Type:	Package
Title:	Meta-Analysis with Mean Differences
Version:	0.8-3
Date:	2022-08-07
Maintainer:	AC Del Re <acdelre@gmail.com>
Description:	A collection of functions for conducting a meta-analysis with mean differences data. It uses recommended procedures as described in The Handbook of Research Synthesis and Meta-Analysis (Cooper, Hedges, & Valentine, 2009).
Depends:	R (≥ 2.10.1)
Suggests:	metafor, ggplot2
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
URL:	https://www.acdelre.com
NeedsCompilation:	no
Packaged:	2022-08-06 22:10:17 UTC; acdel
Author:	AC Del Re [aut, cre], William Hoyt [aut]
Repository:	CRAN
Date/Publication:	2022-08-06 22:40:02 UTC

Meta-Analysis with Mean Differences

Description

The Mad package contains a variety of functions for conducting a mean differences meta-analysis using recommended procedures as described in The Handbook of Research Synthesis and Meta-Analysis (Cooper, Hedges, and Valentine, 2009). The goal in creating this package was to provide user-friendly functions to assist researchers in the process of conducting a meta-analysis, from the initial to final stages of their analytic endeavor. The meta-analyst can begin their project by using MAd functions to derive d (standardized mean differences) and g (unbiased d) from a variety of statistics/values reported in the primary studies (e.g., raw means and sd, t-test). Then, the analyst can aggregate all within-study effect sizes (while accounting for within-study correlations among outcome measures and eliminating any dependencies in the dataset), calculate omnibus effect sizes under a fixed and random effects model, and assess for significant moderators (categorical and continuous, single and multi-predictor models) in the dataset. Finally, the meta-analyst can use one of several user-friendly graphics functions to visually represent their data.

Details

The MAd package has integrated functions to facilitate the meta-analytic process at nearly every analytical stage. There are five broad areas of analysis that the MAd package targets:

1. Computations to Calculate Mean Differences:

There are a variety of functions to compute d (standardized mean difference) and g (unbiased d) from various designs reported in the primary studies. Most functions were derived from Borenstein's chapter in The Handbook of Research Synthesis and Meta-Analysis (Cooper, Hedges, & Valentine, 2009; pp. 228-234). For additional conversion formulas see the compute.es package: https://CRAN.R-project.org/package=compute.es

2. Within-Study Aggregation of Effect Sizes:

This fuction will simultaneously aggregate all within-study effect sizes while taking into account the correlations among the within-study outcome measures (Gleser & Olkin 2009; Gleser & Olkin 2009; Hedges & Olkin, 1985; Rosenthal et al., 2006). The default imputed correlation between within-study effect sizes is set at .50 (Wampold et al., 1997) and will compute an aggregated effect size for each study. This default of .50 is adjustable and can vary between outcome types. This MAd aggregation function implements Gleser & Olkin (1994; 2009) and Borenstein et al. (2009) procedures for aggregating dependent effect sizes. To our knowledge, this is the first statistical package/program to explicitly utilize and automate this type of aggregation procedure, which has a dual effect of saving the researcher substantial time while improving the accuracy of their analyses.

3. Fixed and Random Effects Omnibus Analysis:

This package contains all the relevant functions to calculate fixed and random effects omnibus effect sizes, outputting the omnibus (i.e., overall) effect size, variance, standard error, upper and lower confidence intervals, and the Q-statistic (heterogeneity test).

4. Moderator Analyses:

There are user-friendly functions to compute fixed and random effects moderator analyses. These include single and multiple predictor models for both categorical and continuous moderator data.

5. Graphics:

This package has a variety of functions visually representing data. This includes boxplots and meta-regression scatterplots.

6. Sample of Additional Functions:

Export MA output to nicely formatted Word tables.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

Cooper, H., Hedges, L.V., & Valentine, J.C. (2009). The handbook of research synthesis and meta-analysis (2nd edition). New York: Russell Sage Foundation.

Gleser & Olkin (1994). Stochastically dependent effect sizes. In H. Cooper, & L. V. Hedges, & J. C.(Eds.), The handbook of research synthesis (pp. 339-356). New York: Russell Sage Foundation.

Gleser & Olkin (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 357-376). New York: Russell Sage Foundation.

Viechtbauer, W (2010). metafor: Meta-Analysis Package for R. R package version 1.1-0. https://CRAN.R-project.org/package=metafor

Wampold, B. E., Mondin, G. W., Moody, M., Stich, F., Benson, K., & Ahn, H. (1997). A meta-analysis of outcome studies comparing bona fide psychotherapies: Empiricially, 'all must have prizes.' Psychological Bulletin, 122(3), 203-215.

See Also

compute.es package: https://CRAN.R-project.org/package=compute.es;

metafor package: https://CRAN.R-project.org/package=metafor

Examples

 
## EXAMPLES FOR EACH BROAD AREA

# SAMPLE DATA:
MA <- data.frame(id=factor(rep(1:5, 3)),
                 measure=c(rep("dep",5), rep("anx",5), rep("shy",5)),
                 es=c(rnorm(5, 0.8, .2), rnorm(5, 0.5, .1), rnorm(5, 0.4, .1)),
                 var.es=abs(rnorm(5*3,0.05, .03)),
                 nT=round(rnorm(5*3, 30, 5),0),
                 nC=round(rnorm(5*3, 30, 5),0),
                 mod1=factor(rep(c("a","b","c","d","e"),3)),
                 mod2=rep(seq(20, 60, 10), 3))
                 
# 1. COMPUTE MEAN DIFFERENCE STATISTIC FROM 
# REPORTED STATS (GENERALLY FROM A PRIMARY STUDY):
 
# suppose the primary study reported an log odds ratio for different 
# proportions between 2 groups. Then, running:

lor_to_d(.9070,.0676)
           
# reported log odds ratio (lor = .9070) and variance (.0676) will output the 
# standardized mean difference (d) and its variance (var.d) that can be used in 
# a meta-analysis.

