimates of competence and answers to a series of questions.
Given a series of related questions, the agreement between people's reported answers is used to estimate their cultural competence.