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Note: This vignette is a work in progress.
This vignette will walk you through estimating barebones meta-analyses of correlations between multiple constructs. For more vignettes, see the psychmeta overview.
To begin, you will need your meta-analytic data sheet for analysis. We recommend the rio package for importing data to R. For an introduction to rio, see vignette("rio", "rio")
.
psychmeta assumes that your data are in “long” format, with each row corresponding to one effect size. For example, this is the format used in this data frame:
sample_id | moderator | x_name | y_name | n | rxyi | rxxi | ryyi | citekey |
---|---|---|---|---|---|---|---|---|
1 | 1 | X | Y | 416 | 0.49 | 0.79 | 0.77 | Watson2005 |
1 | 1 | X | Z | 416 | 0.40 | 0.79 | 0.77 | Watson2005 |
1 | 1 | Y | Z | 416 | 0.36 | 0.77 | 0.77 | Watson2005 |
2 | 1 | X | Y | 241 | 0.54 | 0.82 | 0.84 | Watson2005 |
2 | 1 | X | Z | 241 | 0.56 | 0.82 | 0.89 | Watson2005 |
2 | 1 | Y | Z | 241 | 0.62 | 0.84 | 0.89 | Watson2005 |
3 | 1 | X | Y | 479 | 0.34 | 0.73 | 0.87 | Zellars2006 |
3 | 1 | X | Z | 479 | 0.40 | 0.73 | 0.79 | Zellars2006 |
3 | 1 | Y | Z | 479 | 0.53 | 0.87 | 0.79 | Zellars2006 |
4 | 1 | X | Y | 167 | 0.37 | 0.78 | 0.79 | Bandura1980 |
In this table, - sample_id
contains labels indicating the sample each effect size is drawn from; - moderator
is a moderator variable, each row containing the effect size’s level for that moderator; - x_name
and y_name
are columns indicating the variables/constructs being related in the effect size; - n
is the sample size for the effect size; - rxyi
is the effect size (the correlation between the two constructs/variables); - rxxi
and ryyi
are the sample reliability values for the measures of the x_name
and y_name
variables, respectively; - citekey
contains the citations keys for each study (used to generate bibliographies of included studies).
You can see this data set includes correlations among three variables: X
, Y
, and Z
, and that each sample contributes several effect sizes, one each for for different pairs of variables/constructs.
If your data are in a different format, you can use the reshape_wide2long()
function to reshape it.
Let’s assume your data frame is called coding_sheet
.
coding_sheet <- data_r_meas_multi
head(coding_sheet)
#> sample_id moderator x_name y_name n rxyi rxxi ryyi citekey
#> 1 1 1 X Y 416 0.49 0.79 0.77 Watson2005
#> 2 1 1 X Z 416 0.40 0.79 0.77 Watson2005
#> 3 1 1 Y Z 416 0.36 0.77 0.77 Watson2005
#> 4 2 1 X Y 241 0.54 0.82 0.84 Watson2005
#> 5 2 1 X Z 241 0.56 0.82 0.89 Watson2005
#> 6 2 1 Y Z 241 0.62 0.84 0.89 Watson2005
The primary function to conduct meta-analyses of correlations is ma_r()
. To conduct barebones meta-analyses, run:
ma_res <- ma_r(rxyi = rxyi,
n = n,
construct_x = x_name,
construct_y = y_name,
sample_id = sample_id,
moderators = moderator,
data = coding_sheet
)
#> **** Running ma_r: Meta-analysis of correlations ****
data
is your data frame.rxyi
, n
, construct_x
, construct_y
, sample_id
, and moderators
are the names of the columns in your data frame that contain the appropriate values.
rxyi
is the correlation effect sizes;n
is the sample sizes;construct_x
and construct_y
are the labels for the variables/constructs being correlated;sample_id
is the sample identification labels;moderators
is a vector of moderator variable names for the meta-analyses."rxyi"
, "n"
) or without (e.g., rxyi
, n
).To conduct a barebones meta-analysis, at minimum, n
and rxyi
are needed.
By default, correlations are weighted by sample size. You can specify alternative weights using the wt_type
argument.