## 2. ACCOUNT FOR DEPENDENCIES: WITHIN-STUDY EFFECT SIZES (ES): 

## 2 EXAMPLES:  
# EXAMPLE 1:  AGGREGATING EFFECT SIZES FOR A DATA FRAME 
# (MULTIPLE STUDIES AT LEAST SOME OF WHICH HAVE MULTIPLE DEPENDENT EFFECT SIZES)   
# EXAMPLE 2:  AGGREGATING EFFECT SIZES FOR SINGLE STUDY WITH THREE OR MORE
# EFFECT SIZES WHEN PAIRS OF DVS HAVE DIFFERENT CORRELATIONS 

## EXAMPLE 1:  MA IS A DATA FRAME CONTAINING MULTIPLE STUDIES (id),
## EACH WITH MULTIPLE EFFECT SIZES (CORRELATIONS BETWEEN ALL PAIRS OF DVS ARE r=.5.)


# AGGREGATION PROCEDURE:  
# method="GO1"; GLESER AND OLKIN (1994) PROCEDURE WHEN d IS COMPUTED 
# USING POOLED SD IN THE DENOMINATOR

MA1 <- agg(id=id, es=es, var=var.es, n.1=nT, n.2=nC, cor = .5, method="GO1", data=MA)   

MA1

## EXAMPLE 2: STUDY 1 COMPARES A TREATMENT AND CONTROL GROUP ON 
## THREE OUTCOME MEASURES (DEPRESSION, ANXIETY, and SHYNESS).
# THE CORRELATION AMONG THE THREE PAIRS OF DVS ARE r12=.5, r13=.2, and r23=.3.  

study1 <- data.frame( id=factor(rep(1, 3)), 
                      measure=c("dep", "anx", "shy"),
                      es=c(0.8, 0.5, 0.4), 
                      var.es=c(0.01, 0.02, 0.1), 
                      nT=rep(30, 3), 
                      nC=rep(30, 3))  

# ONE WOULD CONSTRUCT THE CORRELATION MATRIX AS FOLLOWS:  

cors <- matrix(c(1,.5,.2, 
                 .5,1,.3, 
                 .2,.3,1), nrow=3)  

# AGGREGATION PROCEDURE:
# method="GO1"; GLESER AND OLKIN (1994) PROCEDURE WHEN d 
# IS COMPUTED USING POOLED SD IN THE DENOMINATOR 

agg(id=id, es=es, var=var.es, n.1=nT, n.2=nC, cor=cors, method="GO1", mod = NULL, data=study1)   


# where MA = data.frame with columns for id, es (standardized
# mean difference), var.es (variance of es), n.1 (sample size of group
# one), and n.2 (sample size of comparison group) with multiple rows per
# study. Outputs an aggregated data.frame with 1 effect size per study. 

## 3.OMNIBUS ANALYSIS

# FIRST ADD MODERATORS TO THE AGGREGATED DATASET:

MODS <- data.frame(id=1:5,
                   mod1=factor(c("a","b","a","b","b")),
                   mod2=as.numeric(c(20, 30, 25, 35, 40)))
                   
MA2 <- merge(MA1, MODS, by='id')

# Random Effects
m0 <- mareg(es1~ 1, var = var1, method = "REML", data = MA2)

# where MA = data.frame with columns for id, es (standardized
# mean difference), var.es (variance of es), n.1 (sample size of group
# one), and n.2 (sample size of comparison group).
 
# view output:
summary(m0)


# 4. MODERATOR ANALYSIS:

# Random Effects
m1 <- mareg(es1~ mod1 + mod2 , var = var1, method = "REML", data = MA2) 
 
# view output:
summary(m1)

# 5. Graphics:

## Not run: plotcon(g = es1, var = var1, mod = mod1, data = MA2, method= "random", 
modname= "Moderator") 
## End(Not run)

# Additional Functions

# Export MA output to nicely formatted Word tables.

# install R2wd
# install.packages('R2wd', dependencies = TRUE)

# Export data to Word in formatted table

#  wd(m1, get = TRUE, new = TRUE)

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Inter-Rater Agreement

Description

Kappa coefficients for assessing inter-rater agreement between two coders (for categorical
variables/moderators).

Usage

Kappa(rater1, rater2)

Arguments

Value

Kappa coefficients for inter-rater reliability (categorical variables).

