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Sample Size Planning for a Contrast in Randomized ANCOVA From the Accuracy in Parameter Estimation (AIPE) Perspective

Source: R/ss_aipe_c_ancova.R
ss_aipe_c_ancova.Rd

Plans the sample size per group so that the confidence interval for an unstandardized contrast in a one-covariate randomized ANCOVA is sufficiently narrow, following the accuracy in parameter estimation (AIPE) approach. To the extent the covariate correlates with the response, the covariate adjustment shrinks the error variance, so the desired precision is reached with a smaller sample size than the corresponding ANOVA design requires.

Usage

ss_aipe_c_ancova(
  error_var_ancova = NULL,
  error_var_anova = NULL,
  rho = NULL,
  c_weights,
  width,
  conf_level = 0.95,
  assurance = NULL
)

Arguments

error_var_ancova

The population error variance of the ANCOVA model (i.e., the mean square within of the ANCOVA model)

error_var_anova

The population error variance of the ANOVA model (i.e., the mean square within of the ANOVA model)

rho

The population correlation coefficient of the response and the covariate

c_weights

The contrast weights

width

The desired full width of the obtained confidence interval

conf_level

The desired confidence interval coverage, (i.e., 1 - Type I error rate)

assurance

Parameter to ensure that the obtained confidence interval width is narrower than the desired width with a specified degree of certainty (must be NULL or between zero and unity)

Value

A 1-row data.frame with columns term and value:

necessary_n_per_group

The necessary sample size per group

Details

Either the error variance of the ANCOVA model or of the ANOVA model can be used to plan the appropriate sample size per group. When using the error variance of the ANOVA model to plan sample size, the correlation coefficient of the response and the covariate is also needed.

References

Kelley, K., Maxwell, S. E., & Rausch, J. R. (2003). Obtaining power or obtaining precision: Delineating methods of sample size planning. Evaluation and the Health Professions, 26(3), 258–287. doi:10.1177/0163278703255242

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. 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 9.)

See also

ci_c_ancova, ci_sc_ancova, ss_aipe_c

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Author

Ken Kelley kkelley@nd.edu

Examples

# Suppose the population error variance of some three-group ANOVA model
# is believed to be 40, and the population correlation coefficient
# of the response and the covariate is 0.22. The researcher is
# interested in the difference between the mean of group 1 and
# the average of means of group 2 and 3. To plan the sample size so
# that, with 90 percent certainty, the obtained 95 percent full
# confidence interval width is no wider than 3:

ss_aipe_c_ancova(error_var_anova = 40, rho = .22, c_weights = c(1, -0.5, -0.5),
                 width = 3, assurance = .90)
#>  term                  value
#>  necessary_n_per_group 109  
#> 
#> Confidence level: 95%