Critical CVR value for a given panel size

Returns the minimum Content Validity Ratio considered statistically significant for a panel of N experts at the specified alpha level. The calculation uses the exact binomial distribution under the null hypothesis that each expert independently rates "essential" with probability 0.5, following the corrected approach of Wilson, Pan, and Schumsky (2012).

Usage

cvr_critical(n_experts, alpha = 0.05)

Arguments

n_experts

Positive integer. Number of experts on the panel.

alpha

Numeric. One-tailed significance level. Defaults to 0.05.

Value

Numeric. The critical CVR value. CVR values at or above this threshold are statistically significant. Returns NA_real_ if no CVR value can reach significance at the specified alpha (which can happen for very small panels with stringent alpha).

Details

The critical value is determined as the smallest \(k\) such that \(P(X \geq k) \leq \alpha\) when \(X \sim Binomial(N, 0.5)\), then transformed to the CVR scale via \(CVR_{crit} = (k - N/2) / (N/2)\).

Wilson, Pan, and Schumsky (2012) demonstrated that Lawshe's (1975) original critical-value table contained errors, especially for small panels. The exact binomial computation used here is their recommended replacement.

References

Wilson, F. R., Pan, W., & Schumsky, D. A. (2012). Recalculation of the critical values for Lawshe's content validity ratio. Measurement and Evaluation in Counseling and Development, 45(3), 197-210. doi:10.1177/0748175612440286

See also

cvr()

Examples

cvr_critical(10)         # 0.80 -- need 9 of 10 experts to call it essential
#> [1] 0.8
cvr_critical(20)         # 0.50
#> [1] 0.5
cvr_critical(40)         # 0.25
#> [1] 0.3
cvr_critical(10, alpha = 0.01)
#> [1] 1