R Notebook

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Load packages.

rm(list = ls())
library(dplyr)
library(metafor)
library(ggplot2)

Read in data.

d = read.csv("InWordDB_artifical_seed.csv")

Step 1: Calculate effect sizes and variances for each row.

Two methods. First, using the reported group means and standard deviations.

d = mutate(d, pooled_SD  = sqrt((SD_1 ^ 2 + SD_2 ^ 2) / 2),
           d_calc_by_M = (x_1 - x_2) / pooled_SD)

Second method: Using reported t test-statistic.

d = mutate(d, corr = .5,
              wc = sqrt(2 * (1 - corr)),
              d_calc_by_t = (t / sqrt(n_1)) * wc)

Note, that for within-subject designs, we need to know the correlation between the two conditions. This is often not reported. Here we estimated it to be .5.

Compare effect sizes.

ggplot(d, aes(x = d_calc_by_t, y= d_calc_by_M)) +
  geom_point(size = 3) +
  geom_smooth(method= "lm") +
  theme_bw()

Reasonabily compraable.

Put all effect sizes in same column

d = mutate(d, d_calc = ifelse(!is.na(d_calc_by_M), 
                              d_calc_by_M, d_calc_by_t))

Now, get d variances.

d = mutate(d, d_var_calc = (1 / n_1) + (d_calc ^ 2 / (2 * n_1)) * 2 * (1 - corr))

Step 2: Fit random effect model

res <- rma(d_calc, d_var_calc, data = d)
forest(res, slab = d$short_cite)

res

Overall estimate: .18, with condfidience interval that includes 0. No evidence for the effect. Lots of evidence for heteroneity. Run fixed effect for comparison (method = “FE”)

Funnel plot

funnel(res)

Very heterogenous.

Step 3: Fit random effect model with moderators

Effect size as a function of age.

ggplot(d, aes(x = mean_age_1, y = d_calc)) +
  geom_point(size = 3) +
  geom_smooth(method= "lm") +
  theme_bw()

Add age as a predictor of effect size.

res_age <- rma(d_calc ~ mean_age_1, d_var_calc, data = d)
res_age
forest(res_age, slab = d$short_cite)
funnel(res_age, slab = d$short_cite)

More variance acounted for by including age as a moderator.

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