*t, p, & Effect Size Estimator*

## t, p, & Effect Size Estimator

Estimate t from p and vice versa, including associated effect sizes.
Instructions

- This tool estimates
*t*-scores from *p*-values and vice versa for a given number of degrees of freedom υ.
- Just enter a (
*t*,υ) or (*p*,υ) pair and this tool will solve for the missing term.
- The tool also estimates the effect sizes associated to the (
*t*,*p*,υ) triplet.

What is computed?

- This tool computes
*t*-scores from *p*-values and vice versa. These conversions are the same as those obtained from our

- The tool also estimates the statistics that one would obtain if the computed estimates correspond to a set of paired variables
*(x, y)*, or to effect sizes from any two samples of same sizes (*n*_{1} and *n*_{2}); i.e. samples with same degrees of freedom (υ_{1} and υ_{2}).
- The following are estimated

- Pearson's Correlation Coefficient,
- Standard Error of Correlations,
- Signal (explained variations) or
*r*^{2},
- Noise (unexplained variations) or
*1 - r*^{2},
- Signal-to-Noise Ratio or Cohen's
*f*^{2},
- Square Root of Signal/Noise Ratio or Cohen's
*f*,
- Omega Squared,
- Standardized Mean Difference or Cohen's
*d*,
- Hedges's
*g*,
- Log Odds Ratio
*L*,

Although *SE* and *N* are not effect sizes, these are listed as supporting data. Conversions between effect sizes are available online (Beasley, 2007; Borenstein, Hedges, Higgins, & Rothstein, 2009; Psychometrica.de, 2017; Rosenthal & Rubin, 1982).

Who can use this tool?

- Anyone that need to do
*t, p* and effect sizes testing.

Suggested Exercises

- Show that for any two samples of equal sizes .
- Show that a log odds ratio
*L* is about 3.6 times Cohen's *f*; i.e.,

*L = (3.62759...)f*.
- What is the statistical meaning of the following statements?

- Cohen's
*d* is twice Cohen's *f*; i.e. *d = 2f*.
*d* is the derivative of *S/N = f*^{2} respect to *t*.
*1/N* is found in the PDF expression of *Student's t Distribution*.

References

- Beasley, M. (2007).Conversion of Common Test Statistics to r and d Values Retrieved from UAB.edu site.
- Borenstein, M., Larry V. Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009).
Converting Among Effect Sizes. Introduction to Meta-Analysis. Chapter 7. Wiley Online Library.
- Pyschometrica.de (2017). Computation of Effect Sizes.
- Rosenthal, R., & Rubin, D. B. (1982). A Simple, General Purpose Display of Magnitude of Experimental Effect. Journal of Educational Psychology, Vol 74, 2, 166-169. American Psychological Association.

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