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

Examples

# sample data

study <- c(1,1,2,2,3,3) # study coded
rater <- rep(1:2, 3)  # 2 raters
mod1 <- as.factor(round(rnorm(6, 10, 1))) # values coded for mod 1
mod2 <- as.factor(round(rnorm(6, 10, 1)))
mod3 <- as.factor(round(rnorm(6, 10, 1)))
mod4 <- as.factor(round(rnorm(6, 10, 1)))
mod5 <- as.factor(round(rnorm(6, 10, 1)))
mod6 <- as.factor(round(rnorm(6, 10, 1)))
w <-data.frame(study, rater,mod1, mod2, mod3, mod4, mod5, mod6)
w

# if data is in this format:
# study rater mod1 mod2 mod3 mod4 mod5 mod6
#     1     1    8   10    9    9   10   10
#     1     2   10   11   10   10   13   12
#     2     1   11   10   11   11   10   12
#     2     2   13   10   10   11   12    9
#     3     1   11   10   11   10   10    9
#     3     2   10   10   11    9   10   11
#
# the data will need to be reshaped to be processed by the 
# Kappa function:

long <- reshape(w, varying=colnames(w)[3:8], v.names="code", 
            idvar=c('study', 'rater'), timevar= 'mods', direction='long')
wide <- reshape(long, idvar=c('mods', 'study'), timevar='rater')
wide

# running the function:

Kappa(wide$code.1, wide$code.2)

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Assess for Publication Bias

Description

Assess for publication bias in the meta-analytic data

Usage

PubBias(data)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Sutton, A. J. (2009). Publication bias. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 435-452). New York: Russell Sage Foundation.

See Also

weights

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Aggregate Dependent Effect Sizes

Description

This function will simultaneously aggregate all within-study effect sizes while taking into account the correlations among the within-study outcomes. The default correlation between outcome measures is set at .50 (Wampold et al., 1997), and can be adjusted as needed. An aggregate effect size and its variance is computed for each study. This MAd aggregation function implements Gleser & Olkin (1994) and Borenstein et al. (2009) procedures for aggregating dependent effect sizes..

Usage

agg(id, es, var, n.1=NULL, n.2=NULL, method = "BHHR", cor = .50,  mod=NULL, data)

Arguments

Value

Outputs a data.frame with aggregated effect sizes and variances of effect sizes where each study is reduced to one row per study (unless aggregated by a moderator) by a weighted average formula.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

Cooper, H., Hedges, L.V., & Valentine, J.C. (2009). The handbook of research synthesis and meta-analysis (2nd edition). New York: Russell Sage Foundation.

Gleser & Olkin (1994). Stochastically dependent effect sizes. In H. Cooper, & L. V. Hedges, & J. C.(Eds.), The handbook of research synthesis(pp. 339-356). New York: Russell Sage Foundation.

Gleser & Olkin (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 357-377). New York: Russell Sage Foundation.

Shadish & Haddock (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 257-278). New York: Russell Sage Foundation.

Examples

## 2 EXAMPLES:  

# EXAMPLE 1:  Aggregating effect sizes for a data frame
# (multiple studies at least some of which have multiple
# effect sizes), assuming equal correlations (r=.5) between
# pairs of DVs.
# EXAMPLE 2:  Aggregating effect sizes for a single study
# with 3 or more effect sizes when pairs of DVs have 
# different correlations.

# LOAD DATA (EXAMPLE DATA FROM HOYT & DEL RE, 2015 SIMULATION):
data(dat.hoyt)

## EXAMPLE 1:  dat.hoyt is a data frame with multiple studies identified
## by variable 'id'.  Each study has multiple effect sizes based on 
## multiple DVs.  Correlations between all pairs of DVs are r=.5.

# NOTE: Based on a simulation study by Hoyt & Del Re (2015), it is
# recommended that methods "G01" and "G02" (Gleser and Olkin) 
# should aggregate Cohen's d, without using Hedges & Olkin's 
# recommended bias correction.  (Studies providing only a single
# effect size should still be corrected for bias, after aggregation.)

# Method "BHHR" should aggregate Hedges' g, after bias correction.


# Option 1: method="BHHR"; Borenstein et al. (2009) procedure. 
# Use with Hedges' g; can also be used with any other effect 
# size (e.g., z', LOR).

agg(id=id, es=g, var=vg,  cor=.5,
    method="BHHR", mod=NULL, data=dat.hoyt) 

#  Option 2: method="GO1"; Gleser & Olkin (1994) procedure when
#  d is computed using pooled sd in denominator. 

agg(id=id, es=d, var=vd, n.1=n.T, n.2=n.C, cor = .5, 
    method="GO1", mod = NULL, data=dat.hoyt)   

# Option 3: method="GO2"; Gleser & Olkin (1994) procedure when
# d is computed using sd.2 (typically control group sd)
# in denominator

agg(id=id, es=d, var=vd, n.1=n.T, n.2=n.C, cor = .5, 
    method="GO2", mod = NULL, data=dat.hoyt)   


## EXAMPLE 2: Single study comparing T and C group
## on three DVs:  depression, anxiety, and shyness
## r12=.5; r13=.2; r23=.3

data <- dat.hoyt[20:22,]

# Step 1:  Create the correlation matrix, based on r12, r13, and r23:  

cors <- matrix(c(1,.5,.2, 
                 .5,1,.3, 
                 .2,.3,1), nrow=3)  

# Step 2:  Aggregate using agg() function.

# Option 1: method="BHHR"; Borenstein et al. (2009) procedure. 
# Use with Hedges' g; can also be used with any other effect 
# size (e.g., z', LOR).

agg(id=id, es=g, var=vg,  cor=cors,
    method="BHHR", mod=NULL, data=data) 

#  Option 2: method="GO1"; Gleser & Olkin (1994) procedure when
#  d is computed using pooled sd in denominator. 

agg(id=id, es=d, var=vd, n.1=n.T, n.2=n.C, cor = cors, 
    method="GO1", mod = NULL, data=data)   

# Option 3: method="GO2"; Gleser & Olkin (1994) procedure when
# d is computed using sd.2 (typically control group sd)
# in denominator

agg(id=id, es=d, var=vd, n.1=n.T, n.2=n.C, cor = cors, 
    method="GO2", mod = NULL, data=data)   


## Citation ##
# Hoyt, W. T., & Del Re, A. C. (2013).  Comparison of methods for 
# aggregating dependent effect sizes in meta-analysis.  
# Manuscript submitted for publication.

