`escalc.Rd`

The function can be used to calculate various effect sizes or outcome measures (and the corresponding sampling variances) that are commonly used in meta-analyses.

escalc(measure, ai, bi, ci, di, n1i, n2i, x1i, x2i, t1i, t2i, m1i, m2i, sd1i, sd2i, xi, mi, ri, ti, sdi, r2i, ni, yi, vi, sei, data, slab, subset, add=1/2, to="only0", drop00=FALSE, vtype="LS", var.names=c("yi","vi"), add.measure=FALSE, append=TRUE, replace=TRUE, digits, …)

measure | a character string indicating which effect size or outcome measure should be calculated. See ‘Details’ for possible options and how the data should be specified. |
---|---|

ai | vector to specify the \(2 \times 2\) table frequencies (upper left cell). |

bi | vector to specify the \(2 \times 2\) table frequencies (upper right cell). |

ci | vector to specify the \(2 \times 2\) table frequencies (lower left cell). |

di | vector to specify the \(2 \times 2\) table frequencies (lower right cell). |

n1i | vector to specify the group sizes or row totals (first group/row). |

n2i | vector to specify the group sizes or row totals (second group/row). |

x1i | vector to specify the number of events (first group). |

x2i | vector to specify the number of events (second group). |

t1i | vector to specify the total person-times (first group). |

t2i | vector to specify the total person-times (second group). |

m1i | vector to specify the means (first group or time point). |

m2i | vector to specify the means (second group or time point). |

sd1i | vector to specify the standard deviations (first group or time point). |

sd2i | vector to specify the standard deviations (second group or time point). |

xi | vector to specify the frequencies of the event of interest. |

mi | vector to specify the frequencies of the complement of the event of interest or the group means. |

ri | vector to specify the raw correlation coefficients. |

ti | vector to specify the total person-times. |

sdi | vector to specify the standard deviations. |

r2i | vector to specify the \(R^2\) values. |

ni | vector to specify the sample/group sizes. |

yi | vector to specify the observed effect size or outcomes. |

vi | vector to specify the corresponding sampling variances. |

sei | vector to specify the corresponding standard errors. |

data | optional data frame containing the variables given to the arguments above. |

slab | optional vector with labels for the studies. |

subset | optional vector indicating the subset of studies that should be used. This can be a logical vector or a numeric vector indicating the indices of the studies to include. |

add | a non-negative number indicating the amount to add to zero cells, counts, or frequencies. See ‘Details’. |

to | a character string indicating when the values under |

drop00 | logical indicating whether studies with no cases/events (or only cases) in both groups should be dropped when calculating the observed outcomes of the individual studies. See ‘Details’. |

vtype | a character string indicating the type of sampling variances to calculate (either |

var.names | a character string with two elements, specifying the name of the variable for the observed outcomes and the name of the variable for the corresponding sampling variances (the default is |

add.measure | logical indicating whether a variable should be added to the data frame (with default name |

append | logical indicating whether the data frame specified via the |

replace | logical indicating whether existing values for |

digits | integer specifying the number of decimal places to which the printed results should be rounded (if unspecified, the default is 4). Note that the values are stored without rounding in the returned object. |

… | other arguments. |

Before a meta-analysis can be conducted, the relevant results from each study must be quantified in such a way that the resulting values can be further aggregated and compared. Depending on (a) the goals of the meta-analysis, (b) the design and types of studies included, and (c) the information provided therein, one of the various effect size or outcome measures described below may be appropriate for the meta-analysis and can be computed with the `escalc`

function.

The `measure`

argument is a character string specifying which outcome measure should be calculated (see below for the various options), arguments `ai`

through `ni`

are then used to specify the information needed to calculate the various measures (depending on the chosen outcome measure, different arguments need to be specified), and `data`

can be used to specify a data frame containing the variables given to the previous arguments. The `add`

, `to`

, and `drop00`

arguments may be needed when dealing with frequency or count data that may need special handling when some of the frequencies or counts are equal to zero (see below for details). Finally, the `vtype`

argument is used to specify how to estimate the sampling variances (again, see below for details).

