Show the code
library(dplyr)
library(metafor)
library(tidyr)
library(Hmisc)
library(emmeans)
options(scipen = 9999999)
col.contour = c("gray75", "gray85", "gray95")
data <- rio::import("AI_Blended.xlsx") |>
select(-3,-9,-10) AI x Blended learning
Preparation
Importing packages and data
Calculating effect sizes
Show the code
# Assume a correlation of 0.7 between pre-test and post-test scores
r <- 0.7
# Modify the data transformation with the correlation
datah <- data |> rowwise() |>
mutate(
# Mean differences for experimental and control groups
MD_exp = MEpost - ifelse(is.na(MEpre),0,MEpre),
MD_con = MCpost - ifelse(is.na(MCpre),0,MCpre),
# Pooled SD considering the correlation between pre and post
SD_pooled_exp = ifelse(is.na(SDEpre), SDEpost, sqrt(SDEpre^2 + SDEpost^2 - 2 * r * SDEpre * SDEpost)), # For experimental group
SD_pooled_con = ifelse(is.na(SDCpre), SDCpost, sqrt(SDCpre^2 + SDCpost^2 - 2 * r * SDCpre * SDCpost)), # For control group
# Hedge's g calculation considering the correlation
SD_pooled = sqrt(((NC - 1) * SD_pooled_con^2 + (NE - 1) * SD_pooled_exp^2) / (NC + NE - 2)),
g = (MD_exp - MD_con) / SD_pooled, # Hedge's g without correction
J = 1 - (3 / (4 * (NC + NE) - 9)), # Correction factor for small sample sizes
Hedge_g = g * J # Apply correction factor
)
# Now you can use escalc() to calculate variance and other stats
results <- escalc(
measure = "SMD",
yi = Hedge_g,
vi = (1/NC + 1/NE) + Hedge_g^2 / (2*(NC + NE)),
data = datah
) |> data.frame()
# Comment this to NOT flip the ES of the only post papers
results |> mutate(
Hedge_g = ifelse(is.na(MCpre), -Hedge_g, Hedge_g),
yi = ifelse(is.na(MCpre), -yi, yi)
) -> resultsMeta-analysis
Estimation
Show the code
m.gen <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `X.`,
data = results,
fixed = FALSE,
random = TRUE,
method.tau = "REML",
hakn = T)Plotting
Show the code
meta:::forest.meta(m.gen,
layout = "meta",
sortvar = -g,
digits = 3,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
leftcols = c("Author..year."),
col.square = "orange",
col.diamond = "red",
plotwidth = "5cm",
colgap.forest.left = "5cm")
Bias
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m_multi = metafor::rma(results$Hedge_g,results$vi,
data = results, slab = results$Author..year.)
meta:::funnel.meta(m.gen, xlim = c(-2, 4.5), contour = c(0.9, 0.95, 0.99), col.contour = col.contour)
Show the code
metafor::ranktest(m_multi)
Rank Correlation Test for Funnel Plot Asymmetry
Kendall's tau = 0.4381, p = 0.0050Show the code
metafor::regtest(m_multi)
Regression Test for Funnel Plot Asymmetry
Model: mixed-effects meta-regression model
Predictor: standard error
Test for Funnel Plot Asymmetry: z = 3.1906, p = 0.0014
Limit Estimate (as sei -> 0): b = -0.1209 (CI: -0.5676, 0.3258)Outliers (https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/heterogeneity.html?q=OUTLIERS#basic-outlier)
Show the code
outliers <- dmetar::find.outliers(m.gen)
m.gen.inf <- dmetar::InfluenceAnalysis(m.gen, random = TRUE)[===========================================================================] DONE Show the code
ggplot2::theme_set(ggplot2::theme_minimal())
plot(m.gen.inf, "baujat") 
Show the code
plot(m.gen.inf, "es")
Show the code
plot(m.gen.inf, "i2")
Remove outliers
Show the code
results2 <- results |> filter(!(X. %in% outliers$out.study.random))Re-estimate without outliers
Show the code
m.gen2 <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `X.`,
data = results2,
fixed = FALSE,
random = TRUE,
method.tau = "REML",
hakn = T)Plotting
Show the code
meta:::forest.meta(m.gen2,
layout = "meta",
sortvar = -g,
digits = 3,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
leftcols = c("Author..year."),
plotwidth = "5cm",
colgap.forest.left = "5cm")
Bias after removing outliers
Show the code
m_multi2 = metafor::rma(results2$Hedge_g,results2$vi,
data = results2, slab = results2$Author..year.)