  

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

ANCOVA F-statistic to d

Description

Converts an ANCOVA F-statistic to d (standardized mean difference)

Usage

ancova_to_d1(m.1.adj, m.2.adj, sd.adj, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

ANCOVA F-statistic to d II

Description

Converts an ANCOVA F-statistic with pooled standard deviation to d (standardized mean difference)

Usage

ancova_to_d2(m.1.adj, m.2.adj, s.pooled, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Correction for Attenuation

Description

Used to correct for attenuated effect sizes due to measurement unreliability.

Usage

atten(g, xx, yy, data)

Arguments

Value

A new column for g corrected for attenuation (g.corrected) will be added to the data, for those xx & yy columns with complete data.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Hunter, J. E., Schmidt, F. L. (2004). Methods of meta-analysis (2nd edition). Thousand Oaks, CA: Sage.

Examples

# Sample data:

id<-c(1, 1:19)
n<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
g<-c(.68,.56,.23,.64,.49,-.04,.49,.33,.58,.18,-.11,.27,.26,.40,.49,
 .51,.40,.34,.42,.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
  .049,.0051,.040,.034,.0042,.016)
xx<-c(.88,.86,.83,.64,.89,.84,.89,.83,.99,.88,.81,.77,.86,.70,.79,
 .71,.80,.74,.82,.86)  # Reliability of "independent variable"
yy<-c(.99,.86,.83,.94,.89,.94,.89,.93,.99,.88,.81,.77,.86,.70,.79,
 .71,.80,.94,.92,.96)  # Reliability of "dependent variable"
   
df<-data.frame(id,n,g, var.g, xx,yy)

# Example        
atten(g= g, xx = xx, yy = yy, data= df) 

Computes Vector of Standardized Mean Differences

Description

Adds d & g (standardized mean difference) to a data.frame. Required inputs are: n.1 (sample size of group one), m.1 (raw post-mean value of group one), sd.1 (standard deviation of group one), n.2 (sample size of group two), m.2 (raw post-mean value of group two), sd.2 (standard deviation of group two).

Usage

compute_dgs(n.1, m.1, sd.1 , n.2, m.2, sd.2, data, denom = "pooled.sd")

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

compute_ds, compute_gs

Examples

id <- c(1:20)
n.1 <- c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
m.1 <- c(.68,.56,.23,.64,.49,.4,1.49,.53,.58,1.18,.11,1.27,.26,.40,.49,
         .51,.40,.34,.42,.66)
m.2 <- c(.38,.36,.23,.34,.29,.4,1.9,.33,.28,1.1,.111,.27,.21,.140,.149,
         .51,.140,.134,.42,.16)
sd.1 <- c(.28,.26,.23,.44,.49,.34,.39,.33,.58,.38,.31,.27,.26,.40,
          .49,.51,.140,.134,.42,.46)
sd.2 <- c(.28,.26,.23,.44,.49,.44,.39,.33,.58,.38,.51,.27,.26,.40,
          .49,.51,.140,.134,.142,.36)
mod1 <- c(1,2,3,4,1,2,8,7,5,3,9,7,5,4,3,2,3,5,7,1)
mod2 <- factor(c(rep(c(1,2,3,4),5)))
dfs <- data.frame(id, n.1,m.1, sd.1, n.2, m.2, sd.2, mod1, mod2)

# Example
compute_dgs(n.1, m.1, sd.1, n.2, m.2, sd.2, data = dfs)

Computes Vector of Standardized Mean Differences

Description

Adds d (standardized mean difference) to a data.frame. Required inputs are: n.1 (sample size of group one), m.1 (raw post-mean value of group one), sd.1 (standard deviation of group one), n.2 (sample size of group two), m.2 (raw post-mean value of group two), sd.2 (standard deviation of group two).

Usage

compute_ds(n.1, m.1, sd.1 , n.2, m.2, sd.2 , data, denom = "pooled.sd")

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

compute_ds, compute_dgs

Examples

id <- c(1:20)
n.1 <- c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
m.1 <- c(.68,.56,.23,.64,.49,.4,1.49,.53,.58,1.18,.11,1.27,.26,.40,.49,
         .51,.40,.34,.42,.66)
m.2 <- c(.38,.36,.23,.34,.29,.4,1.9,.33,.28,1.1,.111,.27,.21,.140,.149,
         .51,.140,.134,.42,.16)
sd.1 <- c(.28,.26,.23,.44,.49,.34,.39,.33,.58,.38,.31,.27,.26,.40,
          .49,.51,.140,.134,.42,.46)
sd.2 <- c(.28,.26,.23,.44,.49,.44,.39,.33,.58,.38,.51,.27,.26,.40,
          .49,.51,.140,.134,.142,.36)
mod1 <- c(1,2,3,4,1,2,8,7,5,3,9,7,5,4,3,2,3,5,7,1)
mod2 <- factor(c(rep(c(1,2,3,4),5)))
dfs <- data.frame(id, n.1,m.1, sd.1, n.2, m.2, sd.2, mod1, mod2)

# Example
compute_ds(n.1, m.1, sd.1, n.2, m.2, sd.2, data = dfs)

Converts Vector of Standardized Mean Differences

Description

Adds g (unbiassed standardized mean difference) to a data.frame. Required inputs are: n.1 (sample size of group one), sd.1 (standard deviation of group one), n.2 (sample size of group two).

