Calculates confidence interval for partial eta-squared in a fixed-effects ANOVA

get.ci.partial.eta.squared() calculates the confidence interval for partial eta-squared from an F-value and the degrees of freedom for it, for an effect in a fixed-effects ANOVA. apa.aov.table uses it for the intervals in the ANOVA table.

Usage

get.ci.partial.eta.squared(F.value, df1, df2, conf.level = 0.9)

Arguments

F.value: The F-value for the fixed effect.
df1: Degrees of freedom for the fixed effect.
df2: Degrees of freedom for error.
conf.level: Confidence level (0 to 1). For partial eta-squared a confidence level of .90 is traditionally used rather than .95.

Value

A list with the lower (LL) and upper (UL) limits of the interval.

Details

The interval is found for the noncentrality parameter (lambda) of the F distribution with MBESS::conf.limits.ncf(), and each limit is converted to partial eta-squared as lambda / (lambda + df1 + df2 + 1), the approach described by Smithson (2001) and Fidler and Thompson (2001). A lower limit that cannot be found is set to 0, and an upper limit to 1.

References

Fidler, F., & Thompson, B. (2001). Computing correct confidence intervals for ANOVA fixed- and random-effects effect sizes. Educational and Psychological Measurement, 61(4), 575-604.

Smithson, M. (2001). Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals. Educational and Psychological Measurement, 61(4), 605-632.

Examples

# Smithson (2001) p. 619, with the published 90% intervals
# row effect: published [.0117, .2801]
get.ci.partial.eta.squared(F.value = 6.00, df1 = 1, df2 = 42, conf.level = .90)
#> $LL
#> [1] 0.01170243
#> 
#> $UL
#> [1] 0.2801166
#> 
# column effect: published [.0174, .3577]
get.ci.partial.eta.squared(F.value = 2.65, df1 = 6, df2 = 42, conf.level = .90)
#> $LL
#> [1] 0.01744483
#> 
#> $UL
#> [1] 0.3577174
#> 
# interaction: published [.0093, .3455]; this gives [.0094, .3455], the
# difference being rounding in the fourth decimal
get.ci.partial.eta.squared(F.value = 2.50, df1 = 6, df2 = 42, conf.level = .90)
#> $LL
#> [1] 0.009356531
#> 
#> $UL
#> [1] 0.3455225
#> 

# Fidler & Thompson (2001) Fixed Effects 2x4 p. 594 (Table 6) / p. 596 (Table 8)
get.ci.partial.eta.squared(F.value = 1.50, df1 = 1, df2 = 16, conf.level = .90)
#> $LL
#> [1] 0
#> 
#> $UL
#> [1] 0.3166901
#> 
get.ci.partial.eta.squared(F.value = 4.00, df1 = 3, df2 = 16, conf.level = .90)
#> $LL
#> [1] 0.03574041
#> 
#> $UL
#> [1] 0.5670909
#> 
get.ci.partial.eta.squared(F.value = 1.50, df1 = 3, df2 = 16, conf.level = .90)
#> $LL
#> [1] 0
#> 
#> $UL
#> [1] 0.3777952
#>