Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have seen two formulas without explanation online:

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


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

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.

share|improve this question
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
Yes, sorry. The first formula is from…, slide 29, and the second formula is from, page 6 – Tyro Nov 21 '12 at 23:16
Here's the URL for the first formula:… – 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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.