Generic t Test

With generic t tests you can perform power analyses for any test that depends on the t distribution. All parameters of the noncentral t distribution can be manipulated independently. Note that with Generic t tests you cannot perform a priori power analyses, the reason being that there is no definite association between N and df (the degrees of freedom). You need to tell G*Power the values of both N and df explicitly. You may, however, enter appropriate values for N and df iteratively in a post-hoc power analysis until the desired level of β is achieved.

Effect size index

In the generic case, the noncentrality parameter δ of the noncentral t distribution may be interpreted as the effect size.

Options

This test has no options.

Examples

To illustrate the use of the generic t test procedure we calculate the power of a one-sample t test. We assume N = 25, µ₀ = 0, µ₁ = 1, and σ = 4, resulting in an effect size of d = (µ₀ − µ₁)/σ = (0 − 1)/4 = −0.25 and a noncentrality parameter of δ = d√N = −0.25√25 = −1.25. The degrees of freedom are df = N − 1 = 24. We choose a post hoc analysis and a two-sided test. As result we get a power of (1 − β) = 0.224525; this is exactly the same value that we also get from the specialized routine for this case in G*Power.

Related tests

Correlation: Point biserial model
Means: Difference between two independent means (two groups)
Means: Difference between two dependent means (matched pairs)
Means: Difference from constant (one sample case)

Implementation notes

One distribution is fixed to the central Student t distribution t(df). The other distribution is a noncentral t distribution t(df, δ) with noncentrality parameter δ.

In the case of a one-sided test the critical value t_c has the same sign as the noncentrality parameter, otherwise there are two critical values t_1c = −t _2c .

Validation

The results were checked against the values produced by GPower 2.0.