meta:::funnel.meta(m.gen2, xlim = c(-2, 4.5), contour = c(0.9, 0.95, 0.99), col.contour = col.contour)
Show the code
metafor::ranktest(m_multi2)
Rank Correlation Test for Funnel Plot Asymmetry
Kendall's tau = 0.4000, p = 0.0326Show the code
metafor::regtest(m_multi2)
Regression Test for Funnel Plot Asymmetry
Model: mixed-effects meta-regression model
Predictor: standard error
Test for Funnel Plot Asymmetry: z = 2.0942, p = 0.0362
Limit Estimate (as sei -> 0): b = 0.0021 (CI: -0.3700, 0.3743)Subgroup analysis
Show the code
subgroup.results <- function(current_meta, pretty = T) {
subgroup_df <- data.frame(
Subgroup = current_meta$bylevs,
k = current_meta$k.w,
g = current_meta$TE.random.w,
SE = current_meta$seTE.random.w,
CI_Lower = current_meta$lower.random.w,
CI_Upper = current_meta$upper.random.w,
p = current_meta$pval.random.w,
Tau = current_meta$tau.w,
Tau2 = current_meta$tau2.w
) |>
mutate(
stars = case_when(
p <= 0.001 ~ "***",
p <= 0.01 ~ "**",
p <= 0.05 ~ "*",
TRUE ~ ""
)
) |>
mutate_if(is.numeric, \(x) format(x, digits = 2)) |>
mutate(
`95%-CI` = paste0("[",CI_Lower,"; ",CI_Upper,"]"),
) |>
mutate_if(is.character, \(x) ifelse(is.na(x), "", x)) |>
select(Subgroup, k, g, SE, `95%-CI`, p, stars, Tau2, Tau)
if (isTRUE(pretty)) {
gt::gt(subgroup_df) |>
gt::fmt_number(decimals = 2) |>
gt::sub_missing(
columns = everything(),
rows = everything(),
missing_text = "_"
)
} else {
subgroup_df
}
}By AI technology
Show the code
m.genAI <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `Author..year.`,
data = results,
sm = "SMD",
fixed = FALSE,
random = TRUE,
subgroup = results$AI,
cluster = results$`X.`,
method.tau = "REML",
hakn = TRUE)
meta:::forest.meta(m.genAI,
layout = "meta",
sortvar = g,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
subgroup.name = "AI technology",
col.square = "orange",
plotwidth = "5.5cm",
col.diamond = "red",
leftcols = c("studlab"),
colgap.forest.left = "5cm")
m.genAINumber of studies: k = 21
SMD 95%-CI t p-value
Random effects model (HK) 0.5310 [0.2658; 0.7961] 4.18 0.0005
Quantifying heterogeneity:
tau^2 = 0.2159 [0.1305; 0.9291]; tau = 0.4647 [0.3612; 0.9639]
I^2 = 87.0% [81.5%; 90.9%]; H = 2.77 [2.32; 3.31]
Test of heterogeneity:
Q d.f. p-value
153.86 20 < 0.0001
Results for subgroups (random effects model (HK)):
k SMD 95%-CI tau^2 tau Q I^2
AI = ITS 16 0.4635 [ 0.1314; 0.7957] 0.2308 0.4804 129.41 88.4%
AI = Personalized 4 0.8764 [ 0.2612; 1.4916] 0.0938 0.3062 7.54 60.2%
AI = Chatbot 1 0.3382 [-0.1714; 0.8479] -- -- 0.00 --
Test for subgroup differences (random effects model (HK)):
Q d.f. p-value
Between groups 3.77 2 0.1517
Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau
- Hartung-Knapp adjustment for random effects model (df = 20)
Show the code
res2 = metafor::rma(results$Hedge_g,results$vi, method="REML", mods= ~ `AI`, data = results)
Binded = cbind(res2$m, res2$QM, res2$QMp, res2$QE, res2$QEp )
colnames(Binded)= c( "DF", "QM", "P", "QE", "P")
res2
Mixed-Effects Model (k = 21; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.2068 (SE = 0.0854)
tau (square root of estimated tau^2 value): 0.4547
I^2 (residual heterogeneity / unaccounted variability): 87.48%
