# Critical value

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Critical value may refer to:

## Topology

In differential topology, a critical value of a differentiable function ƒ : MN between differentiable manifolds is the image (value of) ƒ(x) in N of a critical point x in M.[1]

## Statistics

In statistical hypothesis testing, a critical value is the value corresponding to a given significance level. This cutoff value determines the boundary between those samples resulting in a test statistic that leads to rejecting the null hypothesis and those that lead to a decision not to reject the null hypothesis. If the calculated value from the statistical test is less than the critical value, then you fail to reject the null hypothesis. If the calculated statistic is outside of the critical value, you may reject the null hypothesis at the pre-specified level of significance. Usually this also entails accepting some alternative hypothesis.

## Complex dynamics

In complex dynamics, a critical value is the image of a critical point.

## References

1. ^ do Carmo, Manfredo Perdigão, Differential geometry of curves and surfaces, Prentice Hall, 1976.