Random-effects variance (τ2 or SDres2) is estimated using the Hunter-Schmidt estimator, computed using the unbiased sample variance estimator (i.e., dividing by \(k-1\) rather than \(k\)). To use the maximum-likelihood estimator instead, specify var_unbiased = FALSE
.
Barebones results are corrected for the small-sample bias in the correlation coefficient. To disable this correction, specify correct_bias = FALSE
.
By default, confidence and credibility intervals are constructed using a t distribution with \(k-1\) degrees of freedom. To use a normal distribution instead, specify, conf_method = "norm"
and cred_method = "norm"
. To customize the coverage levels for these intervals, use the conf_level
and cred_level
arguments.
A psychmeta meta-analsyis object is a data frame, with each row being a meta-analysis or subanalysis and each column containing information about or results from that analysis. For example, the results of the analysis above look like this:
ma_res
#> Overview tibble of psychmeta meta-analysis of correlations
#> ----------------------------------------------------------------------
#> # A tibble: 9 × 8
#> analysis_id pair_id construct_x construct_y analysis_type moderator meta_tables escalc
#> * <int> <int> <fct> <fct> <fct> <fct> <named list> <named list>
#> 1 1 1 X Y Overall All Levels <named list [3]> <named list [4]>
#> 2 2 1 X Y Simple Moderator 1 <named list [3]> <named list [4]>
#> 3 3 1 X Y Simple Moderator 2 <named list [3]> <named list [4]>
#> 4 4 2 X Z Overall All Levels <named list [3]> <named list [4]>
#> 5 5 2 X Z Simple Moderator 1 <named list [3]> <named list [4]>
#> 6 6 2 X Z Simple Moderator 2 <named list [3]> <named list [4]>
#> 7 7 3 Y Z Overall All Levels <named list [3]> <named list [4]>
#> 8 8 3 Y Z Simple Moderator 1 <named list [3]> <named list [4]>
#> 9 9 3 Y Z Simple Moderator 2 <named list [3]> <named list [4]>
#>
#> To extract results, try summary() or the get_stuff functions (run ?get_stuff for help).
Each row corresponds to a different pair of variables/constructs (X-Y; X-Z; Y-Z) and level of the moderator variable (overall/all levels pooled together; moderator = 1; moderator = 2).
analysis_id
is a numeric label for each analysis;
pair_id
is a numeric label for each pair of variables/constructs (X-Y; X-Z; Y-Z);
construct_x
and construct_y
indicate which variables/constructs are being meta-analyzed.
analysis_type
indicates the type of analysis.
“Overall” means an overall meta-analysis, pooling across all moderator levels.
“Simple Moderator” means a subgroup moderator analysis of only studies with the specified levels of the moderator variable(s) in the next column(s).
(See below for how to conduct meta-analyses with multiple moderator variables or with continuous moderators)
meta_tables
contains the principal meta-analysis results tables.
escalc
contains tables of effect sizes, sampling error variances, weights, residuals, and other data. These tables can be used for follow-up analyses or with the metafor package for additional meta-analysis techniques.