To provide a structure to the various effect size or outcome measures that can be calculated with the `escalc`

function, we can distinguish between measures that are used to:

contrast two independent (either experimentally created or naturally occurring) groups,

describe the direction and strength of the association between two variables,

summarize some characteristic or attribute of individual groups, or

quantify change within a single group or the difference between two matched pairs samples.

Furthermore, where appropriate, we can further distinguish between measures that are applicable when the characteristic, response, or dependent variable assessed in the individual studies is:

a dichotomous (binary) variable (e.g., remission versus no remission),

a count of events per time unit (e.g., number of migraines per year),

a quantitative variable (e.g., amount of depression as assessed by a rating scale).

outcome 1 | outcome 2 | total | |

group 1 | `ai` | `bi` | `n1i` |

group 2 | `ci` | `di` | `n2i` |

`ai`

, `bi`

, `ci`

, and `di`

denote the cell frequencies (i.e., the number of people falling into a particular category) and `n1i`

and `n2i`

are the row totals (i.e., the group sizes).
For example, in a set of randomized clinical trials, group 1 and group 2 may refer to the treatment and placebo/control group, respectively, with outcome 1 denoting some event of interest (e.g., death, complications, failure to improve under the treatment) and outcome 2 its complement. Similarly, in a set of cohort studies, group 1 and group 2 may denote those who engage in and those who do not engage in a potentially harmful behavior (e.g., smoking), with outcome 1 denoting the development of a particular disease (e.g., lung cancer) during the follow-up period. Finally, in a set of case-control studies, group 1 and group 2 may refer to those with the disease (i.e., cases) and those free of the disease (i.e., controls), with outcome 1 denoting, for example, exposure to some risk environmental risk factor in the past and outcome 2 non-exposure. Note that in all of these examples, the stratified sampling scheme fixes the row totals (i.e., the group sizes) by design.
A meta-analysis of studies reporting results in terms of \(2 \times 2\) tables can be based on one of several different outcome measures, including the risk ratio (also called the relative risk), the odds ratio, the risk difference, and the arcsine square root transformed risk difference (e.g., Fleiss & Berlin, 2009, Rücker et al., 2009). For any of these outcome measures, one needs to specify the cell frequencies via the `ai`

, `bi`

, `ci`

, and `di`

arguments (or alternatively, one can use the `ai`

, `ci`

, `n1i`

, and `n2i`

arguments).
The options for the `measure`

argument are then:
`"RR"`

for the*log risk ratio*.`"OR"`

for the*log odds ratio*.`"RD"`

for the*risk difference*.`"AS"`

for the*arcsine square root transformed risk difference*(Rücker et al., 2009).`"PETO"`

for the*log odds ratio*estimated with Peto's method (Yusuf et al., 1985).

`to="only0"`

(the default), the value of `add`

(the default is `1/2`

; but see ‘Note’) is added to each cell of those \(2 \times 2\) tables with at least one cell equal to 0. When `to="all"`

, the value of `add`

is added to each cell of all \(2 \times 2\) tables. When `to="if0all"`

, the value of `add`

is added to each cell of all \(2 \times 2\) tables, but only when there is at least one \(2 \times 2\) table with a zero cell. Setting `to="none"`

or `add=0`

has the same effect: No adjustment to the observed table frequencies is made. Depending on the outcome measure and the data, this may lead to division by zero inside of the function (when this occurs, the resulting value is recoded to `NA`

). Also, studies where `ai=ci=0`

or `bi=di=0`

may be considered to be uninformative about the size of the effect and dropping such studies has sometimes been recommended (Higgins & Green, 2008). This can be done by setting `drop00=TRUE`

