Effect Sizes for Meta-Analysis of Interactions from Factorial Experiments

Compute effect sizes and their sampling variances from factorial experimental designs. The package supports calculation of simple effects, overall effects, and interaction effects for use in factorial meta-analyses. See Gurevitch et al. (2000) , Morris et al. (2007) , Lajeunesse (2011) and Macartney et al. (2022) .

minter

minter is a collection of functions for calculating effect sizes for meta-analysis of interactions.

The interaction can be between two factors (2-by-2 factorials) or between a factor and time (repeated measures experiments). For both design types, four effect size measures are available:

lnRR: Log Response Ratio
SMD: Standardized Mean Difference
lnVR: Log Variability Ratio
lnCVR: Log Coefficient of Variation Ratio

Typical effect sizes compare two values, the treatment vs. the control. However, factorial experiments allow computing different contrasts (and minter has functions for each):

Individual effects: Direct comparisons between single treatments, the classic effect size.
Main effects: Average effect of one factor across levels of another factor, analogous to the main effect in ANOVA.
Interaction effects: How the effect of one factor depends on the level of another factor.

For repeated measures experiments, the effect size quantifies the interaction between a factor and time.

See References for more.

Installation

From CRAN:

install.packages("minter")

Examples

For a real example, see the article recreating the results from Macartney et al. 2022

For a quick example, suppose you need to estimate the effect size of the interaction between fertilization × drought on plant biomass:

library(minter)

# Dummy data from 8 studies examining fertilization × drought on plant biomass
studies <- data.frame(
  study_id = 1:8,
  # Control: No fertilization, well-watered
  Ctrl_mean = c(12.3, 15.7, 10.8, 14.2, 11.9, 13.5, 16.1, 12.7),
  Ctrl_sd   = c(2.1, 3.2, 1.8, 2.7, 2.3, 2.9, 3.5, 2.4),
  Ctrl_n    = c(20, 24, 18, 22, 19, 25, 23, 21),
  # Fertilization only
  Fert_mean = c(18.5, 21.3, 16.2, 19.8, 17.1, 20.4, 22.7, 18.9),
  Fert_sd   = c(3.1, 4.1, 2.7, 3.6, 3.2, 3.8, 4.2, 3.4),
  Fert_n    = c(22, 25, 20, 24, 21, 26, 25, 23),
  # Drought only  
  Drought_mean = c(8.7, 11.2, 7.9, 10.1, 8.3, 9.8, 11.7, 9.4),
  Drought_sd   = c(1.8, 2.4, 1.6, 2.1, 1.9, 2.3, 2.6, 2.0),
  Drought_n    = c(19, 23, 17, 21, 18, 24, 22, 20),
  # Both treatments
  Both_mean = c(14.2, 17.8, 12.9, 16.3, 13.7, 16.1, 18.4, 15.2),
  Both_sd   = c(2.9, 3.7, 2.5, 3.3, 2.8, 3.4, 3.9, 3.1),
  Both_n    = c(21, 26, 19, 23, 20, 27, 24, 22)
)

# Calculate interaction effect: Does fertilization work differently under drought?
interaction_results <- lnRR_inter(
  data = studies,
  Ctrl_mean = "Ctrl_mean", Ctrl_sd = "Ctrl_sd", Ctrl_n = "Ctrl_n",
  A_mean = "Fert_mean", A_sd = "Fert_sd", A_n = "Fert_n", 
  B_mean = "Drought_mean", B_sd = "Drought_sd", B_n = "Drought_n",
  AB_mean = "Both_mean", AB_sd = "Both_sd", AB_n = "Both_n"
)

head(interaction_results)
#>   study_id Ctrl_mean Ctrl_sd ... yi        vi
#> 1        1      12.3     2.1     0.081  0.0069
#> 2        2      15.7     3.2     0.158  0.0068
#> 3        3      10.8     1.8     0.084  0.0073

# Meta-analysis
library(metafor)
res <- rma(yi, vi, ..., data = interaction_results)