Statistics conversion program

Francis, G. (2017). Equivalent statistics and data interpretation, Behavior Research Methods, 49(4), 1524-1538. The R software mentioned in the text is available at the Open Science Framework.

When you run a two-sample t-test you report a variety of statistics. What might not be obvious is that this reporting is often redundant because the statistics are mathematically related in a one-to-one fashion. Given the experimental sample sizes, this program takes any of the indicated statistics and uses algebra and calculus to compute any of the others. These calculations are one-to-one and exact. (Although there may be rounding error in the calculations reported here.) The ability to do these transformations highlights that each of these statistical terms contains equivalent information about whatever effect exists in the data set. Discussions about which term is most meaningful (e.g., p-value, effect size, confidence interval, Bayes Factor) should not be about the information in the statistic but about describing and interpreting that information.

Label	Value	Description
Error criterion		When computing confidence intervals for a standardized effect size, the algorithm has to search through possible limits to find those that correspond to the desired probability in the tail of a non-central t-distribution. This parameter provides a criterion for how close the produced probability must be to the desired probability. Smaller criterion values will produce more precise estimates, but may take longer to calculate. The same criterion is also used when converting a confidence interval limit to an effect size and when converting a JZS BF to a t value. An error message is given below the statistics table whenever this error criterion is not satisfied in a conversion.
Maximum number of searches		When computing confidence intervals for a standardized effect size, the algorithm has to search through possible limits to find those that correspond to the desired probability in the tail of a non-central t-distribution. This parameter sets an upper limit on the number of searches that will be made before halting. A larger value may give more accurate estimates, but may also take longer to calculate. The same criterion is also used when converting a confidence interval limit to an effect size and when converting a JZS BF to a t value.
JZS BF scale for prior		The Cauchy component of the prior distribution is scaled by this value. The default value is sqrt(2)/2.
Integration step size		Converting a t-value to a JZS BF requires integrating over a prior distribution for effect sizes. This parameter is the step size of that integration process. Smaller values will produce more precise estimates but will take longer to compute.
Integration limits		Converting a t-value to a JZS BF requires integrating over a prior distribution for effect sizes. This parameter is the upper limit of that integration (the lower limit is the negative of this value). Larger values may produce more precise estimates but will take longer to compute.
Number of significant digits		The statistics table reports this many significant digits. Note that the number of reported digits may be more than what is justified by the computational algorithms.

Statistic	Value
t-value
p-value
Cohen's d
Lower limit for Cohen's d 95% confidence interval
Upper limit for Cohen's d 95% confidence interval
Hedge's g
Lower limit for Hedges' g 95% confidence interval
Upper limit for Hedges' g 95% confidence interval
Post hoc power (from d)
Post hoc power (from g)
JZS Bayes Factor (alt / null)		(might take a long time)
Λ, log likelihood ratio (full / null)		(cannot be negative or zero)
ΔAIC (null - full)
ΔAICc (null - full)
ΔBIC (null - full)