est.sd.2g: Estimating Sample Standard Deviations of Two Groups using...

In metaquant: Estimating Means, Standard Deviations and Visualising Distributions using Quantiles

Estimating Sample Standard Deviations of Two Groups using Quantiles

Description

This function estimates the sample standard deviations (SD) from a two group study presenting quantile summary measures with the sample size (n). The quantile summaries of each group can fall into one of the following categories:

• S_1: { minimum, median, maximum }

• S_2: { first quartile, median, third quartile }

• S_3: { minimum, first quartile, median, third quartile, maximum }

The est.sd.2g function uses a novel quantile-based distribution methods for estimating sample SD for two groups such as 'Treatment' and 'Control' (De Livera et al., 2024). The method is based on the following quantile-based distributions:

• Generalized Lambda Distribution (GLD) for estimating sample SDs using 5-number summaries (S_3).

• Skew Logistic Distribution (SLD) for estimating sample SDs using 3-number summaries (S_1 and S_2).

Usage

est.sd.2g(
   min.g1 = NULL, 
   q1.g1 = NULL, 
   med.g1 = NULL, 
   q3.g1 = NULL, 
   max.g1 = NULL,
   min.g2 = NULL, 
   q1.g2 = NULL, 
   med.g2 = NULL, 
   q3.g2 = NULL, 
   max.g2 = NULL,
   n.g1, 
   n.g2, 
   opt = TRUE
)

Arguments

min.g1	numeric value representing the sample minimum of group 1.
q1.g1	numeric value representing the first quartile of group 1.
med.g1	numeric value representing the median of group 1.
q3.g1	numeric value representing the third quartile of group 1.
max.g1	numeric value representing the sample maximum of group 1.
min.g2	numeric value representing the sample minimum of group 2.
q1.g2	numeric value representing the first quartile of group 2.
med.g2	numeric value representing the median of group 2.
q3.g2	numeric value representing the third quartile of group 2.
max.g2	numeric value representing the sample maximum of group 2.
n.g1	numeric value specifying the sample size of group 1.
n.g2	numeric value specifying the sample size of group 2.
opt	logical value indicating whether to apply the optimization step in estimating the parameters of GLD or SLD. Default is TRUE.

Details

For details explaining the method of estimating using GLD or SLD, check est.mean.2g.

Value

A list containing the estimated sample SDs for the two groups:

• sd.g1: numeric value representing the estimated standard deviation of group 1.

• sd.g2: numeric value representing the estimated standard deviation of group 2.

References

Alysha De Livera, Luke Prendergast, and Udara Kumaranathunga. A novel density-based approach for estimating unknown means, distribution visualisations, and meta-analyses of quantiles. Submitted for Review, 2024, pre-print available here: https://arxiv.org/abs/2411.10971

See Also

est.sd for estimating standard deviation from one-group quantile data.

Examples

#Generate 5-point summary data for two groups
set.seed(123)
n_t <- 1000
n_c <- 1500
x_t <- stats::rlnorm(n_t, 5, 0.5)
x_c <- 1.1*(stats::rlnorm(n_c, 5, 0.5))
q_t <- c(min(x_t), stats::quantile(x_t, probs = c(0.25, 0.5, 0.75)), max(x_t))
q_c <- c(min(x_c), stats::quantile(x_c, probs = c(0.25, 0.5, 0.75)), max(x_c))
obs_sd_t <- sd(x_t)
obs_sd_c <- sd(x_c)

#Estimate sample SD using s3 (5 number summary)
est_sds_s3 <- est.sd.2g(q_t[1],q_t[2],q_t[3],q_t[4],q_t[5],
                        q_c[1],q_c[2],q_c[3],q_c[4],q_c[5],
                        n.g1 = n_t,
                        n.g2 = n_c)
est_sds_s3

#Estimate sample SD using s1 (min, med, max)
est_sds_s1 <- est.sd.2g(min.g1=q_t[1], med.g1=q_t[3], max.g1=q_t[5],
                        min.g2=q_c[1], med.g2=q_c[3], max.g2=q_c[5],
                        n.g1 = n_t,
                        n.g2 = n_c)
est_sds_s1

#Estimate sample SD using s2 (q1, med, q3)
est_sds_s2 <- est.sd.2g(q1.g1=q_t[2], med.g1=q_t[3], q3.g1=q_t[4],
                        q1.g2=q_c[2], med.g2=q_c[3], q3.g2=q_c[4],
                        n.g1 = n_t,
                        n.g2 = n_c)
est_sds_s2

metaquant documentation built on April 3, 2025, 10:34 p.m.