. The values for such studies will then be set to `NA`

.
Datasets corresponding to data of this type are provided in `dat.bcg`

, `dat.collins1985a`

, `dat.collins1985b`

, `dat.egger2001`

, `dat.hine1989`

, `dat.laopaiboon2015`

, `dat.lee2004`

, `dat.li2007`

, `dat.linde2005`

, `dat.nielweise2007`

, and `dat.yusuf1985`

.
Assuming that the dichotomous outcome is actually a dichotomized version of the responses on an underlying quantitative scale, it is also possible to estimate the standardized mean difference based on \(2 \times 2\) table data, using either the probit transformed risk difference or a transformation of the odds ratio (e.g., Cox & Snell, 1989; Chinn, 2000; Hasselblad & Hedges, 1995; Sánchez-Meca et al., 2003). The options for the `measure`

argument are then:
`"PBIT"`

for the*probit transformed risk difference*as an estimate of the standardized mean difference.`"OR2DN"`

for the*transformed odds ratio*as an estimate of the standardized mean difference (normal distributions).`"OR2DL"`

for the*transformed odds ratio*as an estimate of the standardized mean difference (logistic distributions).

`dat.gibson2002`

.
number of events | total person-time | |

group 1 | `x1i` | `t1i` |

group 2 | `x2i` | `t2i` |

`x1i`

and `x2i`

denote the number of events in the first and the second group, respectively, and `t1i`

and `t2i`

the corresponding total person-times at risk. Often, the person-time is measured in years, so that `t1i`

and `t2i`

denote the total number of follow-up years in the two groups.
This form of data is fundamentally different from what was described in the previous section, since the total follow-up time may differ even for groups of the same size and the individuals studied may experience the event of interest multiple times. Hence, different outcome measures than the ones described in the previous section must be considered when data are reported in this format. These include the incidence rate ratio, the incidence rate difference, and the square root transformed incidence rate difference (Bagos & Nikolopoulos, 2009; Rothman et al., 2008). For any of these outcome measures, one needs to specify the total number of events via the `x1i`

and `x2i`

arguments and the corresponding total person-time values via the `t1i`

and `t2i`

arguments.
The options for the `measure`

argument are then:
`"IRR"`

for the*log incidence rate ratio*.`"IRD"`

for the*incidence rate difference*.`"IRSD"`

for the*square root transformed incidence rate difference*.

`to="only0"`

(the default), the value of `add`

(the default is `1/2`

; but see ‘Note’) is added to `x1i`

and `x2i`

only in the studies that have zero events in one or both groups. When `to="all"`

, the value of `add`

is added to `x1i`

and `x2i`

in all studies. When `to="if0all"`

, the value of `add`

is added to `x1i`

and `x2i`

in all studies, but only when there is at least one study with zero events in one or both groups. Setting `to="none"`

or `add=0`

has the same effect: No adjustment to the observed number of events is made. Depending on the outcome measure and the data, this may lead to division by zero inside of the function (when this occurs, the resulting value is recoded to `NA`

). Like for \(2 \times 2\) table data, studies where `x1i=x2i=0`

may be considered to be uninformative about the size of the effect and dropping such studies has sometimes been recommended. This can be done by setting `drop00=TRUE`

. The values for such studies will then be set to `NA`

.
Datasets corresponding to data of this type are provided in `dat.hart1999`

and `dat.nielweise2008`

.
mean | standard deviation | group size | |

group 1 | `m1i` | `sd1i` | `n1i` |

group 2 | `m2i` | `sd2i` | `n2i` |

`m1i`

and `m2i`

are the observed means of the two groups, `sd1i`

and `sd2i`

are the observed standard deviations, and `n1i`

and `n2i`

denote the number of individuals in each group. Again, the two groups may be experimentally created (e.g., a treatment and control group based on random assignment) or naturally occurring (e.g., men and women). In either case, the raw mean difference, the standardized mean difference, and the (log transformed) ratio of means (also called log response ratio) are useful outcome measures when meta-analyzing studies of this type (e.g., Borenstein, 2009).
The options for the `measure`

argument are then:
`"MD"`

for the*raw mean difference*.`"SMD"`

for the*standardized mean difference*.`"SMDH"`

for the*standardized mean difference*with heteroscedastic population variances in the two groups (Bonett, 2008, 2009).`"ROM"`

for the*log transformed ratio of means*(Hedges et al., 1999; Lajeunesse, 2011).

