TreeBUGS (version 1.5.0)

testHetChi: Chi-Square Test of Heterogeneity

Description

Tests whether whether participants (items) are homogeneous under the assumption of item (participant) homogeneity.

Usage

testHetChi(freq, tree)

Arguments

freq

matrix with observed frequencies (rows: persons/items; columns: categories). Can also be the path to a .csv file with frequencies (comma-separated; first line defines category labels)

tree

a vector defining which columns of x belong to separate multinomial distributions (i.e., MPT trees). For instance, if x has five categories from two MPT trees: tree=c(1,1,2,2,2) or tree=c("t1","t1","t2","t2","t2")

Author

Daniel W. Heck

Details

If an item/person has zero frequencies on all categories in an MPT tree, these zeros are neglected when computing mean frequencies per column. As an example, consider a simple recognition test with a fixed assignments of words to the learn/test list. In such an experiment, all learned words will result in hits or misses (i.e., the MPT tree of old items), whereas new words are always false alarms/correct rejections and thus belong to the MPT tree of new items (this is not necessarily the case if words are assigned randomly).

Note that the test assumes independence of observations and item homogeneity when testing participant heterogeneity. The latter assumption can be dropped when using a permutation test (testHetPerm).

References

Smith, J. B., & Batchelder, W. H. (2008). Assessing individual differences in categorical data. Psychonomic Bulletin & Review, 15, 713-731. tools:::Rd_expr_doi("10.3758/PBR.15.4.713")

See Also

testHetPerm, plotFreq

Examples

# some made up frequencies:
freq <- matrix(
  c(
    13, 16, 11, 13,
    15, 21, 18, 13,
    21, 14, 16, 17,
    19, 20, 21, 18
  ),
  ncol = 4, byrow = TRUE
)
# for a product-binomial distribution:
# (categories 1 and 2 and categories 3 and 4 are binomials)
testHetChi(freq, tree = c(1, 1, 2, 2))
# => no significant deviation from homogeneity (low power!)