The p-value is the smallest significance level (i.e. α) at which H0 would be rejected. So if p≤α′, you reject H0. If p>α′, you do not reject (α′ is usually 0.01 or 0.05, etc).
When H0 is rejected, we say the data is significant.
An equivalent definition: The p-value is the probability, calculated assuming H0 is true, of obtaining a test statistic value at least as contradictory to H0 as the value that actually resulted.
In other words, given H0 is true, what is the probability of getting the observed value?
The P-Value for a Z Test
For an approximately normal distribution:
- For upper-tailed, p=1−Φ(z)
- For lower-tailed, p=Φ(z)
- For two-tailed, p=2(1−Φ(|z|))
P-Values for t Test
Just use the tables or software.