es_from_plot_ancova_means function

Converts the means and bounds of an error bar (generally extracted from a plot) into four effect measures (SMD, MD, OR, COR)

es_from_plot_ancova_means(
  n_exp,
  n_nexp,
  plot_ancova_mean_exp,
  plot_ancova_mean_nexp,
  plot_ancova_mean_sd_lo_exp,
  plot_ancova_mean_sd_lo_nexp,
  plot_ancova_mean_sd_up_exp,
  plot_ancova_mean_sd_up_nexp,
  plot_ancova_mean_se_lo_exp,
  plot_ancova_mean_se_lo_nexp,
  plot_ancova_mean_se_up_exp,
  plot_ancova_mean_se_up_nexp,
  plot_ancova_mean_ci_lo_exp,
  plot_ancova_mean_ci_lo_nexp,
  plot_ancova_mean_ci_up_exp,
  plot_ancova_mean_ci_up_nexp,
  cov_outcome_r,
  n_cov_ancova,
  smd_to_cor = "viechtbauer",
  reverse_plot_ancova_means
)

Arguments

• n_exp: number of participants in the experimental/exposed group.
• n_nexp: number of participants in the non-experimental/non-exposed group.
• plot_ancova_mean_exp: ancova_mean of participants in the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_nexp: ancova_mean of participants in the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_sd_lo_exp: lower bound of an error bar depicting -1 SD from the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_sd_lo_nexp: lower bound of an error bar depicting -1 SD from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_sd_up_exp: upper bound of an error bar depicting +1 SD from the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_sd_up_nexp: upper bound of an error bar depicting +1 SD from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_se_lo_exp: lower bound of an error bar depicting -1 SE from the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_se_lo_nexp: lower bound of an error bar depicting -1 SE from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_se_up_exp: upper bound of an error bar depicting +1 SE from the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_se_up_nexp: upper bound of an error bar depicting +1 SE from the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_ci_lo_exp: lower bound of an error bar depicting the 95% CI of the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_ci_lo_nexp: lower bound of an error bar depicting the 95% CI of the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• plot_ancova_mean_ci_up_exp: upper bound of an error bar depicting the 95% CI of the ancova_mean of the experimental/exposed group (extracted from a plot).
• plot_ancova_mean_ci_up_nexp: upper bound of an error bar depicting the 95% CI of the ancova_mean of the non-experimental/non-exposed group (extracted from a plot).
• cov_outcome_r: correlation between the outcome and covariate (multiple correlation when multiple covariates are included in the ANCOVA model).
• n_cov_ancova: number of covariates in the ANCOVA model.
• smd_to_cor: formula used to convert the cohen_d value into a coefficient correlation (see details).
• reverse_plot_ancova_means: a logical value indicating whether the direction of the generated effect sizes should be flipped.

Returns

This function estimates and converts between several effect size measures.

natural effect size measure	MD + D + G
converted effect size measure	OR + R + Z
required input data	See 'Section 22. From plot: adjusted means and dispersion (adjusted)'
	https://metaconvert.org/input.html

Details

This function uses the bounds of an error bar of a mean obtained from a plot into a standard deviation. Then, a mean difference (MD), Cohen's d (D), and Hedges' g (G) are estimated. Odds ratio (OR), risk ratio (RR) and correlation coefficients (R/Z) are converted from the Cohen's d value.

To convert the bound of an error bar into a standard deviation,

this function always prioritizes information from the plot_ancova_mean_sd_* arguments, then those from the plot_ancova_mean_se_* arguments, then those from the plot_ancova_mean_ci_* arguments.

1. If the bounds of the standard deviations are provided, the following formulas are used:

$$ancova\_mean\_sd\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_sd\_lo\_exp$$ $$ancova\_mean\_sd\_up\_exp = plot\_ancova\_mean\_sd\_up\_exp - plot\_ancova\_mean\_exp$$ $$ancova\_mean\_sd\_exp = \frac{ancova\_mean\_sd\_lo\_exp + ancova\_mean\_sd\_up\_exp}{2}$$ $$mean\_sd\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_sd\_lo\_nexp$$ $$mean\_sd\_up\_nexp = plot\_ancova\_mean\_sd\_up\_nexp - plot\_ancova\_mean\_nexp$$ $$mean\_sd\_nexp = \frac{mean\_sd\_lo\_nexp + mean\_sd\_up\_nexp}{2}$$

Then, calculations of the es_from_ancova_means_sd are used.

1. If the bounds of the standard errors are provided, the following formulas are used:

$$ancova\_mean\_se\_lo\_exp = plot\_ancova\_mean\_exp - plot\_ancova\_mean\_se\_lo\_exp$$ $$ancova\_mean\_se\_up\_exp = plot\_ancova\_mean\_se\_up\_exp - plot\_ancova\_mean\_exp$$ $$ancova\_mean\_se\_exp = \frac{ancova\_mean\_se\_lo\_exp + ancova\_mean\_se\_up\_exp}{2}$$ $$mean\_se\_lo\_nexp = plot\_ancova\_mean\_nexp - plot\_ancova\_mean\_se\_lo\_nexp$$ $$mean\_se\_up\_nexp = plot\_ancova\_mean\_se\_up\_nexp - plot\_ancova\_mean\_nexp$$ $$mean\_se\_nexp = \frac{mean\_se\_lo\_nexp + mean\_se\_up\_nexp}{2}$$

Then, calculations of the es_from_ancova_means_se are used.

1. If the bounds of the 95% confidence intervals are provided, the calculations of the es_from_ancova_means_ci() are used.

Examples

es_from_plot_ancova_means(
  n_exp = 35, n_nexp = 35,
  cov_outcome_r = 0.2, n_cov_ancova = 4,
  plot_ancova_mean_exp = 89, plot_ancova_mean_nexp = 104,
  plot_ancova_mean_sd_lo_exp = 69, plot_ancova_mean_sd_lo_nexp = 83,
  plot_ancova_mean_sd_up_exp = 109, plot_ancova_mean_sd_up_nexp = 125
)