To view meta-anlaysis results tables, use the summary()
function:
summary(ma_res)
#> Bare-bones meta-analysis results
#> ----------------------------------------------------------------------
#> analysis_id pair_id construct_x construct_y analysis_type moderator k N mean_r sd_r se_r sd_res CI_LL_95 CI_UL_95 CR_LL_80 CR_UL_80
#> 1 1 1 X Y Overall All Levels 40 11927 0.317 0.1249 0.0198 0.1135 0.277 0.357 0.169 0.465
#> 2 2 1 X Y Simple Moderator 1 20 5623 0.397 0.0886 0.0198 0.0729 0.356 0.439 0.300 0.494
#> 3 3 1 X Y Simple Moderator 2 20 6304 0.245 0.1086 0.0243 0.0948 0.194 0.296 0.119 0.371
#> 4 4 2 X Z Overall All Levels 40 11927 0.324 0.1288 0.0204 0.1179 0.282 0.365 0.170 0.477
#> 5 5 2 X Z Simple Moderator 1 20 5623 0.422 0.0922 0.0206 0.0780 0.379 0.465 0.319 0.526
#> 6 6 2 X Z Simple Moderator 2 20 6304 0.236 0.0861 0.0193 0.0677 0.195 0.276 0.146 0.326
#> 7 7 3 Y Z Overall All Levels 40 11927 0.311 0.1369 0.0217 0.1265 0.268 0.355 0.146 0.476
#> 8 8 3 Y Z Simple Moderator 1 20 5623 0.405 0.1100 0.0246 0.0979 0.354 0.457 0.275 0.535
#> 9 9 3 Y Z Simple Moderator 2 20 6304 0.228 0.0997 0.0223 0.0841 0.181 0.274 0.116 0.339
#>
#>
#> Information available in the meta-analysis object includes:
#> - meta_tables [ access using get_metatab() ]
#> - escalc [ access using get_escalc() ]
In this table,
analysis_id
, pair_id
, construct_x
, construct_y
, and the moderator columns are defined as above.k
is the number of effect sizes contributing to each meta-analysis. N
is the total sample size contributing to each meta-analysis.mean_r
is the weighted mean correlation.sd_r
is the weighted observed standard deviation of correlations.se_r
is the standard error of mean_r
.sd_res
is the estimated random-effects standard deviation (residual SD of correlations after accounting for sampling error).CI_LL_95
and CI_UL_95
are the upper and lower bounds of the confidence interval for mean_r
; the number indicates the coverage level (default: 95%).CR_LL_80
and CR_UL_80
are the upper and lower bounds of the credibility interval for the estimated population distribution; the number indicates the coverage level (default: 80%).To view additional results, such as observed variance (var_r
) or standard deviation of sampling errors (sd_e
), use the get_metatab()
function and select the appropriate columns:
names(get_metatab(ma_res))
#> [1] "analysis_id" "pair_id" "construct_x" "construct_y" "analysis_type" "moderator" "k" "N" "mean_r"
#> [10] "var_r" "var_e" "var_res" "sd_r" "se_r" "sd_e" "sd_res" "CI_LL_95" "CI_UL_95"
#> [19] "CR_LL_80" "CR_UL_80"
get_metatab(ma_res)$var_r
#> [1] 0.015607018 0.007854615 0.011804107 0.016601343 0.008502949 0.007418860 0.018751347 0.012097853 0.009938716
To view all columns of this table, convert it to a data.frame
or tibble
:
dplyr::as_tibble(get_metatab(ma_res))
#> # A tibble: 9 × 20
#> analysis_id pair_id construct_x construct_y analysis_type moderator k N mean_r var_r var_e var_res sd_r se_r sd_e sd_res CI_LL_95 CI_UL_95
#> <int> <int> <fct> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 X Y Overall All Leve… 40 11927 0.317 0.0156 0.00273 0.0129 0.125 0.0198 0.0523 0.113 0.277 0.357
#> 2 2 1 X Y Simple Moderat… 1 20 5623 0.397 0.00785 0.00255 0.00531 0.0886 0.0198 0.0504 0.0729 0.356 0.439
#> 3 3 1 X Y Simple Moderat… 2 20 6304 0.245 0.0118 0.00281 0.00899 0.109 0.0243 0.0530 0.0948 0.194 0.296
#> 4 4 2 X Z Overall All Leve… 40 11927 0.324 0.0166 0.00270 0.0139 0.129 0.0204 0.0520 0.118 0.282 0.365
#> 5 5 2 X Z Simple Moderat… 1 20 5623 0.422 0.00850 0.00242 0.00608 0.0922 0.0206 0.0492 0.0780 0.379 0.465
