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I have seen two formulas without explanation online:

$$Z_{\beta} = t - Z_{\alpha}$$

and

$$Z_{\beta} = \frac{t - \text{EffectSize}}{\sqrt{1 + t^2 / (2 \text{df})}}$$

Of course the simplicity of the first formula is attractive, but I would be proceeding blindly. I do not have training in statistics, and can barely handle the rudimentary concepts. I am hoping someone can help me proceed with a cookbook answer.

Thank you.

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So that we don't guess incorrectly, please tell us the setting or context of your question, what these formulas are for, and what the variables mean (variable names are not universal). Do you have a link to the online explanation you are quoting? – whuber♦ Nov 21 '12 at 22:59
1  
Yes, sorry. The first formula is from uta.edu/faculty/ricard/stats/Lectures/Chapter%25208/…, slide 29, and the second formula is from userwww.sfsu.edu/efc/classes/biol458/power/power1.pdf, page 6 – Tyro Nov 21 '12 at 23:16
1  
Here's the URL for the first formula: uta.edu/faculty/ricard/stats/Lectures/Chapter%208/… – Tyro Nov 21 '12 at 23:41
It seems strange to me that the second formula doesn't use Z-alpha. – Tyro Nov 22 '12 at 17:15
"$t$" in that formula stands for $t_{\alpha, df}$, which plays the same role as $Z_\alpha$. – whuber♦ Nov 23 '12 at 15:15

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