Critical value意思

"Critical value" is a term used in various contexts, but it is most commonly used in statistics and mathematics. In statistics, a critical value is a value on the distribution of a test statistic that is used to determine whether to reject the null hypothesis. The critical value is determined by the level of significance, which is the probability of incorrectly rejecting a true null hypothesis.

For example, if you are performing a hypothesis test with a significance level of 0.05, you would look up the critical value for your test statistic (such as the z-score, t-score, or chi-square) at the 0.05 level. If the test statistic falls in the critical region (i.e., beyond the critical value), you would reject the null hypothesis. If the test statistic does not exceed the critical value, you would fail to reject the null hypothesis.

In mathematics, the term "critical value" may refer to a value at which the derivative of a function is equal to zero or does not exist, which is a point of inflection or a local maximum or minimum. These critical points are important in calculus because they help identify the behavior of the function.

In other contexts, such as engineering or physics, the term "critical value" may refer to a value that determines the onset of a phase transition or a point of instability.