`m1i`

and `m2i`

have opposite signs, this outcome measure cannot be computed.
The positive bias in the standardized mean difference is automatically corrected for within the function, yielding Hedges' g for `measure="SMD"`

(Hedges, 1981). Similarly, the same bias correction is applied for `measure="SMDH"`

(Bonett, 2009). For `measure="SMD"`

, one can choose between `vtype="LS"`

(the default) and `vtype="UB"`

. The former uses the usual large-sample approximation to compute the sampling variances. The latter provides unbiased estimates of the sampling variances. Finally, for `measure="MD"`

and `measure="ROM"`

, one can choose between `vtype="LS"`

(the default) and `vtype="HO"`

. The former computes the sampling variances without assuming homoscedasticity (i.e., that the true variances of the measurements are the same in group 1 and group 2 within each study), while the latter assumes homoscedasticity.
A dataset corresponding to data of this type is provided in `dat.normand1999`

(for mean differences and standardized mean differences). A dataset showing the use of the ratio of means measure is provided in `dat.curtis1998`

.
It is also possible to transform standardized mean differences into log odds ratios (e.g., Cox & Snell, 1989; Chinn, 2000; Hasselblad & Hedges, 1995; Sánchez-Meca et al., 2003). The options for the `measure`

argument are then:
`"D2ORN"`

for the*transformed standardized mean difference*as an estimate of the log odds ratio (normal distributions).`"D2ORL"`

for the*transformed standardized mean difference*as an estimate of the log odds ratio (logistic distributions).

`dat.gibson2002`

.
Finally, interest may also be focused on differences between the two groups with respect to their variability. Here, the (log transformed) ratio of the coefficient of variation of the two groups (also called the coefficient of variation ratio) can be a useful measure (Nakagawa et al., 2015). If focus is solely on the variability of the measurements within the two groups, then the (log transformed) ratio of the standard deviations (also called the variability ratio) can be used (Nakagawa et al., 2015). For the latter, one only needs to specify `sd1i`

, `sd2i`

, `n1i`

, and `n2i`

. The options for the `measure`

argument are:
`"CVR"`

for the*log transformed coefficient of variation ratio*.`"VR"`

for the*log transformed variability ratio*.

`measure="CVR"`

is computed as given by equation 12 in Nakagawa et al. (2015), but without the ‘\(-2 \rho \ldots\)’ terms, since for normally distributed data (which we assume here) the mean and variance (and transformations thereof) are independent.
`ri`

, the vector with the raw correlation coefficients, and `ni`

, the corresponding sample sizes. The options for the `measure`

argument are then:
`"COR"`

for the*raw correlation coefficient*.`"UCOR"`

for the*raw correlation coefficient*corrected for its slight negative bias (based on equation 2.3 in Olkin & Pratt, 1958).`"ZCOR"`

for*Fisher's r-to-z transformed correlation coefficient*(Fisher, 1921).

`measure="UCOR"`

, one can choose between `vtype="LS"`

(the default) and `vtype="UB"`

. The former uses the usual large-sample approximation to compute the sampling variances. The latter provides unbiased estimates of the sampling variances (see Hedges, 1989, but using the exact equation instead of the approximation).
Datasets corresponding to data of this type are provided in `dat.mcdaniel1994`

and `dat.molloy2014`

.
`ai`

, `bi`

, `ci`

, and `di`

arguments (or alternatively, one can use the `ai`

, `ci`

, `n1i`

, and `n2i`

arguments). The options for the `measure`

argument are then:
`"OR"`

for the*log odds ratio*.`"PHI"`

for the*phi coefficient*.`"YUQ"`

for*Yule's Q*(Yule, 1912).`"YUY"`

for*Yule's Y*(Yule, 1912).`"RTET"`

for the*tetrachoric correlation*.