H^2 (unaccounted variability / sampling variability): 7.99
R^2 (amount of heterogeneity accounted for): 4.23%
Test for Residual Heterogeneity:
QE(df = 18) = 136.9433, p-val < .0001
Test of Moderators (coefficients 2:3):
QM(df = 2) = 2.1751, p-val = 0.3370
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.3382 0.5238 0.6457 0.5185 -0.6884 1.3649
AIITS 0.1206 0.5391 0.2236 0.8230 -0.9361 1.1772
AIPersonalized 0.5354 0.5854 0.9146 0.3604 -0.6120 1.6828
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
Binded DF QM P QE P
[1,] 2 2.175068 0.3370466 136.9433 0.00000000000000000002481715Show the code
subgroup.results(m.genAI)| Subgroup | k | g | SE | 95%-CI | p | stars | Tau2 | Tau |
|---|---|---|---|---|---|---|---|---|
| ITS | 16 | 0.46 | 0.16 | [ 0.13; 0.80] | 0.0095 | ** | 0.231 | 0.48 |
| Personalized | 4 | 0.88 | 0.19 | [ 0.26; 1.49] | 0.0201 | * | 0.094 | 0.31 |
| Chatbot | 1 | 0.34 | 0.26 | [-0.17; 0.85] | 0.1933 | NA | NA |
By research design
Show the code
m.genRD <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `Author..year.`,
data = results,
sm = "SMD",
fixed = FALSE,
random = TRUE,
subgroup = results$Research.Design,
cluster = results$`X.`,
method.tau = "REML",
hakn = TRUE)
meta:::forest.meta(m.genRD,
layout = "meta",
sortvar = g,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
subgroup.name = "Research design",
col.square = "orange",
plotwidth = "5.5cm",
col.diamond = "red",
leftcols = c("studlab"),
colgap.forest.left = "5cm")
m.genRDNumber of studies: k = 21
SMD 95%-CI t p-value
Random effects model (HK) 0.5310 [0.2658; 0.7961] 4.18 0.0005
Quantifying heterogeneity:
tau^2 = 0.2159 [0.1305; 0.9291]; tau = 0.4647 [0.3612; 0.9639]
I^2 = 87.0% [81.5%; 90.9%]; H = 2.77 [2.32; 3.31]
Test of heterogeneity:
Q d.f. p-value
153.86 20 < 0.0001
Results for subgroups (random effects model (HK)):
k SMD 95%-CI tau^2 tau
Research.Design = Experimental 16 0.5671 [0.2119; 0.9223] 0.2811 0.5302
Research.Design = Quasi-experimental 5 0.4141 [0.0123; 0.8160] 0.0525 0.2291
Q I^2
Research.Design = Experimental 145.78 89.7%
Research.Design = Quasi-experimental 7.70 48.0%
Test for subgroup differences (random effects model (HK)):
Q d.f. p-value
Between groups 0.48 1 0.4883
Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau
- Hartung-Knapp adjustment for random effects model (df = 20)
Show the code
res2 = metafor::rma(results$Hedge_g,results$vi, method="REML", mods= ~ `Research.Design`, data = results)
Binded = cbind(res2$m, res2$QM, res2$QMp, res2$QE, res2$QEp )
colnames(Binded)= c( "DF", "QM", "P", "QE", "P")
res2
Mixed-Effects Model (k = 21; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.2299 (SE = 0.0913)
tau (square root of estimated tau^2 value): 0.4795
I^2 (residual heterogeneity / unaccounted variability): 88.08%
H^2 (unaccounted variability / sampling variability): 8.39
R^2 (amount of heterogeneity accounted for): 0.00%
Test for Residual Heterogeneity:
QE(df = 19) = 153.4810, p-val < .0001
Test of Moderators (coefficient 2):
QM(df = 1) = 0.1466, p-val = 0.7018
Model Results:
estimate se zval pval ci.lb
intrcpt 0.5578 0.1334 4.1827 <.0001 0.2964
Research.DesignQuasi-experimental -0.1062 0.2773 -0.3829 0.7018 -0.6496