#> 6 6 2 X Z Simple Moderat… 2 20 6304 0.236 0.00742 0.00284 0.00458 0.0861 0.0193 0.0533 0.0677 0.195 0.276
#> 7 7 3 Y Z Overall All Leve… 40 11927 0.311 0.0188 0.00275 0.0160 0.137 0.0217 0.0525 0.126 0.268 0.355
#> 8 8 3 Y Z Simple Moderat… 1 20 5623 0.405 0.0121 0.00251 0.00959 0.110 0.0246 0.0501 0.0979 0.354 0.457
#> 9 9 3 Y Z Simple Moderat… 2 20 6304 0.228 0.00994 0.00286 0.00708 0.0997 0.0223 0.0535 0.0841 0.181 0.274
#> # … with 2 more variables: CR_LL_80 <dbl>, CR_UL_80 <dbl>
as.data.frame(get_metatab(ma_res))
#> analysis_id pair_id construct_x construct_y analysis_type moderator k N mean_r var_r var_e var_res sd_r se_r
#> 1 1 1 X Y Overall All Levels 40 11927 0.3166643 0.015607018 0.002731165 0.012875853 0.12492805 0.01975286
#> 2 2 1 X Y Simple Moderator 1 20 5623 0.3971059 0.007854615 0.002545026 0.005309589 0.08862626 0.01981744
#> 3 3 1 X Y Simple Moderator 2 20 6304 0.2449125 0.011804107 0.002813166 0.008990941 0.10864671 0.02429414
#> 4 4 2 X Z Overall All Levels 40 11927 0.3235671 0.016601343 0.002704401 0.013896942 0.12884620 0.02037237
#> 5 5 2 X Z Simple Moderator 1 20 5623 0.4220597 0.008502949 0.002422999 0.006079950 0.09221143 0.02061910
#> 6 6 2 X Z Simple Moderator 2 20 6304 0.2357143 0.007418860 0.002839689 0.004579171 0.08613281 0.01925988
#> 7 7 3 Y Z Overall All Levels 40 11927 0.3113684 0.018751347 0.002751395 0.015999952 0.13693556 0.02165141
#> 8 8 3 Y Z Simple Moderator 1 20 5623 0.4053224 0.012097853 0.002505340 0.009592513 0.10999024 0.02459457
#> 9 9 3 Y Z Simple Moderator 2 20 6304 0.2275640 0.009938716 0.002862440 0.007076275 0.09969311 0.02229206
#> sd_e sd_res CI_LL_95 CI_UL_95 CR_LL_80 CR_UL_80
#> 1 0.05226055 0.11347182 0.2767104 0.3566182 0.1687380 0.4645905
#> 2 0.05044825 0.07286692 0.3556276 0.4385843 0.3003585 0.4938534
#> 3 0.05303929 0.09482057 0.1940642 0.2957607 0.1190165 0.3708084
#> 4 0.05200385 0.11788529 0.2823600 0.3647741 0.1698872 0.4772469
#> 5 0.04922396 0.07797403 0.3789034 0.4652160 0.3185314 0.5255880
#> 6 0.05328873 0.06766957 0.1954029 0.2760257 0.1458675 0.3255611
#> 7 0.05245374 0.12649092 0.2675743 0.3551626 0.1464700 0.4762669
#> 8 0.05005337 0.09794137 0.3538453 0.4567994 0.2752828 0.5353619
#> 9 0.05350178 0.08412060 0.1809062 0.2742218 0.1158747 0.3392533
Results for subgroup analyses for different levels of categorical moderators are shown in the rows of the meta-analysis results table. To estimate confidence intervals for differences between levels or an omnibus ANOVA statistic, use the anova()
function:
anova(ma_res)
#> Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if `.name_repair` is omitted as of tibble 2.0.0.
#> Using compatibility `.name_repair`.
#> This warning is displayed once every 8 hours.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
#> pair_id construct_x construct_y moderator F value df_num df_denom level_1 level_2 mean_1 mean_2 diff CI_LL_95 CI_UL_95
#> 1 1 X Y moderator 23.6 1 36.5 1 2 0.397 0.245 0.152 0.0887 0.216
#> 2 2 X Z moderator 43.6 1 37.8 1 2 0.422 0.236 0.186 0.1292 0.243
#> 3 3 Y Z moderator 28.7 1 37.6 1 2 0.405 0.228 0.178 0.1106 0.245
See Artifact corrections](artifact_corrections.html).
To output the main meta-analysis results table to RMarkdown, Word, HTML, PDF, or other formats, use the metabulate()
function. For example, to output the above results to a Word document, run:
You can add plots for each meta-analysis in ma_res
using the plot_forest()
and plot_funnel()
functions:
ma_res <- plot_funnel(ma_res)
#> Funnel plots have been added to 'ma_obj' - use get_plots() to retrieve them.
ma_res <- plot_forest(ma_res)
#> Forest plots have been added to 'ma_obj' - use get_plots() to retrieve them.