`measure="PHI"`

, one must indicate via `vtype="ST"`

or `vtype="CS"`

whether the data for the studies were obtained using stratified or cross-sectional (i.e., multinomial) sampling, respectively (it is also possible to specify an entire vector for the `vtype`

argument in case the sampling schemes differed for the various studies).
A dataset corresponding to data of this type is provided in `dat.bourassa1996`

.
`m1i`

and `m2i`

for the observed means of the two groups, `sd1i`

and `sd2i`

for the observed standard deviations, and `n1i`

and `n2i`

for the number of individuals in each group. The options for the `measure`

argument are then:
`"RPB"`

for the*point-biserial correlation*.`"RBIS"`

for the*biserial correlation*.

`measure="RPB"`

, one must indicate via `vtype="ST"`

or `vtype="CS"`

whether the data for the studies were obtained using stratified or cross-sectional (i.e., multinomial) sampling, respectively (it is also possible to specify an entire vector for the `vtype`

argument in case the sampling schemes differed for the various studies).
`xi`

and `ni`

, denoting the number of individuals experiencing the event of interest and the total number of individuals, respectively. Instead of specifying `ni`

, one can use `mi`

to specify the number of individuals that do not experience the event of interest. The options for the `measure`

argument are then:
`"PR"`

for the*raw proportion*.`"PLN"`

for the*log transformed proportion*.`"PLO"`

for the*logit transformed proportion*(i.e., log odds).`"PAS"`

for the*arcsine square root transformed proportion*(i.e., the angular transformation).`"PFT"`

for the*Freeman-Tukey double arcsine transformed proportion*(Freeman & Tukey, 1950).

`to="only0"`

(the default), the value of `add`

(the default is `1/2`

; but see ‘Note’) is added to `xi`

and `mi`

only for studies where `xi`

or `mi`

is equal to 0. When `to="all"`

, the value of `add`

is added to `xi`

and `mi`

in all studies. When `to="if0all"`

, the value of `add`

is added in all studies, but only when there is at least one study with a zero value for `xi`

or `mi`

. Setting `to="none"`

or `add=0`

has the same effect: No adjustment to the observed values is made. Depending on the outcome measure and the data, this may lead to division by zero inside of the function (when this occurs, the resulting value is recoded to `NA`

).
Datasets corresponding to data of this type are provided in `dat.pritz1997`

and `dat.debruin2009`

.
`xi`

and `ti`

, denoting the number of events that occurred and the total person-times at risk, respectively. The options for the `measure`

argument are then:
`"IR"`

for the*raw incidence rate*.`"IRLN"`

for the*log transformed incidence rate*.`"IRS"`

for the*square root transformed incidence rate*.`"IRFT"`

for the*Freeman-Tukey transformed incidence rate*(Freeman & Tukey, 1950).

`to="only0"`

(the default), the value of `add`

(the default is `1/2`

; but see ‘Note’) is added to `xi`

only in the studies that have zero events. When `to="all"`

, the value of `add`

is added to `xi`

in all studies. When `to="if0all"`

, the value of `add`

is added to `xi`

in all studies, but only when there is at least one study with zero events. Setting `to="none"`

or `add=0`

has the same effect: No adjustment to the observed number of events is made. Depending on the outcome measure and the data, this may lead to division by zero inside of the function (when this occurs, the resulting value is recoded to `NA`

).
`mi`

, `sdi`

, and `ni`

for the observed means, the observed standard deviations, and the sample sizes, respectively. For ratio scale measurements, the log transformed mean or the log transformed coefficient of variation (with bias correction) may also be of interest (Nakagawa et al., 2015). If focus is solely on the variability of the measurements, then the log transformed standard deviation (with bias correction) is a useful measure (Nakagawa et al., 2015; Raudenbush & Bryk, 1987). Here, one only needs to specify `sdi`

and `ni`

.
The options for the `measure`

argument are:
`"MN"`

for the*raw mean*.`"MNLN"`

for the*log transformed mean*.`"CVLN"`

for the*log transformed coefficient of variation*.`"SDLN"`

for the*log transformed standard deviation*.