Usage

compute_gs(d , var.d , n.1, n.2, data)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

compute_ds, compute_dgs

Examples

id <- c(1:20)
n.1 <- c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
m.1 <- c(.68,.56,.23,.64,.49,.4,1.49,.53,.58,1.18,.11,1.27,.26,.40,.49,
         .51,.40,.34,.42,.66)
m.2 <- c(.38,.36,.23,.34,.29,.4,1.9,.33,.28,1.1,.111,.27,.21,.140,.149,
         .51,.140,.134,.42,.16)
sd.1 <- c(.28,.26,.23,.44,.49,.34,.39,.33,.58,.38,.31,.27,.26,.40,
          .49,.51,.140,.134,.42,.46)
sd.2 <- c(.28,.26,.23,.44,.49,.44,.39,.33,.58,.38,.51,.27,.26,.40,
          .49,.51,.140,.134,.142,.36)
mod1 <- c(1,2,3,4,1,2,8,7,5,3,9,7,5,4,3,2,3,5,7,1)
mod2 <- factor(c(rep(c(1,2,3,4),5)))
dfs <- data.frame(id, n.1,m.1, sd.1, n.2, m.2, sd.2, mod1, mod2)

# Example

# first compute d
dfs2 <- compute_ds(n.1, m.1, sd.1, n.2, m.2, sd.2, data = dfs)

# now, compute g
compute_gs(d, var.d, n.1, n.2, dfs2)

Standardized Mean Difference (d) Statistic to Unbiased Standardized Mean Difference (g)

Description

Eliminates the small upward bias of d to provide an unbiased estimate of the population effect size parameter (g). This procedure will compute g for a single value of d.

Usage

d_to_g(d, var.d, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

Data from Table 15.3 in The Handbook for Research Synthesis and Meta-Analysis (Cooper et al., 2009)

Description

Data from Table 15.3 in The Handbook for Research Synthesis and Meta-Analysis (Cooper et al., 2009)

Data from Table A2 in The Handbook for Research Synthesis and Meta-Analysis (Cooper et al., 2009)

Description

Data from Table A2 in The Handbook for Research Synthesis and Meta-Analysis (Cooper et al., 2009)

Subset of simulated data to demonstrate aggregation for dependent effect sizes

Description

Subset of simulated data to demonstrate aggregation for dependent effect sizes. This data comes from: Hoyt, W. T., & Del Re, A. C. (2013). Comparison of methods for aggregating dependent effect sizes in meta-analysis. Manuscript submitted for publication.

Subset of simulated psychotherapy treatment studies (k=8) with dependent effect sizes

Description

This data set includes effect sizes for treatment vs control groups for a random subset of 8 simulated psychotherapy treatment studies (total population k = 1000). The known population standardized mean difference for outcome one is g = 0.50 and for outcome two g = 0.80. The data set also includes two correlated study-level variables (i.e., moderators): treatment duration (dose) and average participant distress (stress).

This data accompanies a tutorial for meta-analysis:

Del Re, A. C. (2015). A Practical Tutorial on Conducting Meta-Analysis in R. The Quantitative Methods for Psychology.

Final aggregated dataset of simulated psychotherapy treatment studies (k=8)

Description

This data set includes aggregated effect sizes for treatment vs control groups for a random subset of 8 simulated psychotherapy treatment studies (total population k = 1000). The known population standardized mean difference for outcome one is g = 0.50 and for outcome two g = 0.80. The data set also includes two correlated study-level variables (i.e., moderators): treatment duration (dose) and average participant distress (stress).

This data accompanies a tutorial for meta-analysis:

Del Re, A. C. (2015). A Practical Tutorial on Conducting Meta-Analysis in R. The Quantitative Methods for Psychology.

Subset of simulated psychotherapy treatment studies (k=8) with means and SD

Description

This data set includes means and standard deviations for treatment and control groups for a subset of k = 8 simulated psychotherapy treatment studies from a population of k = 1000 (see dat.sim1 and dat.sim2 for the k = 1000 studies for outcome 1 and 2, respectfully). Although effect sizes are not calculated in this dataset, the known population standardized mean difference for outcome one is d=0.50 and for outcome two g=0.80. The data set also includes two correlated study-level variables (i.e., moderators): treatment duration (dose) and average participant distress (stress).

This data accompanies a tutorial for meta-analysis:

Del Re, A. C. (2015). A Practical Tutorial on Conducting Meta-Analysis in R. The Quantitative Methods for Psychology.

Simulated psychotherapy treatment studies for 'outcome one'

Description

This data set includes 1000 simulated psychotherapy treatment studies. The population standardized mean difference for outcome one is d=0.50. The data set also includes two correlated study-level variables (i.e., moderators): treatment duration (dose) and average participant distress (stress).

This data accompanies a tutorial for meta-analysis:

Del Re, A. C. (2015). A Practical Tutorial on Conducting Meta-Analysis in R. The Quantitative Methods for Psychology.

Simulated psychotherapy treatment studies for 'outcome two'

Description

This data set includes 1000 simulated psychotherapy treatment studies. The population standardized mean difference for outcome two is d=0.80. The data set also includes two correlated study-level variables (i.e., moderators): treatment duration (dose) and average participant distress (stress).

