Bayesian Independent-Sample Inference: Prior Distribution

You can specify the following prior distribution criteria for your Bayesian Independent-Sample Inference:

Note: Many applied researchers may question the need to specify a prior. Reference priors minimize the concern where the prior is generally overwhelmed as the data increases. When informative prior information is specified, Bayesian methods can effectively use the information. The requirement to specify a prior should not be viewed as a deterrent to using Bayesian analysis.

Data Variance

Provides options for defining data variance settings.

Variance known

When selected, allows you to enter two known group variances. Both values must be > 0.

Group 1 variance: Enter the first known group variance value.
Group 2 variance: Enter the second known group variance value.

Assume equal variance

Controls whether or not the two group variances are assumed to be equal. By default, it is assumed that group variances are unequal. This setting is ignored when values are entered for the two group variances.

Assume unequal variance

Controls whether or not the two group variances are assumed to be unequal. By default, it is assumed that group variances are unequal. This setting is ignored when values are entered for the two group variances.

Prior on variance

Specify the prior distribution for the two equal variances.

Jeffreys: When selected, a non-informative (objective) prior distribution for a parameter space is used.

Inverse-ChiSquare

Specifies the continuous probability distribution of a positive-valued random variable and the parameters for inverse-χ²(ν₀,σ²₀), where ν₀ > 0 is the degree of freedom, and σ²₀ > 0 is the scale parameter.

Degrees of freedom: Specify a value for the number of values in the final calculation that are free to vary.
Scale Parameter: Specify the scale parameter σ²₀ > 0 for inverse-χ²(ν₀,σ²₀). You must enter a single value that is greater than 0. The larger the scale parameter, the more spread out the distribution.

Prior on mean conditional on variance

Provides options for specifying the prior distribution for the two group means.

Note: The Diffuse and Normal options are available only when the Variance known option is selected.

Diffuse: The default setting. Specifies the diffuse prior.
Normal: When selected, you must specify location and scale parameters for the defined group means.
Location Parameter: Enter a numeric values that specifies the location parameters for the group distributions.
Scale Parameter: Specify the scale parameter σ²₀ > 0 for inverse-χ²(ν₀,σ²₀). For each group, you must enter a single value that is greater than 0. The larger the scale parameter, the more spread out the distribution.