# Finding $p$ value corresponding to $z$ value, using the table with standard normal probabilities

Assuming a table for both negative and positive $z$ values, showing lower tail probabilities
Two sided
##### $p$ value is the probability of finding the observed $z$ value or more extreme, given that the null hypothesis is true.
If you have found a positive $z$ value ($z \geq 0$):
1. Find the row corresponding to the $z$ value you found up to the first decimal, and the column corresponding to the second decimal. At the intersection point of this row and column, you find the left sided $p$ value $p_{left}$
2. The two sided $p$ value is $2 \times (1 - p_{left})$
If you have found a negative $z$ value ($z < 0$):
1. Find the row corresponding to the $z$ value you found up to the first decimal, and the column corresponding to the second decimal. At the intersection point of this row and column, you find the left sided $p$ value $p_{left}$
2. The two sided $p$ value is $2 \times p_{left}$
Right sided
##### $p$ value is the probability of finding the observed $z$ value or larger, given that the null hypothesis is true.
1. Find the row corresponding to the $z$ value you found up to the first decimal, and the column corresponding to the second decimal. At the intersection point of this row and column, you find the left sided $p$ value $p_{left}$
2. The right sided $p$ value is $1 - p_{left}$
Note that if you decided in advance to test right sided but you find a negative $z$ value, you still compute the right sided $p$ value $1 - p_{left}$, resulting in a $p$ value larger than 0.5.
Left sided
##### $p$ value is the probability of finding the observed $z$ value or smaller, given that the null hypothesis is true.
1. Find the row corresponding to the $z$ value you found up to the first decimal, and the column corresponding to the second decimal. At the intersection point of this row and column, you find the left sided $p$ value
Note that if you decided in advance to test left sided but you find a positive $z$ value, you still compute the left sided $p$ value, resulting in a $p$ value larger than 0.5.