A significance test is performed to determine if an observed value of a statistic differs enough from a hypothesized value of a parameter to draw the inference that the hypothesized value of the parameter is not the true value. The hypothesized value of the parameter is called the "null hypothesis." A significance test consists of calculating the probability of obtaining a statistic as different or more different from the null hypothesis (given that the null hypothesis is correct) than the statistic obtained in the sample. If this probability is sufficiently low, then the difference between the parameter and the statistic is said to be "statistically significant."

Just how low is sufficiently low? The choice is somewhat arbitrary but by convention levels of 0.05 and 0.01 are most commonly used.

For instance, an experimenter may hypothesize that the size of a food reward does not affect the speed a rat runs down an alley. One group of rats receives a large reward and another receives a small reward for running the alley. Suppose the mean running time for the large reward were 1.5 seconds and the mean running time for the small reward were 2.1 seconds.