Definition:Significance Level/Motivation

Significance Levels: Motivation

Until relatively recently, these significance levels have been the only ones which were used in practice.

This is because, prior to the advent of high speed electronic computation devices, the process to calculate the $p$-value was time-consuming and generally unfeasible.

Hence critical values corresponding to the above significance levels have been tabulated for many of the commonly used test statistics, such as for the $t$-test, the $F$-test and the $\chi$-squared test.

However, modern statistical software makes it easy to calculate an exact value of $p$.

Hence it is possible to achieve a greater level of information than just to state that $p$ lies between two of the above bounds.

However, these conventional significance levels can still be considered useful criteria for establishing significance.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypothesis testing
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypothesis testing