DMAR (version 1.0.0)

ci_sc: Confidence Interval for a Standardized Contrast in a Fixed Effects ANOVA

Description

Computes the exact noncentral t-based confidence interval for a standardized contrast of means in a fixed effects analysis of variance: the contrast of interest divided by the error standard deviation, so groups measured in raw units are compared on a common standardized scale.

Usage

ci_sc(
  means = NULL,
  s_anova = NULL,
  c_weights = NULL,
  n = NULL,
  N = NULL,
  psi = NULL,
  ncp = NULL,
  conf_level = 0.95,
  alpha_lower = NULL,
  alpha_upper = NULL,
  df_error = NULL,
  ...
)

Value

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

Arguments

means

A vector of the group means or the means of the particular level of the effect (for fixed effect designs)

s_anova

The standard deviation of the errors from the ANOVA model (i.e., the square root of the mean square error)

c_weights

The contrast weights (chose weights so that the positive c-weights sum to 1 and the negative c-weights sum to -1; i.e., use fractional values not integers).

n

Sample sizes per group or sample sizes for the level of the particular factor (if length 1 it is assumed that the sample size per group or for the level of the particular factor are are equal)

N

Total sample size

psi

The (unstandardized) contrast effect, obtained by multiplying the jth mean by the jth contrast weight (this is the unstandardized effect)

ncp

The noncentrality parameter from the t-distribution

conf_level

Desired level of confidence for the computed interval (i.e., 1 - the Type I error rate)

alpha_lower

The Type I error rate for the lower confidence interval limit

alpha_upper

The Type I error rate for the upper confidence interval limit

df_error

The degrees of freedom for the error. In one-way designs, this is simply N-length (means) and need not be specified; it must be specified if the design has multiple factors.

...

Optional additional specifications for nested functions

Author

Ken Kelley [email protected]

References

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

Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 350--370. tools:::Rd_expr_doi("10.1111/j.2044-8317.2011.02029.x")

Steiger, J. H. (2004). Beyond the F Test: Effect size confidence intervals and tests of close fit in the Analysis of Variance and Contrast Analysis. Psychological Methods, 9(2), 164--182. tools:::Rd_expr_doi("10.1037/1082-989X.9.2.164")

See Also

ci_nc_t, ci_src, ci_smd, ci_smd_c, ci_sm, ci_c ci_c_ancova

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_ancova(), ci_sm(), ci_smd(), ci_smd_c(), ci_snr(), ci_src(), ci_srsnr(), contrast_adjusted(), plot_smd()

Examples

# Here is a four group example. Suppose that the means of groups 1--4 are 2, 4, 9,
# and 13, respectively. Further, let the error variance be .64 and thus the standard
# deviation would be .80 (note we use the standard deviation in the function, not the
# variance). The standardized contrast of interest here is the average of groups 1 and 4
# versus the average of groups 2 and 3.

ci_sc(means = c(2, 4, 9, 13), s_anova = .80, c_weights = c(.5, -.5, -.5, .5),
      n = c(3, 3, 3, 3), N = 12, conf_level = .95)

# Here is an example with two groups.
ci_sc(means = c(1.6, 0), s_anova = .80, c_weights = c(1, -1),
      n = c(10, 10), N = 20, conf_level = .95)