Statistical calculators

The detection calculator

Please select the number of groups (1 or 2) for the hypothesis test you wish to use. Then select the button of the variable that you wish to calculate. (The "Hypothesis" headings link to one-page summaries of each test.)

Hypothesis Number of groups    Sample   
size
Significance
level
Detection
probability
    Effect    
size
One-Sided  1 Group   2 Groups
Point-null  1 Group   2 Groups
Equivalence n α Δ
Hypothesis = one-sided: postulates that a parameter is less than (or greater than) a standard value
    point-null: postulates that the parameter equals a standard value
    equivalence: postulates that a parameter is within (or beyond) a stated interval
Group = a set of data, not an individual datum.
n = the number of data in each set of samples (the “sample size”).
α = the significance level, the probability that the tested hypothesis will be rejected when in fact it is true.
D = detection probability. In most cases this is the test's "Statistical Power" (the probability that the tested hypothesis will be rejected), but for testing the hypothesis of inequivalence it is the test's "Operating Characteristic" (the probability that the tested hypothesis will not be rejected).
Δ = effect size. This is (μ-μ0)/σ for the one-group case and (δ-δ0)/σ for the two-group case, where μ is the true mean (standard value μ0), δ is the difference between two means (standard value δ0), and σ is the true standard deviation.

We assume that sampling is from normal distributions with common variances.