CI for the Non-Centrality Parameter of the F Distribution

Based on the inversion principle, parametric CIs for the non-centrality parameter (NCP) Delta of the F distribution are calculated. To keep the input interface simple, we do not provide bootstrap CIs here.

ci_f_ncp(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))

Arguments

x

The result of stats::lm() or the F test statistic.

df1

The numerator df. Only used if x is a test statistic.

df2

The denominator df. Only used if x is a test statistic.

probs

Lower and upper probabilities, by default c(0.025, 0.975).

Value

An object of class "cint", see ci_mean() for details.

Details

A positive lower \((1 - \alpha) \cdot 100\%\)-confidence limit for the NCP goes hand-in-hand with a significant F test at level \(\alpha\). According to stats::pf(), the results might be unreliable for very large F values.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

See also

ci_rsquared()

Examples

fit <- lm(Sepal.Length ~ ., data = iris)
ci_f_ncp(fit)
#> 
#> 	Two-sided 95% F confidence interval for the non-centrality parameter of
#> 	the F-distribution
#> 
#> Sample estimate: 980.4737 
#> Confidence interval:
#>      2.5%     97.5% 
#>  704.6598 1200.8313 
#> 
ci_f_ncp(fit, probs = c(0.05, 1))
#> 
#> 	One-sided 95% F confidence interval for the non-centrality parameter of
#> 	the F-distribution
#> 
#> Sample estimate: 980.4737 
#> Confidence interval:
#>       5%     100% 
#> 738.8387      Inf 
#>