- The fourth step is to calculate the
probability value (often called the p value). The p value is the
probability of obtaining a statistic as different or more different
from the parameter specified in the null hypothesis as the statistic
computed from the data. The calculations are made assuming that the
null hypothesis is true. (click here for a
concrete example)

- The probability value computed in Step 4 is compared
with the significance level chosen in Step 2. If the probability is less
than or equal to the significance level, then the null hypothesis is
rejected; if the probability is greater than the significance level
then the null hypothesis is not rejected. When the null hypothesis is
rejected, the outcome is said to be "statistically
significant"
when the null hypothesis is not rejected then the outcome is said be "not
statistically significant."

- If the outcome is statistically significant,
then the null hypothesis is rejected in favor of the alternative hypothesis.
If the rejected null hypothesis were that μ
_{1}- μ_{2}= 0, then the alternative hypothesis would be that μ_{1}≠ μ_{2}. If M_{1}were greater than M_{2}then the researcher would naturally conclude that μ_{1}≥ μ_{2}. (Click here to see why you can conclude more than μ_{1 }≠ μ_{2})