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Sample Size Planning for an ANOVA Contrast From the Accuracy in Parameter Estimation (AIPE) Perspective

Source: R/ss_aipe_c.R
ss_aipe_c.Rd

Plans the sample size per group so that the confidence interval for an unstandardized contrast of means in a fixed effects analysis of variance is sufficiently narrow, following the accuracy in parameter estimation (AIPE) approach: the design goal is a contrast estimated with the precision the research question requires, not merely one detected as nonzero. AIPE sample size planning for ANOVA and ANCOVA contrasts is developed in Lai and Kelley (2012).

Usage

ss_aipe_c(
  error_variance = NULL,
  c_weights,
  width,
  conf_level = 0.95,
  assurance = NULL,
  MSwithin = NULL,
  SD = NULL,
  ...
)

Arguments

error_variance

The common error variance; i.e., the mean square error

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)

MSwithin

An alias for error_variance

SD

The standard deviation of the common error in ANOVA model

...

Allows one to potentially include parameter values for inner functions

Value

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

necessary_n_per_group

the necessary sample size per group

Note

Be sure to use the error variance and not its square root (i.e., the standard deviation of the errors).

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 also

ss_aipe_sc, ss_aipe_c_ancova, ci_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. 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(error_variance = 40, c_weights = c(1, -0.5, -0.5),
          width = 3, assurance = .90)
#>  term                  value
#>  necessary_n_per_group 114  
#> 
#> Confidence level: 95%