DMAR (version 1.0.0)

ci_c: Confidence Interval for a Contrast in a Fixed Effects ANOVA

Description

Computes the confidence interval for an unstandardized contrast of means in a fixed effects analysis of variance, so a focused comparison among groups (a pairwise difference or any weighted combination of the means) is reported with its precision and in the units of the response. Homogeneity of variance is assumed, as in the ANOVA on which s_anova is based.

Usage

ci_c(
  means = NULL,
  s_anova = NULL,
  c_weights = NULL,
  n = NULL,
  N = NULL,
  psi = 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 population contrast), "contrast" (the estimated unstandardized 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 (choose 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 level of the particular factor (if length 1 it is assumed that the per group/level sample sizes are equal)

N

Total sample size

psi

The contrast effect, obtained by multiplying the jth mean by the jth contrast weight.

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

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.

...

Allows one to potentially include parameter values for inner 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")

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons of means.)

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_sc

Other confidence intervals for effect sizes: ci_R2(), 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_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 contrast of interest here is the average of groups 1 and 4 versus the
# average of groups 2 and 3.
ci_c(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_c(means = c(1.6, 0), s_anova = .80, c_weights = c(1, -1),
n = c(10, 10), N = 20, conf_level = .95)

# An example given by Maxwell, Delaney, & Kelley (2027) :
# 20 subjects of mild hypertensives are assigned to one of four treatments: drug
# therapy, biofeedback, dietary modification, and a treatment combining all the
# three previous treatments. Subjects' blood pressure is measured two weeks
# after the termination of treatment. Now we want to form a 95% level
# confidence interval for the difference in blood pressure between subjects
# who received drug treatment and those who received biofeedback treatment

## Drug group's mean = 94; group size=4
## Biofeedback group's mean = 91; group size=6
## Diet group's mean = 92; group size=5
## Combination group's mean = 83; group size=5
## Mean Square Within (i.e., 'error_variance') = 67.375

ci_c(means = c(94, 91, 92, 83), s_anova = sqrt(67.375), c_weights = c(1, -1, 0, 0),
n = c(4, 6, 5, 5), N = 20, conf_level = .95)