You can view these plots using the get_plots()
function. This will return a list of all of the plots in this results. Specify which meta-analysis you want to view plots for by passing its analysis_id
to [[
:
get_plots(ma_res)[["forest"]][[2]]
#> $moderated
#> NULL
#>
#> $unmoderated
#> $unmoderated$barebones
#>
#> $unmoderated$individual_correction
#> NULL
get_plots(ma_res)[["funnel"]][[2]]
#> $barebones
#>
#> $individual_correction
#> list()
#>
#> $artifact_distribution
#> list()
For forest plots, if you select an “Overall” meta-analysis, it will include plots faceted by moderator levels ("moderated"
) and not ("unmoderated"
):
psychmeta reports the random-effects standard deviaton (τ or SD_res_) and credibility intervals (mean_r
± crit × SDres) in the main meta-analaysis results tables. To view confidence intervals for SD_res_ or additional heterogeneity statistics, use the heterogeneity()
function:
ma_res <- heterogeneity(ma_res)
#> Heterogeneity analyses have been added to 'ma_obj' - use get_heterogeneity() to retrieve them.
get_heterogeneity(ma_res)[[1]][["barebones"]]
#>
#> Heterogeneity results for r
#> ---------------------------
#>
#> Accounted for a total of 17.500% of variance
#>
#> Correlation between r values and artifactual perturbations: 0.418
#>
#> The reliability of observed effect sizes is: 0.825
#>
#>
#> Random effects variance estimates
#> ---------------------------------
#> Hunter-Schmidt method (with k-correction):
#> sd_res (tau): 0.113, SE = 0.016, 95% CI = [0.088, 0.152]
#> var_res (tau^2): 0.013, SE = 0.004, 95% CI = [0.008, 0.023]
#>
#> Q statistic: 222.862 (df = 39, p = 0.000)
#> H: 2.390 H^2: 5.714 I^2: 82.500
#>
#> DerSimonian-Laird method:
#> sd_res (tau): 0.114
#> var_res (tau^2): 0.013
#>
#> Q statistic: 223.408
#> H: 2.393 H^2: 5.728 I^2: 82.543
#>
#> Outlier-robust method (absolute deviation from mean):
#> sd_res (tau_r): 0.121
#> var_res (tau_r^2): 0.015
#>
#> Q_r statistic: 78.734
#> H_r: 2.498 H_r^2: 6.242 I_r^2: 0.840
#>
#> Outlier-robust method (absolute deviation from median):
#> sd_res (tau_m): 0.118
#> var_res (tau_m^2): 0.014
#>
#> Q_m statistic: 77.813
#> H_m: 2.438 H_m^2: 5.944 I_m^2: 0.832
psychmeta supports cumulative meta-analysis for publication/small-sample bias detection, leave-1-out sensitivity analyses, and bootstrap confidence intervals using the sensitivity function:
ma_res <- sensitivity(ma_res)
#> **** Computing sensitivity analyses ****
#> Bootstrapped meta-analyses have been added to 'ma_obj' - use get_bootstrap() to retrieve them.
#> leave-1-out meta-analyses have been added to 'ma_obj' - use get_leave1out() to retrieve them.
#> Cumulative meta-analyses have been added to 'ma_obj' - use get_cumulative() to retrieve them.