This data accompanies a tutorial for meta-analysis:

Del Re, A. C. (2015). A Practical Tutorial on Conducting Meta-Analysis in R. The Quantitative Methods for Psychology.

ANCOVA F-statistic to Standardized Mean Difference (d)

Description

Converts an ANCOVA F-statistic to d (standardized mean difference).

Usage

f.ancova_to_d(f, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

F-test to Standardized Mean Difference (d)

Description

Converts F-test value to standardized mean difference (d).

Usage

f_to_d(f, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein, M. (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Internal MAd objects

Description

Internal MAd objects.

Details

These are not to be called by the user.

Failure groups to Standardized Mean Difference (d)

Description

Converts number of 'failure' groups reported in the primary study to standardized mean difference (d).

Usage

fail_to_d(B, D, n.1, n.0)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, r_from_chi, r_from_d, r_from_d1, r_from_t

Intraclass correlation coefficient (ICC) for oneway and twoway models

Description

Computes single score or average score ICCs as an index of interrater reliability of quantitative data. Additionally, F-test and confidence interval are computed.

Usage

icc(ratings, model = c("oneway", "twoway"), 
    type = c("consistency", "agreement"), 
    unit = c("single", "average"), r0 = 0, conf.level = 0.95)

Arguments

Details

This function was created by Matthias Gamer for the irr package. For more details, see:

http://rss.acs.unt.edu/Rdoc/library/irr/html/icc.html

Details for the function:

Missing data are omitted in a listwise way. When considering which form of ICC is appropriate for an actual set of data, one has take several decisions (Shrout & Fleiss, 1979):

1. Should only the subjects be considered as random effects (oneway model) or are subjects and raters randomly chosen from a bigger pool of persons (twoway model).

2. If differences in judges' mean ratings are of interest, interrater agreement instead of consistency should be computed.

3. If the unit of analysis is a mean of several ratings, unit should be changed to average. In most cases, however, single values (unit = single) are regarded.

Value

A list with class icclist containing the following components:

Author(s)

Matthias Gamer

References

Bartko, J.J. (1966). The intraclass correlation coefficient as a measure of reliability. Psychological Reports, 19, 3-11.

McGraw, K.O., & Wong, S.P. (1996), Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46.

Shrout, P.E., & Fleiss, J.L. (1979), Intraclass correlation: uses in assessing rater reliability. Psychological Bulletin, 86, 420-428.

Examples

# sample data

study <- c(1,1,2,2,3,3)
rater <- c(rep(1:2,3))
mod1 <- round(rnorm(6, 10, 1))
mod2 <- c(5,5, 9, 9, 8, 8)
mod3 <- c(10,10, 9, 9, 8, 8)
w <-data.frame(study, rater, mod1, mod2, mod3)
w


# if data is in this format:

# study rater mod1 mod2 mod3
#     1     1    9    9   10
#     1     2   11    8   10
#     2     1    9   10   11
#     2     2    9   10   11
#     3     1    9    9    8
#     3     2   12    9    8
#
# the data will need to be reshaped to be processed by the 
# icc function:

long <- reshape(w, varying=colnames(w)[3:5], v.names="Code", 
            idvar=c('study', 'rater'), timevar="mods", direction='long')
wide <- reshape(long, idvar=c('mods', 'study'), timevar='rater')

# icc function (created by Matthias Gamer for the 'irr' package)

icc(cbind(wide$Code.1, wide$Code.2), type= "consistency")

Log Odds Ratio to Standardized Mean Difference (d)

Description

Converts a log odds ratio reported in the primary study to a standardized mean difference (d).

Usage

lor_to_d(lor, var.lor)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Categorical Moderator Analysis

Description

Computes single predictor categorical moderator analysis under a fixed or random effects model.

Usage

macat(g, var, mod, data, method= "random")

Arguments

Details

See Konstantopoulos & Hedges (2009; pp. 280-288) for the computations used in this function.

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Konstantopoulos & Hedges (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

Shadish & Haddock (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 257-278). New York: Russell Sage Foundation.

See Also

plotcat

Examples

id<-c(1:20)
n.1<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
g <- c(.68,.56,.23,.64,.49,-.04,1.49,1.33,.58,1.18,-.11,1.27,.26,.40,.49,
.51,.40,.34,.42,1.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
.049,.0051,.040,.034,.0042,.016)
mod<-factor(c(rep(c(1,1,2,3),5)))
df<-data.frame(id, n.1,n.2, g, var.g,mod)

# Example

# Random effects
macat(g = g, var= var.g, mod = mod, data = df, method= "random")

Direct Categorical Moderator Comparison

Description

Function for a planned comparison between two levels of a moderator under a fixed or random effects model.

Usage

macatC(x1, x2, g, var, mod, data, method= "random", type= "post.hoc")

Arguments

Details

See Konstantopoulos & Hedges (2009; pp. 280-288) for the computations used in this function.

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Konstantopoulos & Hedges (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

Shadish & Haddock (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 257-278). New York: Russell Sage Foundation.

See Also

macat,

Examples

id<-c(1:20)
n.1<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
g <- c(.68,.56,.23,.64,.49,-.04,1.49,1.33,.58,1.18,-.11,1.27,.26,.40,.49,
.51,.40,.34,.42,1.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
.049,.0051,.040,.034,.0042,.016)
mod<-factor(c(rep(c(1,1,2,3),5)))
df<-data.frame(id, n.1,n.2, g, var.g,mod)

# Example
macatC(1, 2, g=g, var=var.g, mod=mod, data=df,  method= "random", 
  type= "post.hoc") 

Meta-Regression

Description

Meta-regression function for a single or multiple predictor model. This function is a wrapper for the rma() function in the metafor package (Viechtbauer, W, 2010). Please see http://CRAN.R-project.org/package=metafor for details or for more advanced functionality with the rma() function.