`sdi`

is used to specify the standard deviations of the observed values of the response, characteristic, or dependent variable and not the standard errors of the means. Also, the sampling variance for `measure="CVLN"`

is computed as given by equation 27 in Nakagawa et al. (2015), but without the ‘\(-2 \rho \ldots\)’ term, since for normally distributed data (which we assume here) the mean and variance (and transformations thereof) are independent.
trt 2 outcome 1 | trt 2 outcome 2 | |

trt 1 outcome 1 | `ai` | `bi` |

trt 1 outcome 2 | `ci` | `di` |

`ai`

, `bi`

, `ci`

, and `di`

denote the cell frequencies. Note that ‘trt1’ and ‘trt2’ may be applied to a single group of subjects or to matched pairs of subjects. The data from such a study can be rearranged into a marginal table of the form:
outcome 1 | outcome 2 | |

trt 1 | `ai+bi` | `ci+di` |

trt 2 | `ai+ci` | `bi+di` |

`measure`

argument that will compute outcome measures based on the marginal table are:
`"MPRR"`

for the matched pairs*marginal log risk ratio*.`"MPOR"`

for the matched pairs*marginal log odds ratio*.`"MPRD"`

for the matched pairs*marginal risk difference*.

`measure`

argument that will compute outcome measures based on the paired table are:
`"MPORC"`

for the*conditional log odds ratio*.`"MPPETO"`

for the*conditional log odds ratio*estimated with Peto's method.

`m1i`

and `m2i`

, the observed means at the two measurement occasions, `sd1i`

and `sd2i`

for the corresponding observed standard deviations, `ri`

for the correlation between the scores observed at the two measurement occasions, and `ni`

for the sample size. The options for the `measure`

argument are then:
`"MC"`

for the*raw mean change*.`"SMCC"`

for the*standardized mean change*using change score standardization.`"SMCR"`

for the*standardized mean change*using raw score standardization.`"SMCRH"`

for the*standardized mean change*using raw score standardization with heteroscedastic population variances at the two measurement occasions (Bonett, 2008).`"ROMC"`

for the*log transformed ratio of means*(Lajeunesse, 2011).

`m1i`

and `m2i`

are unknown, but the raw mean change is directly reported in a particular study, then you can set `m1i`

to that value and `m2i`

to 0 (making sure that the raw mean change was computed as `m1i-m2i`

within that study and not the other way around). Also, for the raw mean change (`"MC"`

) or the standardized mean change using change score standardization (`"SMCC"`

), if `sd1i`

, `sd2i`

, and `ri`

are unknown, but the standard deviation of the change scores is directly reported, then you can set `sd1i`

to that value and both `sd2i`

and `ri`

to 0. Finally, for the standardized mean change using raw score standardization (`"SMCR"`

), argument `sd2i`

is actually not needed, as the standardization is only based on `sd1i`

(Becker, 1988; Morris, 2000), which is usually the pre-test standard deviation (if the post-test standard deviation should be used, then set `sd1i`

to that). Note all of these measures are also applicable for matched-pairs designs (subscripts 1 and 2 then simply denote the first and second group that are formed by the matching).
Finally, interest may also be focused on differences in the variability of the measurements at the two measurement occasions (or between the two matched groups). Here, the (log transformed) ratio of the coefficient of variation (also called the coefficient of variation ratio) can be a useful measure (Nakagawa et al., 2015). If focus is solely on the variability of the measurements, then the (log transformed) ratio of the standard deviations (also called the variability ratio) can be used (Nakagawa et al., 2015). For the latter, one only needs to specify `sd1i`

, `sd2i`

, `ni`

, and `ri`

. The options for the `measure`

argument are:
`"CVRC"`

for the*log transformed coefficient of variation ratio*.`"VRC"`

for the*log transformed variability ratio*.

