Free Type II Error Calculator
Estimate the probability of a Type II error (beta) and statistical power for a one-sample z-test.
Z for Power Calculation
0.2933
Standard Error3.0000
Non-centrality Parameter1.6667
Effect Size d0.3333
Z for Power Calculation vs Null Hypothesis Mean
Understanding Type II Error
Concept
Beta = P(fail to reject H0 | H0 is false)
Power = 1 - Beta
Type II error occurs when you fail to detect a real effect. The probability depends on the true effect size, sample size, significance level, and population variability. A negative z_beta value indicates high power (likely to detect the effect).
Example Calculation
H0: mu = 100. True mu = 105. SD = 15, n = 25, z_crit = 1.96.
- 01SE = 15 / sqrt(25) = 15 / 5 = 3
- 02Non-centrality = (105 - 100) / 3 = 1.667
- 03z_beta = 1.96 - 1.667 = 0.293
- 04A z_beta of 0.293 corresponds to roughly beta = 0.615
- 05Power ≈ 1 - 0.615 = 0.385 (about 39%)
- 06This sample size gives low power to detect this effect
Frequently Asked Questions
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