Usage

mareg(formula, var, data, method = "REML", subset,  digits = 3, ...)

Arguments

Details

See Wolfgang Viechtbauer (2010). metafor: Meta-Analysis Package for R. R package version 1.1-0. for the details of the rma() function. http://CRAN.R-project.org/package=metafor

Value

References

Wolfgang Viechtbauer (2010). metafor: Meta-Analysis Package for R. R package version 1.1-0. http://CRAN.R-project.org/package=metafor

See Also

plotcon

Examples

# install metafor
# install.packages('metafor', dependencies = TRUE)

# Sample data
data(dat.sim.final)


# Examples

# OMNIBUS
m0 <- mareg(es~1, var=var, data=dat.sim.final)
summary(m0)

# META-REGRESSION
m1 <- mareg(es~dose, var=var, data=dat.sim.final)
summary(m1)  # SINGLE MODERATOR

m2 <- mareg(es~stress, var=var, data=dat.sim.final)
summary(m2)  # SINGLE MODERATOR

m3 <- mareg(es~dose + stress, var=var, data=dat.sim.final)
summary(m3)  # MULTIPLE MODERATOR  

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Means to Standardized Mean Difference

Description

Converts raw mean scores reported in the primary study to a standardized mean difference (d).

Usage

mean_to_d(m.1, m.2, sd.1, sd.2, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Means with Pooled SD to Standardized Mean Difference

Description

Converts raw mean scores with pooled standard deviation from the primary study to a standardized mean difference (d).

Usage

mean_to_d2(m.1, m.2, s.pooled, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Omnibus Effect Size (Fixed and Random Effects)

Description

Computes fixed and random effects omnibus effect size for correlations.

Usage

omni(g, var, data, type="weighted", method = "random")

Arguments

Details

Depricated function. Use mareg(es~1, var, data) instead.

Value

Fixed and random effects:

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Shadish & Haddock (2009). Analyzing effect sizes: Fixed-effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 257-278). New York: Russell Sage Foundation.

Examples

id<-c(1:20)
n.1<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
g <- c(.68,.56,.23,.64,.49,-.04,1.49,1.33,.58,1.18,-.11,1.27,.26,.40,.49,
.51,.40,.34,.42,1.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
.049,.0051,.040,.034,.0042,.016)
mod<-factor(c(rep(c(1,1,2,3),5)))
df<-data.frame(id, n.1,n.2, g, var.g,mod)

# Example

omni(g = g, var = var.g, data = df, type="weighted", method = "random")

Odds Ratio to Standardized Mean Difference (d)

Description

Converts odds ratio reported in the primary study to standardized mean difference (d).

Usage

or_to_d(or)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, r_from_chi, r_from_d, r_from_d1, r_from_t

One-tailed p-value from ANCOVA to Standardized Mean Difference (d)

Description

Converts a one-tailed p-value from ANCOVA reported in the primary study to a standardized mean difference (d)

Usage

p.ancova_to_d1(p, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Two-tailed p-value from ANCOVA to Standardized Mean Difference (d)

Description

Converts a two-tailed p-value from ANCOVA reported in the primary study to a standardized mean difference (d)

Usage

p.ancova_to_d2(p, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

One-tailed p-value to Standardized Mean Difference (d)

Description

One-tailed p-value reported in the primary study to Standardized Mean Difference (d)

Usage

p_to_d1(p, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Two-tailed p-value to Standardized Mean Difference (d)

Description

One-tailed p-value reported in primary study to Standardized Mean Difference (d)

Usage

p_to_d2(p, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Internal MAc objects

Description

Internal MAc objects.

Details

These are not to be called by the user.

Categorical Moderator Graph

Description

Outputs boxplot graphic for each level of the specified moderator.

Usage

plotcat(g, var, mod, data, modname=NULL,  title=NULL, ...)

Arguments

Value

Boxplot graph with median, max, min, and outliers from a fixed or random effects categorical moderator analysis. Places jitter points (for each study) on the boxplots. The size of each point (representing a study in the analysis) are based on study weights where more precise studies have larger points. The ggplot2 package outputs the graphics.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (2009). The handbook of research synthesis and meta-analysis (2nd edition). New York: Russell Sage Foundation.

See Also

macat, plotcon

Examples

id<-c(1, 1:19)
n.1<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
g <- c(.68,.56,.23,.64,.49,-.04,1.49,1.33,.58,1.18,-.11,1.27,.26,.40,.49,
.51,.40,.34,.42,1.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
.049,.0051,.040,.034,.0042,.016)
mod<-factor(c(rep(c(1,1,2,3),5)))
df<-data.frame(id, n.1,n.2, g, var.g,mod)

# Example

## Not run: plotcat(g = g, var = var.g, mod = mod, data = df, method= "random",
 modname= "Moderator") 
## End(Not run)

Meta Regression Scatterplot

Description

Outputs a scatterplot from a fixed or random effects meta regression (continuous and/or categorical).

Usage

plotcon(g, var, mod, data, method= "random", modname=NULL, 
  title=NULL, ...)

