and the reason why the suitcase is being checked. Not rejecting the null hypothesis does not mean the null hypothesis is "accepted" (see the Interpretation section). The processes described here are perfectly adequate for computation. They seriously neglect the design of experiments considerations. It is particularly critical that appropriate sample sizes be estimated before conducting the experiment. The phrase "test of significance" was coined by statistician Ronald Fisher. Interpretation The p-value is the probability that a given result (or a more significant result) would occur under the null hypothesis. At a significance level of 0.05, a fair coin would be expected to (incorrectly) reject the null hypothesis (that it is fair) in about 1 out of every 20 tests. The p-value does not provide the probability that either the null hypothesis or its opposite is correct (a common source of confusion). If the p-value is less than the chosen significance threshold (equivalently, if the observed test statistic is in the critical region), then we say the null hypothesis is rejected at the chosen level of significance. If the p-value is not less than the chosen significance threshold (equivalently, if the observed test statistic is outside the critical region), then the null hypothesis is not rejected. In the Lady tasting tea example (below), Fisher required the Lady to properly categorize all of the cups of tea to justify the conclusion that the result was unlikely to result from chance. His test revealed that if the lady was effectively guessing at random (the null hypothesis), there was a 1.4% chance that the observed results (perfectly ordered tea) would occur. Rejecting the hypothesis that a large paw print originated from a bear does not immediately prove the existence of Bigfoot. Hypothesis testing emphasizes the rejection, which is based on a probability, rather than the acceptance. "The probability of rejecting the null hypothesis is a function of five factors: whether the test is one- or two-tailed, the level of significance, the standard deviation, the amount of deviation from the null hypothesis, and the number of observations." Use and importance Statistics are helpful in analyzing most collections of data. This is equally true of hypothesis testing which can justify conclusions even when no scientific theory exists. In the Lady tasting tea example, it was "obvious" that no difference existed between (milk poured into tea) and (tea poured into milk). The data contradicted the "obvious". Real