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 am doing some self study on statistics and noticed that in the notes that I was using the $|Z|$ expression as attached in the photos below. I am confused with the "$|$" that is being used. The only logical conclusion that I was able to draw was that $P(|Z|\le 2)$ represents $P(-2 < Z < 2)$.

I would appreciate some advice on what the "$|$" symbol means.

enter image description here

enter image description here

share|improve this question
Thanks for the link Glen. – user1275515 Apr 19 '14 at 4:51
up vote 6 down vote accepted

It's the absolute value. So |-5| = 5, and |5| = 5.

$$ P( |Z| \leq 2) = P( Z \leq 2\text{ and}-Z \leq 2) = P(Z \leq 2\text{ and }Z \geq -2) = P(-2 \leq Z \leq 2) = P(Z \geq -2) - P(Z \geq 2) = 1 - H(2) - H(2)$$

share|improve this answer
Thanks Benjamin for the speedy reply. I am curious also why when we have the | symbol in place, we are looking at a two-tail in our calculation? Thank you so much once again. =) – user1275515 Apr 18 '14 at 14:52
By defining the p-value using absolute values you don't need 2 defnitinos for 2-tails and 1-tail tests, but rather 1 equation will suffice. – bdeonovic Apr 18 '14 at 14:57
that's another way of saying that the distribution shown in the plot is symmetric. – user603 Apr 18 '14 at 14:58
Thank you so much everyone. The explanation had been lucid, I now understand the concept. Appreciate it lots. – user1275515 Apr 19 '14 at 4:13

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.