Arguments

Value

Scatterplot with fixed or random effects regression line with size of visual points based on study weights, where the more precise studies have larger points. The ggplot2 package outputs the rich graphics.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (2009). The handbook of research synthesis and meta analysis (2nd edition). New York: Russell Sage Foundation.

See Also

mareg, plotcat

Examples

# SAMPLE DATA
MA2 <-read.table(textConnection("
id       es1       var1 n.1 n.2 mod1 mod2
1   1 0.5695938 0.04906967  26  30    a   20
2   2 0.4123667 0.04362541  28  34    b   30
3   3 0.4084333 0.04458363  34  28    a   25
4   4 0.5014756 0.04186354  37  29    b   35
5   5 0.5540745 0.04339382  31  32    b   40
6   1 0.5695938 0.04906967  26  30    a   20
7   2 0.4123667 0.04362541  28  34    b   30
8   3 0.4084333 0.04458363  34  28    a   25
9   4 0.5014756 0.04186354  37  29    b   35
10  5 0.5540745 0.04339382  31  32    b   40"))


# EXAMPLE
plotcon(es1, var1, mod2, data=MA2, method= "fixed", modname="NULL",title="NULL")

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

Chi-Squared to Correlation

Description

Converting Chi-squared statistic (with 1 degree of freedom) reported in primary study to r

Usage

r_from_chi(chi.sq, n)

Arguments

Value

Computes correlation coefficient (r).

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_d, r_from_d1, r_from_t

Correlation from Mean Difference

Description

Converts d (mean difference) to r where n.tmt = n.comparison (see section 12.5.4, Borenstein, 2009; pp. 234).

Usage

r_from_d(d, var.d, a = 4)

Arguments

Value

Outputs a correlation coefficient (r).

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d1, r_from_t

Correlation from Mean Difference II

Description

Converts d (mean difference) reported in primary study to r (correlation coefficient) where sample size of the treatment group is not equal to the sample size of the comparison group (see section 12.5.4, Borenstein, 2009; pp. 234).

Usage

r_from_d1(d, n.1, n.2, var.d)

Arguments

Value

Computes a correlation coefficient (r).

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_t

Correlation from t-test

Description

Compute correlation from t-value reported in the primary study (see section 12.5.4, Borenstein, 2009; pp. 234).

Usage

r_from_t(t, n)

Arguments

Value

Outputs the correlation coefficient (r).

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1,

Correlation (r) to Standardized Mean Difference (d)

Description

Converts a correlation (r) to standardized mean difference (d).

Usage

r_to_d(r, N)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Robust standard error

Description

When the correlation between dependent effect sizes are unknown, one approach is to conduct the meta-analysis by assuming that the effect sizes are independent. Then, Hedges et al. (2010) robust standard error procedure can be calculated to adjust for dependence.

Usage

robustSE(model, cluster=NULL, CI=.95, digits=3)

Arguments

Value

Author(s)

Mike Cheung with modifications by AC Del Re

References

Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods, 1(1), 39-65. doi:10.1002/jrsm.5

Cheung, M.W.L. (2012). metaSEM: An R package for meta-analysis using structural equation modeling. Manuscript submitted for publication.

See Also

mareg,

Examples

# install metafor
# install.packages('metafor', dependencies = TRUE)

# Sample data
id<-c(1:20)
n.1<-c(10,20,13,22,28,12,12,36,19,12,36,75,33,121,37,14,40,16,14,20)
n.2 <- c(11,22,10,20,25,12,12,36,19,11,34,75,33,120,37,14,40,16,10,21)
g <- c(.68,.56,.23,.64,.49,-.04,1.49,1.33,.58,1.18,-.11,1.27,.26,.40,.49,
.51,.40,.34,.42,1.16)
var.g <- c(.08,.06,.03,.04,.09,.04,.009,.033,.0058,.018,.011,.027,.026,.0040,
.049,.0051,.040,.034,.0042,.016)
mod<-factor(c(rep(c(1,1,2,3),5)))
mods2<-c(rep(1:5,4))
df<-data.frame(id, n.1,n.2, g, var.g,mod, mods2)


# Examples

# Adjusted SE
robustSE(mareg(g~ mod + mods2, var = var.g, method = "REML", data = df))

   

Internal anRpackage objects

Description

Internal anRpackage objects.

Details

These are not to be called by the user.

t-test Value to Standardized Mean Difference (d)

Description

Converts a t-test value reported in the primary study to a standardized mean difference (d).

Usage

t_to_d(t, n.1, n.2)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, tt.ancova_to_d, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

t-test Value from ANCOVA to Standardized Mean Difference (d)

Description

Converts a t-test value from ANCOVA to a standardized mean difference (d)

Usage

tt.ancova_to_d(t, n.1, n.2, R, q)

Arguments

Value

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation.

See Also

d_to_g, mean_to_d, mean_to_d2, t_to_d, f_to_d, p_to_d1, p_to_d2, ancova_to_d1, ancova_to_d2, f.ancova_to_d, r_to_d, p.ancova_to_d1, p.ancova_to_d2, lor_to_d, prop_to_or, prop_to_d, r_from_chi, r_from_d, r_from_d1, r_from_t

Weights added to Meta Data

Description

Adds weights to the meta-analysis data set.

Usage

wgts(g, var.g, data)

Arguments

Value

Adds fixed and random-effects weights and confidence intervals to meta data set.

Author(s)

AC Del Re & William T. Hoyt

Maintainer: AC Del Re acdelre@gmail.com

Internal objects

Description

Internal objects.

Details

These are not to be called by the user.