`ai`

, `mi`

, and `ni`

for the observed alpha values, the number of items/replications/parts of the measurement instrument, and the sample sizes, respectively. One can either directly analyze the raw Cronbach's alpha values or transformations thereof (Bonett, 2002, 2010; Hakstian & Whalen, 1976). The options for the `measure`

argument are then:
`"ARAW"`

for*raw alpha*values.`"AHW"`

for*transformed alpha values*(Hakstian & Whalen, 1976).`"ABT"`

for*transformed alpha values*(Bonett, 2002).

`"AHW"`

, the transformation \(1-(1-\alpha)^{1/3}\) is used, while for `"ABT"`

, the transformation \(-ln(1-\alpha)\) is used. This ensures that the transformed values are monotonically increasing functions of \(\alpha\).
A dataset corresponding to data of this type is provided in `dat.bonett2010`

.
`ti`

for the test statistics (i.e., t-tests) of the regression coefficient of interest, `ni`

for the sample sizes of the studies, `mi`

for the number of predictors in the regression models, and `r2i`

for the \(R^2\) value of the regression models (the latter is only needed when `measure="SPCOR"`

). The options for the `measure`

argument are then:
`"PCOR"`

for the*partial correlation coefficient*.`"ZPCOR"`

for*Fisher's r-to-z transformed partial correlation coefficient*.`"SPCOR"`

for the*semi-partial correlation coefficient*.

`ti`

argument. Also, Fisher's variance stabilizing transformation can only be applied to partial correlation coefficient, not semi-partial coefficients.
`measure`

argument to one of the options described above (or to `measure="GEN"`

for a generic outcome measure not further specified) and passes the observed effect sizes or outcomes via the `yi`

argument and the corresponding sampling variances via the `vi`

argument (or the standard errors via the `sei`

argument).
An object of class `c("escalc","data.frame")`

. The object is a data frame containing the following components:

observed outcomes or effect size estimates.

corresponding (estimated) sampling variances.

The variable names specified under `var.names`

should be syntactically valid variable names. If necessary, they are adjusted so that they are.

Although the default value for `add`

is `1/2`

, for certain measures the use of such a bias correction makes little sense and for these measures, the function internally sets `add = 0`

. This applies to the following measures: `"AS"`

, `"PHI"`

, `"RTET"`

, `"IRSD"`

, `"PAS"`

, `"PFT"`

, `"IRS"`

, and `"IRFT"`

. One can still force the use of the bias correction by explicitly setting the `add`

argument to some non-zero value.

Aloe, A. M. (2014). An empirical investigation of partial effect sizes in meta-analysis of correlational data. *Journal of General Psychology*, **141**, 47--64.