get_cumulative(ma_res)[[1]][["barebones"]]
#> Cumulative meta-analysis results
#> ----------------------------------------
#> study_added k N mean_r var_r var_e var_res sd_r se_r sd_e sd_res CI_LL_95 CI_UL_95 CR_LL_80 CR_UL_80
#> 1 28 1 487 0.300 NA 0.00170 NA NA 0.0413 0.0413 NA 0.2194 0.381 NA NA
#> 2 3 2 966 0.320 0.000802 0.00167 -0.000869 0.0283 0.0200 0.0409 0.0000 0.0658 0.575 0.320 0.320
#> 3 31 3 1407 0.270 0.008675 0.00184 0.006838 0.0931 0.0538 0.0429 0.0827 0.0387 0.501 0.114 0.426
#> 4 33 4 1841 0.268 0.005916 0.00188 0.004039 0.0769 0.0385 0.0433 0.0636 0.1453 0.390 0.164 0.372
#> 5 14 5 2273 0.308 0.013208 0.00181 0.011402 0.1149 0.0514 0.0425 0.1068 0.1655 0.451 0.144 0.472
#> 6 1 6 2689 0.336 0.015939 0.00176 0.014180 0.1263 0.0515 0.0419 0.1191 0.2039 0.469 0.161 0.512
#> 7 17 7 3086 0.342 0.013757 0.00177 0.011985 0.1173 0.0443 0.0421 0.1095 0.2336 0.451 0.184 0.500
#> 8 38 8 3461 0.338 0.012208 0.00182 0.010389 0.1105 0.0391 0.0426 0.1019 0.2452 0.430 0.193 0.482
#> 9 6 9 3818 0.338 0.010894 0.00185 0.009040 0.1044 0.0348 0.0431 0.0951 0.2576 0.418 0.205 0.471
#> 10 32 10 4165 0.326 0.011469 0.00192 0.009547 0.1071 0.0339 0.0438 0.0977 0.2498 0.403 0.191 0.462
#> 11 27 11 4510 0.331 0.010806 0.00194 0.008868 0.1040 0.0313 0.0440 0.0942 0.2614 0.401 0.202 0.460
#> 12 37 12 4855 0.317 0.012867 0.00200 0.010862 0.1134 0.0327 0.0448 0.1042 0.2449 0.389 0.175 0.459
#> 13 21 13 5197 0.317 0.011939 0.00203 0.009909 0.1093 0.0303 0.0451 0.0995 0.2505 0.383 0.182 0.452
#> 14 20 14 5536 0.321 0.011481 0.00204 0.009442 0.1072 0.0286 0.0452 0.0972 0.2592 0.383 0.190 0.452
#> 15 24 15 5872 0.324 0.010973 0.00205 0.008923 0.1048 0.0270 0.0453 0.0945 0.2665 0.383 0.197 0.452
#> 16 30 16 6195 0.309 0.015242 0.00212 0.013122 0.1235 0.0309 0.0460 0.1146 0.2428 0.374 0.155 0.462
#> 17 36 17 6515 0.301 0.015529 0.00216 0.013366 0.1246 0.0302 0.0465 0.1156 0.2373 0.365 0.147 0.456
#> 18 23 18 6828 0.306 0.015222 0.00217 0.013051 0.1234 0.0291 0.0466 0.1142 0.2445 0.367 0.154 0.458
#> 19 22 19 7138 0.300 0.015323 0.00221 0.013113 0.1238 0.0284 0.0470 0.1145 0.2403 0.360 0.148 0.452
#> 20 18 20 7441 0.308 0.016155 0.00221 0.013947 0.1271 0.0284 0.0470 0.1181 0.2483 0.367 0.151 0.465
#> 21 11 21 7739 0.313 0.016082 0.00222 0.013867 0.1268 0.0277 0.0471 0.1178 0.2548 0.370 0.156 0.469
#> 22 19 22 8030 0.316 0.015749 0.00223 0.013522 0.1255 0.0268 0.0472 0.1163 0.2601 0.371 0.162 0.470
#> 23 12 23 8315 0.319 0.015428 0.00224 0.013188 0.1242 0.0259 0.0473 0.1148 0.2649 0.372 0.167 0.470
#> 24 40 24 8586 0.315 0.015286 0.00227 0.013012 0.1236 0.0252 0.0477 0.1141 0.2630 0.367 0.165 0.466
#> 25 34 25 8854 0.313 0.014968 0.00230 0.012664 0.1223 0.0245 0.0480 0.1125 0.2624 0.363 0.165 0.461
#> 26 16 26 9110 0.318 0.015639 0.00231 0.013328 0.1251 0.0245 0.0481 0.1154 0.2680 0.369 0.167 0.470
