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

सूत्र देखें →

सूत्र

## 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).

हल किया गया उदाहरण

H0: mu = 100. True mu = 105. SD = 15, n = 25, z_crit = 1.96.

  1. 01SE = 15 / sqrt(25) = 15 / 5 = 3
  2. 02Non-centrality = (105 - 100) / 3 = 1.667
  3. 03z_beta = 1.96 - 1.667 = 0.293
  4. 04A z_beta of 0.293 corresponds to roughly beta = 0.615
  5. 05Power ≈ 1 - 0.615 = 0.385 (about 39%)
  6. 06This sample size gives low power to detect this effect