ci.ub
intrcpt 0.8193 ***
Research.DesignQuasi-experimental 0.4373
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
Binded DF QM P QE P
[1,] 1 0.1466282 0.7017786 153.481 0.00000000000000000000004659398Show the code
subgroup.results(m.genRD)| Subgroup | k | g | SE | 95%-CI | p | stars | Tau2 | Tau |
|---|---|---|---|---|---|---|---|---|
| Experimental | 16 | 0.57 | 0.17 | [0.212; 0.92] | 0.0039 | ** | 0.281 | 0.53 |
| Quasi-experimental | 5 | 0.41 | 0.14 | [0.012; 0.82] | 0.0459 | * | 0.052 | 0.23 |
By educational level
Show the code
m.genEL <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `Author..year.`,
data = results,
sm = "SMD",
fixed = FALSE,
random = TRUE,
subgroup = results$Level.of.education,
cluster = results$`X.`,
method.tau = "REML",
hakn = TRUE)
meta:::forest.meta(m.genEL,
layout = "meta",
sortvar = g,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
subgroup.name = "Educational level",
col.square = "orange",
plotwidth = "5.5cm",
col.diamond = "red",
leftcols = c("studlab"),
colgap.forest.left = "5cm")
m.genELNumber of studies: k = 21
SMD 95%-CI t p-value
Random effects model (HK) 0.5310 [0.2658; 0.7961] 4.18 0.0005
Quantifying heterogeneity:
tau^2 = 0.2159 [0.1305; 0.9291]; tau = 0.4647 [0.3612; 0.9639]
I^2 = 87.0% [81.5%; 90.9%]; H = 2.77 [2.32; 3.31]
Test of heterogeneity:
Q d.f. p-value
153.86 20 < 0.0001
Results for subgroups (random effects model (HK)):
k SMD 95%-CI tau^2
Level.of.education = Secondary education 9 0.4105 [-0.0467; 0.8678] 0.3250
Level.of.education = Higher education 9 0.6845 [ 0.2489; 1.1201] 0.1072
Level.of.education = Primary education 2 0.5525 [-3.9731; 5.0780] 0.1684
Level.of.education = Early childhood 1 0.3117 [ 0.0393; 0.5841] --
tau Q I^2
Level.of.education = Secondary education 0.5701 113.46 92.9%
Level.of.education = Higher education 0.3274 26.13 69.4%
Level.of.education = Primary education 0.4103 2.92 65.8%
Level.of.education = Early childhood -- 0.00 --
Test for subgroup differences (random effects model (HK)):
Q d.f. p-value
Between groups 2.65 3 0.4491
Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau
- Hartung-Knapp adjustment for random effects model (df = 20)
Show the code
res2 = metafor::rma(results$Hedge_g,results$vi, method="REML", mods= ~ `Level.of.education`, data = results)
Binded = cbind(res2$m, res2$QM, res2$QMp, res2$QE, res2$QEp )
colnames(Binded)= c( "DF", "QM", "P", "QE", "P")
res2
Mixed-Effects Model (k = 21; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.2463 (SE = 0.1029)
tau (square root of estimated tau^2 value): 0.4963
I^2 (residual heterogeneity / unaccounted variability): 88.76%
H^2 (unaccounted variability / sampling variability): 8.90
R^2 (amount of heterogeneity accounted for): 0.00%
Test for Residual Heterogeneity:
QE(df = 17) = 142.5146, p-val < .0001
Test of Moderators (coefficients 2:4):
QM(df = 3) = 1.6336, p-val = 0.6518
Model Results:
estimate se zval pval
intrcpt 0.3117 0.5154 0.6048 0.5453
Level.of.educationHigher education 0.4082 0.5507 0.7413 0.4585
Level.of.educationPrimary education 0.2485 0.6571 0.3781 0.7053
Level.of.educationSecondary education 0.0955 0.5443 0.1755 0.8607
ci.lb ci.ub
intrcpt -0.6985 1.3219