#> 27 5 27 9365 0.320 0.015334 0.00233 0.013006 0.1238 0.0238 0.0483 0.1140 0.2715 0.369 0.171 0.470
#> 28 9 28 9619 0.318 0.015125 0.00236 0.012766 0.1230 0.0232 0.0486 0.1130 0.2704 0.366 0.170 0.467
#> 29 35 29 9869 0.318 0.014723 0.00238 0.012342 0.1213 0.0225 0.0488 0.1111 0.2720 0.364 0.172 0.464
#> 30 39 30 10116 0.320 0.014558 0.00240 0.012163 0.1207 0.0220 0.0489 0.1103 0.2754 0.365 0.176 0.465
#> 31 10 31 10360 0.322 0.014260 0.00241 0.011847 0.1194 0.0214 0.0491 0.1088 0.2778 0.365 0.179 0.464
#> 32 2 32 10601 0.327 0.015026 0.00242 0.012610 0.1226 0.0217 0.0492 0.1123 0.2824 0.371 0.180 0.474
#> 33 13 33 10838 0.328 0.014805 0.00243 0.012373 0.1217 0.0212 0.0493 0.1112 0.2851 0.371 0.183 0.474
#> 34 25 34 11075 0.323 0.015912 0.00247 0.013440 0.1261 0.0216 0.0497 0.1159 0.2787 0.367 0.171 0.474
#> 35 8 35 11288 0.321 0.015838 0.00250 0.013334 0.1258 0.0213 0.0500 0.1155 0.2773 0.364 0.170 0.471
#> 36 29 36 11471 0.319 0.015734 0.00254 0.013193 0.1254 0.0209 0.0504 0.1149 0.2765 0.361 0.169 0.469
#> 37 4 37 11638 0.320 0.015536 0.00257 0.012964 0.1246 0.0205 0.0507 0.1139 0.2782 0.361 0.171 0.468
#> 38 15 38 11786 0.318 0.015541 0.00261 0.012928 0.1247 0.0202 0.0511 0.1137 0.2771 0.359 0.170 0.466
#> 39 26 39 11916 0.317 0.015602 0.00266 0.012942 0.1249 0.0200 0.0516 0.1138 0.2760 0.357 0.168 0.465
#> 40 7 40 11927 0.317 0.015607 0.00273 0.012876 0.1249 0.0198 0.0523 0.1135 0.2767 0.357 0.169 0.465
#>
#> See the 'plots' list for data visualizations.
get_cumulative(ma_res)[[1]][["barebones"]][["plots"]]
#> $mean_plot
#> Warning: Removed 1 rows containing missing values (geom_segment).
#> Warning: Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 rows containing missing values (geom_point).
#>
#> $sd_plot
#> Warning: Removed 1 rows containing missing values (geom_point).
#> Warning: Removed 1 row(s) containing missing values (geom_path).
get_bootstrap(ma_res)[[1]][["barebones"]]
#> Bootstrapped meta-analysis results
#> ----------------------------------------
#> boot_mean boot_var CI_LL_95 CI_UL_95
#> k 4.00e+01 0.00e+00 4.00e+01 4.00e+01
#> N 1.19e+04 3.23e+05 1.08e+04 1.30e+04
#> mean_r 3.17e-01 3.95e-04 2.78e-01 3.55e-01
#> var_r 1.51e-02 9.26e-06 1.10e-02 2.38e-02
#> var_e 2.73e-03 2.52e-08 2.47e-03 3.12e-03
#> var_res 1.24e-02 9.05e-06 8.35e-03 2.13e-02
#> sd_r 1.22e-01 1.55e-04 1.05e-01 1.54e-01
#> se_r 1.93e-02 3.86e-06 1.66e-02 2.44e-02
#> sd_e 5.22e-02 2.29e-06 4.97e-02 5.58e-02
#> sd_res 1.10e-01 1.86e-04 9.13e-02 1.46e-01
#> CI_LL_95 2.78e-01 4.59e-04 2.34e-01 3.17e-01
#> CI_UL_95 3.56e-01 3.62e-04 3.20e-01 3.93e-01
#> CR_LL_80 1.73e-01 9.11e-04 1.05e-01 2.23e-01
#> CR_UL_80 4.61e-01 5.11e-04 4.25e-01 5.14e-01
#>
#> See list item 'boot_data' for meta-analysis results from each bootstrap iteration
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