mean_compare: Mean differences for a single variable across 3+ independent groups (one-way ANOVA)

Description

mean_compare compares means across 3+ independent groups with a one-way ANOVA. The function also calculates the descriptive statistics for each group and the variance explained (i.e., R^2 aka eta^2) by the nominal grouping variable. mean_compare is simply a wrapper for oneway.test plus some extra calculations. mean_compare will work with 2 independent groups; however it arguably makes more sense to use mean_diff in that case.

Usage

mean_compare(
  x,
  nom,
  lvl = levels(as.factor(nom)),
  var.equal = TRUE,
  r2.ci.type = "Fdist",
  ci.level = 0.95,
  rtn.table = TRUE,
  check = TRUE
)

Value

list of numeric vectors containing statistical information about the mean comparison: 1) nhst = one-way ANOVA stat info in a numeric vector, 2) desc = descriptive statistics stat info in a numeric vector, 3) std = standardized effect sizes stat info in a numeric vector, 4) anova = traditional ANOVA table in a numeric matrix (only returned if rtn.table = TRUE).

1) nhst = one-way ANOVA stat info in a numeric vector

diff_avg: average mean difference across group pairs

NA to remind the user there is no standard error for the average mean difference

F-value

df_num

numerator degrees of freedom

df_den

denominator degrees of freedom

two-sided p-value

2) desc = descriptive statistics stat info in a numeric vector (note there could be more than 3 groups - groups i, j, and k are just provided as an example)

mean_`lvl[k]`: mean of group k

mean_`lvl[j]`

mean of group j

mean_`lvl[i]`

mean of group i

sd_`lvl[k]`

standard deviation of group k

sd_`lvl[j]`

standard deviation of group j

sd_`lvl[i]`

standard deviation of group i

n_`lvl[k]`

sample size of group k

n_`lvl[j]`

sample size of group j

n_`lvl[i]`

sample size of group i

3) std = standardized effect sizes stat info in a numeric vector

r2_reg_est: R^2 estimate

r2_reg_se

R^2 standard error (only available if r2.ci.type = "classic")

r2_reg_lwr

R^2 lower bound of the confidence interval

r2_reg_upr

R^2 upper bound of the confidence interval

r2_adj_est

R^2-adjusted estimate

r2_adj_se

R^2-adjusted standard error (only available if r2.ci.type = "classic")

r2_adj_lwr

R^2-adjusted lower bound of the confidence interval

r2_adj_upr

R^2-adjusted upper bound of the confidence interval

4) anova = traditional ANOVA table in a numeric matrix (only returned if rtn.table = TRUE).

The dimlabels of the matrix was "effect" for the rows and "info" for the columns. There are two rows with rownames 1. "nom" and 2. "Residuals" where "nom" refers to the between-group effect of the nominal variable and "Residuals" refers to the within-group residual errors. There are 5 columns with colnames 1. "SS" = sum of squares, 2. "df" = degrees of freedom, 3. "MS" = mean squares, 4. "F" = F-value. and 5. "p" = p-value. Note the F-value and p-value will differ from the "nhst" returned vector if var.equal = FALSE because the traditional ANOVA table always assumes variances are equal (i.e. var.equal = TRUE).

Arguments

x: numeric vector.
nom: atomic vector (e.g., factor) the same length as x that is a nominal variable. It identifies the 3+ groups with 3+ unique values (other than missing values).
lvl: character vector with length 3+ specifying the unique values for the 3+ groups. If nom is a factor, then lvl should be the factor levels rather than the underlying integer codes. This argument allows you to specify the order of the descriptive statistics in the return object, which will be opposite the order of lvl for consistency with mean_diff and mean_change.
var.equal: logical vector of length 1 specifying whether the variances of the groups are assumed to be equal (TRUE) or not (FALSE). If TRUE, a traditional one-way ANOVA is computed; if FALSE, Welch's ANOVA is computed. These two tests differ by their denominator degrees of freedom, F-value, and p-value.
r2.ci.type: character vector with length 1 specifying the type of confidence intervals to compute for the variance explained (i.e., R^2 aka eta^2). There are currently two options: 1) "Fdist" which calculates a non-symmetrical confidence interval based on the non-central F distribution (pg. 38, Smithson, 2003), 2) "classic" which calculates the confidence interval based on a large-sample theory standard error (eq. 3.6.3 in Cohen, Cohen, West, & Aiken, 2003), which is taken from Olkin & Finn (1995) - just above eq. 10. The confidence intervals for R^2-adjusted use the same formula as R^2, but replace R^2 with R^2 adjusted. Technically, the R^2 adjusted confidence intervals can have poor coverage (pg. 54, Smithson, 2003)
ci.level: numeric vector of length 1 specifying the confidence level. ci.level must range from 0 to 1.
rtn.table: logical vector of length 1 specifying whether the traditional ANOVA table should be returned as the last element of the return object.
check: logical vector of length 1 specifying whether the input arguments should be checked for errors. For example, if nom has length different than the length of x. This is a tradeoff between computational efficiency (FALSE) and more useful error messages (TRUE).

References

Cohen, J., Cohen, P., West, A. G., & Aiken, L. S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Science - third edition. New York, NY: Routledge.

Olkin, I., & Finn, J. D. (1995). Correlations redux. Psychological Bulletin, 118(1), 155-164.

Smithson, M. (2003). Confidence intervals. Thousand Oaks, CA: Sage Publications.

Examples

Run this code


mean_compare(x = mtcars$"mpg", nom = mtcars$"gear")
mean_compare(x = mtcars$"mpg", nom = mtcars$"gear", var.equal = FALSE)
mean_compare(x = mtcars$"mpg", nom = mtcars$"gear", rtn.table = FALSE)
mean_compare(x = mtcars$"mpg", nom = mtcars$"gear", r2.ci.type = "classic")