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### copy BCG vaccine data into 'dat' dat <- dat.bcg ### calculate log risk ratios and corresponding sampling variances dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat) dat#> trial author year tpos tneg cpos cneg ablat alloc #> 1 1 Aronson 1948 4 119 11 128 44 random #> 2 2 Ferguson & Simes 1949 6 300 29 274 55 random #> 3 3 Rosenthal et al 1960 3 228 11 209 42 random #> 4 4 Hart & Sutherland 1977 62 13536 248 12619 52 random #> 5 5 Frimodt-Moller et al 1973 33 5036 47 5761 13 alternate #> 6 6 Stein & Aronson 1953 180 1361 372 1079 44 alternate #> 7 7 Vandiviere et al 1973 8 2537 10 619 19 random #> 8 8 TPT Madras 1980 505 87886 499 87892 13 random #> 9 9 Coetzee & Berjak 1968 29 7470 45 7232 27 random #> 10 10 Rosenthal et al 1961 17 1699 65 1600 42 systematic #> 11 11 Comstock et al 1974 186 50448 141 27197 18 systematic #> 12 12 Comstock & Webster 1969 5 2493 3 2338 33 systematic #> 13 13 Comstock et al 1976 27 16886 29 17825 33 systematic #> yi vi #> 1 -0.8893 0.3256 #> 2 -1.5854 0.1946 #> 3 -1.3481 0.4154 #> 4 -1.4416 0.0200 #> 5 -0.2175 0.0512 #> 6 -0.7861 0.0069 #> 7 -1.6209 0.2230 #> 8 0.0120 0.0040 #> 9 -0.4694 0.0564 #> 10 -1.3713 0.0730 #> 11 -0.3394 0.0124 #> 12 0.4459 0.5325 #> 13 -0.0173 0.0714### suppose that for a particular study, yi and vi are known (i.e., have ### already been calculated) but the 2x2 table counts are not known; with ### replace=FALSE, the yi and vi values for that study are not replaced dat[1:12,10:11] <- NA dat[13,4:7] <- NA dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat, replace=FALSE) dat#> trial author year tpos tneg cpos cneg ablat alloc #> 1 1 Aronson 1948 4 119 11 128 44 random #> 2 2 Ferguson & Simes 1949 6 300 29 274 55 random #> 3 3 Rosenthal et al 1960 3 228 11 209 42 random #> 4 4 Hart & Sutherland 1977 62 13536 248 12619 52 random #> 5 5 Frimodt-Moller et al 1973 33 5036 47 5761 13 alternate #> 6 6 Stein & Aronson 1953 180 1361 372 1079 44 alternate #> 7 7 Vandiviere et al 1973 8 2537 10 619 19 random #> 8 8 TPT Madras 1980 505 87886 499 87892 13 random #> 9 9 Coetzee & Berjak 1968 29 7470 45 7232 27 random #> 10 10 Rosenthal et al 1961 17 1699 65 1600 42 systematic #> 11 11 Comstock et al 1974 186 50448 141 27197 18 systematic #> 12 12 Comstock & Webster 1969 5 2493 3 2338 33 systematic #> 13 13 Comstock et al 1976 NA NA NA NA 33 systematic #> yi vi #> 1 -0.8893 0.3256 #> 2 -1.5854 0.1946 #> 3 -1.3481 0.4154 #> 4 -1.4416 0.0200 #> 5 -0.2175 0.0512 #> 6 -0.7861 0.0069 #> 7 -1.6209 0.2230 #> 8 0.0120 0.0040 #> 9 -0.4694 0.0564 #> 10 -1.3713 0.0730 #> 11 -0.3394 0.0124 #> 12 0.4459 0.5325 #> 13 -0.0173 0.0714### convert a regular data frame to an 'escalc' object ### dataset from Lipsey & Wilson (2001), Table 7.1, page 130 dat <- data.frame(id = c(100, 308, 1596, 2479, 9021, 9028, 161, 172, 537, 7049), yi = c(-0.33, 0.32, 0.39, 0.31, 0.17, 0.64, -0.33, 0.15, -0.02, 0.00), vi = c(0.084, 0.035, 0.017, 0.034, 0.072, 0.117, 0.102, 0.093, 0.012, 0.067), random = c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1), intensity = c(7, 3, 7, 5, 7, 7, 4, 4, 5, 6)) dat <- escalc(measure="SMD", yi=yi, vi=vi, data=dat, slab=paste("Study ID:", id), digits=3) dat#> id yi vi random intensity #> 1 100 -0.330 0.084 0 7 #> 2 308 0.320 0.035 0 3 #> 3 1596 0.390 0.017 0 7 #> 4 2479 0.310 0.034 0 5 #> 5 9021 0.170 0.072 0 7 #> 6 9028 0.640 0.117 0 7 #> 7 161 -0.330 0.102 1 4 #> 8 172 0.150 0.093 1 4 #> 9 537 -0.020 0.012 1 5 #> 10 7049 0.000 0.067 1 6