Level.of.educationHigher education -0.6711 1.4876
Level.of.educationPrimary education -1.0394 1.5363
Level.of.educationSecondary education -0.9713 1.1624
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
Binded DF QM P QE P
[1,] 3 1.633622 0.6517905 142.5146 0.0000000000000000000007077841Show the code
subgroup.results(m.genEL)| Subgroup | k | g | SE | 95%-CI | p | stars | Tau2 | Tau |
|---|---|---|---|---|---|---|---|---|
| Secondary education | 9 | 0.41 | 0.20 | [-0.047; 0.87] | 0.0722 | 0.33 | 0.57 | |
| Higher education | 9 | 0.68 | 0.19 | [ 0.249; 1.12] | 0.0067 | ** | 0.11 | 0.33 |
| Primary education | 2 | 0.55 | 0.36 | [-3.973; 5.08] | 0.3646 | 0.17 | 0.41 | |
| Early childhood | 1 | 0.31 | 0.14 | [ 0.039; 0.58] | 0.0249 | * | NA | NA |
By subject
Show the code
m.genS <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `Author..year.`,
data = results,
sm = "SMD",
fixed = FALSE,
random = TRUE,
subgroup = results$Subject,
cluster = results$`X.`,
method.tau = "REML",
hakn = TRUE)
meta:::forest.meta(m.genS,
layout = "meta",
sortvar = g,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
subgroup.name = "Subject",
col.square = "orange",
plotwidth = "5.5cm",
col.diamond = "red",
leftcols = c("studlab"),
colgap.forest.left = "5cm")
m.genSNumber of studies: k = 21
SMD 95%-CI t p-value
Random effects model (HK) 0.5310 [0.2658; 0.7961] 4.18 0.0005
Quantifying heterogeneity:
tau^2 = 0.2159 [0.1305; 0.9291]; tau = 0.4647 [0.3612; 0.9639]
I^2 = 87.0% [81.5%; 90.9%]; H = 2.77 [2.32; 3.31]
Test of heterogeneity:
Q d.f. p-value
153.86 20 < 0.0001
Results for subgroups (random effects model (HK)):
k SMD 95%-CI tau^2
Subject = Mathematics 6 0.1040 [-0.0646; 0.2727] <0.0001
Subject = Language 6 0.6707 [ 0.0206; 1.3208] 0.3539
Subject = Science and Social Sciences 3 0.4351 [-0.5839; 1.4540] 0.1100
Subject = Training 1 0.9855 [ 0.3984; 1.5725] --
Subject = ICT & Engineering 5 0.9147 [-0.3511; 2.1804] 0.4505
tau Q I^2
Subject = Mathematics 0.0020 6.47 22.7%
Subject = Language 0.5949 67.78 92.6%
Subject = Science and Social Sciences 0.3316 6.04 66.9%
Subject = Training -- 0.00 --
Subject = ICT & Engineering 0.6712 19.62 79.6%
Test for subgroup differences (random effects model (HK)):
Q d.f. p-value
Between groups 15.92 4 0.0031
Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau
- Hartung-Knapp adjustment for random effects model (df = 20)
Show the code
res2 = metafor::rma(results$Hedge_g,results$vi, method="REML", mods = ~Subject, data = results,intercept = FALSE)
Binded = cbind(res2$m, res2$QM, res2$QMp, res2$QE, res2$QEp )
colnames(Binded)= c( "DF", "QM", "P", "QE", "P")
res2
Mixed-Effects Model (k = 21; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.1923 (SE = 0.0855)
tau (square root of estimated tau^2 value): 0.4385
I^2 (residual heterogeneity / unaccounted variability): 85.68%
H^2 (unaccounted variability / sampling variability): 6.98
R^2 (amount of heterogeneity accounted for): 10.93%
Test for Residual Heterogeneity:
QE(df = 16) = 99.9023, p-val < .0001
Test of Moderators (coefficients 2:5):
QM(df = 4) = 6.1662, p-val = 0.1871
Model Results:
estimate se zval pval ci.lb
intrcpt 0.8288 0.2462 3.3662 0.0008 0.3462
