Converts binary data, that only reported the number of 'failures' in a group, to \(d\) (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.
failes(B, D, n.1, n.0, level = 95, cer = 0.2, dig = 2, verbose = TRUE, id=NULL, data=NULL)Treatment failure.
Non-treatment failure.
Treatment sample size.
Control/comparison sample size.
Confidence level. Default is 95%.
Control group Event Rate (e.g., proportion of cases showing recovery). Default is 0.2 (=20% of cases showing recovery). CER is used exclusively for NNT output. This argument can be ignored if input is not a mean difference effect size. Note: NNT output (described below) will NOT be meaningful if based on anything other than input from mean difference effect sizes (i.e., input of Cohen's d, Hedges' g will produce meaningful output, while correlation coefficient input will NOT produce meaningful NNT output).
Number of digits to display. Default is 2 digits.
Print output from scalar values? If yes, then verbose=TRUE; otherwise, verbose=FALSE. Default is TRUE.
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.
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.
Standardized mean difference (\(d\)).
Variance of \(d\).
lower confidence limits for \(d\).
upper confidence limits for \(d\).
Cohen's \(U_(3)\), for \(d\).
Common Language Effect Size for \(d\).
Cliff's Delta for \(d\).
p-value for \(d\).
Unbiased estimate of \(d\).
Variance of \(g\).
lower confidence limits for \(g\).
upper confidence limits for \(g\).
Cohen's \(U_(3)\), for \(g\).
Common Language Effect Size for \(g\).
p-value for \(g\).
Correlation coefficient.
Variance of \(r\).
lower confidence limits for \(r\).
upper confidence limits for \(r\).
p-value for \(r\).
Fisher's z (\(z'\)).
Variance of \(z'\).
lower confidence limits for \(z'\).
upper confidence limits for \(z'\).
p-value for \(z'\).
Odds ratio.
lower confidence limits for \(OR\).
upper confidence limits for \(OR\).
p-value for \(OR\).
Log odds ratio.
Variance of log odds ratio.
lower confidence limits for \(lOR\).
upper confidence limits for \(lOR\).
p-value for \(lOR\).
Total sample size.
Number needed to treat.
This formula will first compute an odds ratio and then a log odds and its variance. From there, Cohen's \(d\) is computed and the remaining effect size estimates are then derived from \(d\). Computing 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 $$ln(o)=% log(or)$$
$$v_{ln(o)}=% \frac{1}% {A}+% \frac{1}% {B}+% \frac{1}% {C}+% \frac{1}% {D}$$
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.
# NOT RUN {
# CALCULATE SEVERAL EFFECT SIZES BASED ON NUMBER OF 'FAILURES' IN GROUP:
failes(5, 10, 30, 30)
# }
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