Confidence Interval for the Standardized Mean

Computes the exact confidence interval for the standardized mean, the mean divided by the standard deviation, by inverting the noncentral t distribution. The standardized mean is the one-sample analog of the standardized mean difference and shares its noncentral interval theory.

Usage

ci_sm(
  sm = NULL,
  mean = NULL,
  sd = NULL,
  ncp = NULL,
  N = NULL,
  conf_level = 0.95,
  alpha_lower = NULL,
  alpha_upper = NULL,
  ...
)

Arguments

sm

Standardized mean

mean

Mean

sd

Standard deviation

ncp

Noncentral parameter

N

Sample size

conf_level

Confidence interval coverage (i.e., 1 - Type I error rate); default is .95

alpha_lower

Type I error for the lower confidence limit

alpha_upper

Type I error for the upper confidence limit

...

Allows one to potentially include parameter values for inner functions

Value

A 3-row data.frame with columns term and value. The term values are "lower_limit" (the lower confidence limit on the standardized mean), "std_mean" (the standardized mean), and "upper_limit" (the upper confidence limit).

Details

The user must specify the standardized mean in one and only one of the three ways: a) mean and standard deviation (mean and sd), b) standardized mean (sm), and c) noncentral parameter (ncp). The confidence level must be specified in one of following two ways: using confidence interval coverage (conf_level), or lower and upper confidence limits (alpha_lower and alpha_upper). This function uses the exact confidence interval method based on noncentral t-distributions. The confidence interval for noncentral t-parameter can be obtained from the conf_limits_nct function in DMAR.

Note

The standardized mean is the mean divided by the standard deviation.

References

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08

Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See also

conf_limits_nct

Other confidence intervals for effect sizes: ci_R2(), ci_c(), ci_c_ancova(), ci_c_ancova_bp(), ci_correlation, ci_cv(), ci_eta_squared(), ci_eta_squared_generalized(), ci_eta_squared_partial(), ci_mahalanobis(), ci_omega_squared(), ci_pvaf(), ci_rc(), ci_reg_coef(), ci_rmsea(), ci_sc(), ci_sc_ancova(), ci_smd(), ci_smd_c(), ci_snr(), ci_src(), ci_srsnr(), contrast_adjusted(), plot_smd()

Author

Ken Kelley kkelley@nd.edu

Examples

ci_sm(sm = 2.037905, N = 13, conf_level = .95)
#>  term        value
#>  lower_limit 1.05 
#>  std_mean    2.04 
#>  upper_limit 3    
#> 
#> Confidence level: 95%
ci_sm(mean = 30, sd = 14.721, N = 13, conf_level = .95)
#>  term        value
#>  lower_limit 1.05 
#>  std_mean    2.04 
#>  upper_limit 3    
#> 
#> Confidence level: 95%
ci_sm(ncp = 7.347771, N = 13, conf_level = .95)
#>  term        value
#>  lower_limit 1.05 
#>  std_mean    2.04 
#>  upper_limit 3    
#> 
#> Confidence level: 95%
ci_sm(sm = 2.037905, N = 13, alpha_lower = .05, alpha_upper = 0)
#>  term        value
#>  lower_limit 1.2  
#>  std_mean    2.04 
#>  upper_limit Inf  
ci_sm(mean = 50, sd = 10, N = 25, conf_level = .95)
#>  term        value
#>  lower_limit 3.54 
#>  std_mean    5    
#>  upper_limit 6.45 
#> 
#> Confidence level: 95%