SubjectLanguage -0.1584 0.3154 -0.5023 0.6154 -0.7767
SubjectMathematics -0.6528 0.3124 -2.0897 0.0366 -1.2651
SubjectScience and Social Sciences -0.3707 0.3801 -0.9755 0.3293 -1.1156
SubjectTraining 0.1566 0.5854 0.2676 0.7890 -0.9907
ci.ub
intrcpt 1.3114 ***
SubjectLanguage 0.4598
SubjectMathematics -0.0405 *
SubjectScience and Social Sciences 0.3742
SubjectTraining 1.3039
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
Binded DF QM P QE P
[1,] 4 6.166177 0.187077 99.90235 0.00000000000003613081Show the code
subgroup.results(m.genS)| Subgroup | k | g | SE | 95%-CI | p | stars | Tau2 | Tau |
|---|---|---|---|---|---|---|---|---|
| Mathematics | 6 | 0.10 | 0.066 | [-0.065; 0.27] | 0.174 | 0.000004 | 0.002 | |
| Language | 6 | 0.67 | 0.253 | [ 0.021; 1.32] | 0.045 | * | 0.353868 | 0.595 |
| Science and Social Sciences | 3 | 0.44 | 0.237 | [-0.584; 1.45] | 0.208 | 0.109977 | 0.332 | |
| Training | 1 | 0.99 | 0.300 | [ 0.398; 1.57] | 0.001 | ** | NA | NA |
| ICT & Engineering | 5 | 0.91 | 0.456 | [-0.351; 2.18] | 0.115 | 0.450488 | 0.671 |
By duration
Show the code
m.genD <- meta::metagen(TE = Hedge_g,
seTE = vi^.5,
studlab = `Author..year.`,
data = results,
sm = "SMD",
fixed = FALSE,
random = TRUE,
subgroup = results$Duration,
cluster = results$`X.`,
method.tau = "REML",
hakn = TRUE)
meta:::forest.meta(m.genD,
layout = "meta",
sortvar = g,
print.tau2 = TRUE,
prediction = TRUE,
leftlabs = c("Study"),
xlim = c(-2,2),
subgroup.name = "Duration",
col.square = "orange",
plotwidth = "5.5cm",
col.diamond = "red",
leftcols = c("studlab"),
colgap.forest.left = "5cm")
m.genDNumber of studies: k = 21
SMD 95%-CI t p-value
Random effects model (HK) 0.5310 [0.2658; 0.7961] 4.18 0.0005
Quantifying heterogeneity:
tau^2 = 0.2159 [0.1305; 0.9291]; tau = 0.4647 [0.3612; 0.9639]
I^2 = 87.0% [81.5%; 90.9%]; H = 2.77 [2.32; 3.31]
Test of heterogeneity:
Q d.f. p-value
153.86 20 < 0.0001
Results for subgroups (random effects model (HK)):
k SMD 95%-CI tau^2 tau Q I^2
Duration = One semester 14 0.5684 [ 0.2065; 0.9303] 0.2252 0.4745 113.40 88.5%
Duration = One year 4 0.0886 [-0.1042; 0.2814] 0 0 1.84 0.0%
Duration = One month 3 1.1366 [ 0.4791; 1.7940] 0.0028 0.0528 1.70 0.0%
Test for subgroup differences (random effects model (HK)):
Q d.f. p-value
Between groups 44.29 2 < 0.0001
Details on meta-analytical method:
- Inverse variance method
- Restricted maximum-likelihood estimator for tau^2
- Q-Profile method for confidence interval of tau^2 and tau
- Hartung-Knapp adjustment for random effects model (df = 20)
Show the code
res2 = metafor::rma(results$Hedge_g,results$vi, method="REML", mods = ~Duration, data = results,intercept = FALSE)
Binded = cbind(res2$m, res2$QM, res2$QMp, res2$QE, res2$QEp )
colnames(Binded)= c( "DF", "QM", "P", "QE", "P")
# Create a dataframe for the subgroup results
subgroup.results(m.genD)| Subgroup | k | g | SE | 95%-CI | p | stars | Tau2 | Tau |
|---|---|---|---|---|---|---|---|---|
| One semester | 14 | 0.568 | 0.168 | [ 0.21; 0.93] | 0.0048 | ** | 0.2252 | 0.475 |
| One year | 4 | 0.089 | 0.061 | [-0.10; 0.28] | 0.2399 | 0.0000 | 0.000 | |
| One month | 3 | 1.137 | 0.153 | [ 0.48; 1.79] | 0.0176 | * | 0.0028 | 0.053 |