Conversion from Means and Standard Deviations to Cohen's f and Eta-squared

Calculates Cohen's f or Eta-squared for one-way ANOVA/ANCOVA. Set k.cov = 0 for one-way ANOVA (without any pretest or covariate adjustment). Set k.cov > 0 in combination with r.squared > 0 for one-way ANCOVA (with pretest or covariate adjustment).

Usage

means.to.etasq(
  mu.vector,
  sd.vector,
  n.vector,
  k.covariates = 0,
  r.squared = 0,
  factor.levels = NULL,
  verbose = 1
)

Arguments

mu.vector

vector of adjusted means (or estimated marginal means) for each level of a factor.

sd.vector

vector of unadjusted standard deviations for each level of a factor.

n.vector

vector of sample sizes for each level of a factor.

k.covariates

integer; number of covariates in the ANCOVA model. The default is k.covariates = 0, which means an ANOVA model would be of interest.

r.squared

explanatory power of covariates (R-squared) in the ANCOVA model. The default is r.squared = 0, which means an ANOVA model would be of interest.

factor.levels

integer; number of levels or groups in each factor. For example, for two factors each having two levels or groups use e.g. c(2, 2), for three factors each having two levels or groups use e.g. c(2, 2, 2)

verbose

1 by default (returns results), if 0 no output is printed on the console.

Value

f

Cohen's f

eta.squared

(partial) eta-squared.

df1

numerator degrees of freedom.

df2

denominator degrees of freedom.

ncp

non-centrality parameter under alternative.

Details

Note that R has a partial matching feature which allows you to specify shortened versions of arguments, such as mu or mu.vec instead of mu.vector, or such as k or k.cov instead of k.covariates.

References

Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher's handbook (4th ed.). Pearson.

Examples

means.to.etasq(mu.vector = c(0.50, 0), # marginal means
               sd.vector = c(1, 1), # unadjusted standard deviation
               n.vector = c(33, 33), # sample size (will be calculated)
               k.cov = 1, # number of covariates
               r.squared = 0.50)
#>           f eta.squared         df1         df2         ncp 
#>   0.3535534   0.1111111   1.0000000  63.0000000   8.2500000