Compute effect size from Student's t-test

Compute effect size from Student's t-test for independent samples.

esc_t(
  t,
  p,
  totaln,
  grp1n,
  grp2n,
  es.type = c("d", "g", "or", "logit", "r", "f", "eta", "cox.or", "cox.log"),
  study = NULL,
  ...
)

Arguments

t	The t-value of the t-test. One of t or p must be specified.
p	The p-value of the t-test. One of t or p must be specified.
totaln	Total sample size. Either totaln, or grp1n and grp2n must be specified.
grp1n	Treatment group sample size.
grp2n	Control group sample size.
es.type	Type of effect size that should be returned. "d" returns standardized mean difference effect size d "f" returns effect size Cohen's f "g" returns adjusted standardized mean difference effect size Hedges' g "or" returns effect size as odds ratio "cox.or" returns effect size as Cox-odds ratio (see convert_d2or for details) "logit" returns effect size as log odds "cox.log" returns effect size as Cox-log odds (see convert_d2logit for details) "r" returns correlation effect size r "eta" returns effect size eta squared
study	Optional string with the study name. Using combine_esc or as.data.frame on esc-objects will add this as column in the returned data frame.
...	Other parameters, passed down to further functions. For internal use only, can be ignored.

Value

The effect size es, the standard error se, the variance of the effect size var, the lower and upper confidence limits ci.lo and ci.hi, the weight factor w and the total sample size totaln.

Note

This function only applies to independent sample t-tests, either equal or unequal sample sizes. It can't be used for t-values from dependent or paired t-tests, or t-values from other statistical procedures (like regressions).

If es.type = "r", Fisher's transformation for the effect size r and their confidence intervals are also returned.

References

Lipsey MW, Wilson DB. 2001. Practical meta-analysis. Thousand Oaks, Calif: Sage Publications

Wilson DB. 2016. Formulas Used by the "Practical Meta-Analysis Effect Size Calculator". Unpublished manuscript: George Mason University

Examples

# unequal sample size
esc_t(t = 3.3, grp1n = 100, grp2n = 150)
#> 
#> Effect Size Calculation for Meta Analysis
#> 
#>      Conversion: t-value to effect size d
#>     Effect Size:   0.4260
#>  Standard Error:   0.1305
#>        Variance:   0.0170
#>        Lower CI:   0.1703
#>        Upper CI:   0.6818
#>          Weight:  58.7211

# equal sample size
esc_t(t = 3.3, totaln = 200)
#> 
#> Effect Size Calculation for Meta Analysis
#> 
#>      Conversion: t-value to effect size d
#>     Effect Size:   0.4667
#>  Standard Error:   0.1433
#>        Variance:   0.0205
#>        Lower CI:   0.1858
#>        Upper CI:   0.7476
#>          Weight:  48.6748

# unequal sample size, with p-value
esc_t(p = 0.03, grp1n = 100, grp2n = 150)
#> 
#> Effect Size Calculation for Meta Analysis
#> 
#>      Conversion: t-value to effect size d
#>     Effect Size:   0.2818
#>  Standard Error:   0.1297
#>        Variance:   0.0168
#>        Lower CI:   0.0275
#>        Upper CI:   0.5360
#>          Weight:  59.4337

# equal sample size, with p-value
esc_t(p = 0.03, totaln = 200)
#> 
#> Effect Size Calculation for Meta Analysis
#> 
#>      Conversion: t-value to effect size d
#>     Effect Size:   0.3091
#>  Standard Error:   0.1423
#>        Variance:   0.0202
#>        Lower CI:   0.0303
#>        Upper CI:   0.5880
#>          Weight:  49.4098