Are these formulas for transforming P, LSD, MSD, HSD, CI, to SE as an exact or inflated/conservative estimate of $\hat{\sigma}$ correct? Background
I am conducting a meta-analysis that includes previously published data. Often, differences between treatments are reported with P-values, least significant differences (LSD), and other statistics but provide no direct estimate of the variance.
In the context of the model that I am using, an overestimate of variance is okay.
Problem
Here is a list of transformations to $SE$ where $SE=\sqrt{MSE/n}$ (Saville 2003) that I am considering, feedback appreciated; below, I assume that $\alpha=0.05$ so $1-^{\alpha}/_2=0.975$  and variables are normally distributed unless otherwise stated:
Questions:


*

*given $P$, $n$, and treatment means $\bar X_1$ and $\bar X_2$ 
$$SE=\frac{\bar X_1-\bar X_2}{t_{(1-\frac{P}{2},2n-2)}\sqrt{2/n}}$$

*given LSD (Rosenberg 2004), $\alpha$, $n$, $b$ where $b$ is number of blocks, and $n=b$ by default for RCBD
$$SE = \frac{LSD}{t_{(0.975,n)}\sqrt{2bn}}$$

*given MSD (minimum significant difference) (Wang 2000), $n$, $\alpha$, df = $2n-2$
$$SE = \frac{MSD}{t_{(0.975, 2n-2)}\sqrt{2}}$$

*given a 95% Confidence Interval (Saville 2003) (measured from mean to upper or lower confidence limit), $\alpha$, and $n$ $$SE = \frac{CI}{t_{(\alpha/2,n)}}$$

*given Tukey's HSD, $n$, where $q$ is the 'studentized range statistic', $$SE = \frac{HSD}{q_{(0.975,n)}}$$
An R function to encapsulate these equations:


*

*Example Data: 
data <- data.frame(Y=rep(1,5), 
                   stat=rep(1,5), 
                   n=rep(4,5), 
                   statname=c('SD', 'MSE', 'LSD', 'HSD', 'MSD') 


*Example Use:
transformstats(data)    


*The transformstats function:
transformstats <- function(data) {
  ## Transformation of stats to SE
  ## transform SD to SE
  if ("SD" %in% data$statname) {
    sdi <- which(data$statname == "SD")
    data$stat[sdi] <- data$stat[sdi] / sqrt(data$n[sdi])
    data$statname[sdi] <- "SE"
      }
  ## transform MSE to SE
  if ("MSE" %in% data$statname) {
    msei <- which(data$statname == "MSE")
    data$stat[msei] <- sqrt (data$stat[msei]/data$n[msei])
    data$statname[msei] <- "SE"
  }
  ## 95%CI measured from mean to upper or lower CI
  ## SE = CI/t
  if ("95%CI" %in% data$statname) {
    cii <- which(data$statname == '95%CI')
    data$stat[cii] <- data$stat[cii]/qt(0.975,data$n[cii])
    data$statname[cii] <- "SE"
  }
  ## Fisher's Least Significant Difference (LSD)
  ## conservatively assume no within block replication
  if ("LSD" %in% data$statname) {
    lsdi <- which(data$statname == "LSD")
    data$stat[lsdi] <- data$stat[lsdi] / (qt(0.975,data$n[lsdi]) * sqrt( (2 * data$n[lsdi])))
    data$statname[lsdi] <- "SE"
  }
  ## Tukey's Honestly Significant Difference (HSD),
  ## conservatively assuming 3 groups being tested so df =2
  if ("HSD" %in% data$statname) {
    hsdi <- which(data$statname == "HSD" & data$n > 1)
    data$stat[hsdi] <- data$stat[hsdi] / (qtukey(0.975, data$n[lsdi], df = 2))
    data$statname[hsdi] <- "SE"
  }              
  ## MSD Minimum Squared Difference
  ## MSD = t_{\alpha/2, 2n-2}*SD*sqrt(2/n)
  ## SE  = MSD*n/(t*sqrt(2))
  if ("MSD" %in% data$statname) {
    msdi <- which(data$statname == "MSD")
    data$stat[msdi] <- data$stat[msdi] * data$n[msdi] / (qt(0.975,2*data$n[lsdi]-2)*sqrt(2))
    data$statname[msdi] <- "SE"
  }
  if (FALSE %in% c('SE','none') %in% data$statname) {
    print(paste(trait, ': ERROR!!! data contains untransformed statistics'))
  }
  return(data)
}

References
Saville 2003Can J. Exptl Psych. (pdf)
Rosenberg et al 2004 (link)
Wang et al. 2000 Env. Tox. and Chem 19(1):113-117 (link)
 A: Your LSD equation looks fine.  If you want to get back to variance and you have a summary statistic that says something about variability or significance of an effect then you can almost always get back to variance—-you just need to know the formula.  For example, in your equation for LSD you want to solve for MSE, MSE = (LSD/t_)^2 / 2 * b
A: I can only agree with John. Furthermore, perhaps this paper by David Saville helps you with some formula to recalculate variability measures from LSDs et al.:
Saville D.J. (2003). Basic statistics and the inconsistency of multiple comparison procedures. Canadian Journal of Experimental Psychology, 57, 167–175
UPDATE:
If you are looking for more formulas to convert between various effect sizes, books on meta-analysis should provide a lot of these. However, I am not an expert in this area and can't recommend one.
But, I remember that the book by Rosenthal and Rosnow once helped with some formula:
Essentials of Behavioral Research: Methods and Data Analysis
Furthermore, I have heard a lot of good things about the formulas in this book by Rosenthal, Rosnow & Rubin (although I have never used it):
Contrasts and Effect Sizes in Behavioral Research: A Correlational Approach (You should definitely give it a try if a nearby library has it).
If this is not enough, perhaps ask another question on literature for converting effect sizes for meta-analyses. Perhaps someone more into meta-analysis has more grounded recommendations.
A: You may consider trying the R package compute.es. There are several functions for deriving effect size estimates and the variance of the effect size.  
