compute.es (version 0.2-2)

lores: Log Odds Ratio to Standardized Mean Difference (d)

Description

Converts a log odds ratio to an effect size of $d$ (mean difference), $g$ (unbiased estimate of $d$), $r$ (correlation coefficient), $z'$ (Fisher's $z$), and log odds ratio. The variances, confidence intervals and p-values of these estimates are also computed, along with NNT (number needed to treat), U3 (Cohen's $U_(3)$ overlapping proportions of distributions), CLES (Common Language Effect Size) and Cliff's Delta.

Usage

lores(lor, var.lor, n.1, n.2, level=95, dig=2, id=NULL, data=NULL)

Arguments

lor

Log odds ratio reported in the primary study.

var.lor

Variance of the log odds ratio.

n.1

Sample size of treatment group.

n.2

Sample size of comparison group.

level

Confidence level. Default is 95%.

dig

Number of digits to display. Default is 2 digits.

id

Study identifier. Default is NULL, assuming a scalar is used as input. If input is a vector dataset (i.e., data.frame, with multiple values to be computed), enter the name of the study identifier here.

data

name of data.frame. Default is NULL, assuming a scalar is used as input. If input is a vector dataset (i.e., data.frame, with multiple values to be computed), enter the name of the data.frame here.

Value

• d
  Standardized mean difference ($d$).
• var.d
  Variance of $d$.
• l.d
  lower confidence limits for $d$.
• u.d
  upper confidence limits for $d$.
• U3.d
  Cohen's $U_(3)$, for $d$.
• cl.d
  Common Language Effect Size for $d$.
• cliffs.d
  Cliff's Delta for $d$.
• p.d
  p-value for $d$.
• g
  Unbiased estimate of $d$.
• var.g
  Variance of $g$.
• l.g
  lower confidence limits for $g$.
• u.g
  upper confidence limits for $g$.
• U3.g
  Cohen's $U_(3)$, for $g$.
• cl.g
  Common Language Effect Size for $g$.
• p.g
  p-value for $g$.
• r
  Correlation coefficient.
• var.r
  Variance of $r$.
• l.r
  lower confidence limits for $r$.
• u.r
  upper confidence limits for $r$.
• p.r
  p-value for $r$.
• z
  Fisher's z ($z'$).
• var.z
  Variance of $z'$.
• l.z
  lower confidence limits for $z'$.
• u.z
  upper confidence limits for $z'$.
• p.z
  p-value for $z'$.
• OR
  Odds ratio.
• l.or
  lower confidence limits for $OR$.
• u.or
  upper confidence limits for $OR$.
• p.or
  p-value for $OR$.
• lOR
  Log odds ratio.
• var.lor
  Variance of log odds ratio.
• l.lor
  lower confidence limits for $lOR$.
• u.lor
  upper confidence limits for $lOR$.
• p.lor
  p-value for $lOR$.
• N.total
  Total sample size.
• NNT
  Number needed to treat.

Details

This formula will first convert a log odds and its variance to Cohen's $d$. This value will then be used to compute the remaining effect size estimates. One method for deriving the odds ratio involves $$or= \frac{p_{1}(1-p_{2})} {p_{2}(1-p_{1})}$$ The conversion to a log odds and its variance is defined as $$ln(o)= log(or)$$ $$v_{ln(o)}= \frac{1} {A}+ \frac{1} {B}+ \frac{1} {C}+ \frac{1} {D}$$

References

Borenstein (2009). Effect sizes for continuous data. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta analysis (pp. 279-293). New York: Russell Sage Foundation. Cohen, J. (1988). Statistical power for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum. Furukawa, T. A., & Leucht, S. (2011). How to obtain NNT from Cohen's d: comparison of two methods. PloS one, 6(4), e19070. McGraw, K. O. & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111, 361-365. Valentine, J. C. & Cooper, H. (2003). Effect size substantive interpretation guidelines: Issues in the interpretation of effect sizes. Washington, DC: What Works Clearinghouse.

See Also

propes, failes