Exact item-sort significance test

Tests whether the number of assignments to an item's intended construct exceeds the count expected under a binomial chance model. With the default p0 = 0.5, this implements the Howard and Melloy (2016) retention test for item-sort tasks by testing the target-assignment count directly. Unlike the legacy critical-Csv procedure, the count-based test remains applicable when respondents choose among more than two construct alternatives.

The function name is retained for backward compatibility even though the inferential test is performed on n_c, not on the observed Csv value.

Usage

csv_binom_test(n_c, N, p0 = 0.5, alpha = 0.05)

Arguments

n_c

Integer; number of non-missing assignments to the target construct.

N

Integer; total number of non-missing assignments for the item.

p0

Null target-assignment probability. Default 0.5, following Howard and Melloy (2016).

alpha

Significance level. Default 0.05.

Value

A list containing the exact p-value, observed target proportion, one-sided confidence interval, the minimum critical target count, a logical passes_chance flag, a backward-compatible decision label, and a plain-language interpretation.

References

Howard, M. C., & Melloy, R. C. (2016). Evaluating item-sort task methods: The presentation of a new statistical significance formula and methodological best practices. Journal of Business and Psychology, 31(1), 173-186. doi:10.1007/s10869-015-9404-y

Examples

csv_binom_test(n_c = 15, N = 20)
#> $p.value
#> [1] 0.02069473
#> 
#> $estimate
#> [1] 0.75
#> 
#> $conf.int
#> [1] 0.5444176 1.0000000
#> attr(,"conf.level")
#> [1] 0.95
#> 
#> $critical_n_target
#> [1] 15
#> 
#> $passes_chance
#> [1] TRUE
#> 
#> $decision
#> [1] "significant"
#> 
#> $interpretation
#> [1] "Target assignments exceed the exact chance criterion."
#> 
csv_binom_test(n_c = 14, N = 20)
#> $p.value
#> [1] 0.05765915
#> 
#> $estimate
#> [1] 0.7
#> 
#> $conf.int
#> [1] 0.4921816 1.0000000
#> attr(,"conf.level")
#> [1] 0.95
#> 
#> $critical_n_target
#> [1] 15
#> 
#> $passes_chance
#> [1] FALSE
#> 
#> $decision
#> [1] "n.s."
#> 
#> $interpretation
#> [1] "Target assignments do not exceed the exact chance criterion."
#>