Running the analysis

1. To run a Bayesian one sample normal - posterior distribution analysis, from the menus choose: Analyze > Bayesian Statistics > One Sample Normal

   

2. In the Bayesian One Sample Inference: Normal dialog, select logSalary and logSalbegin as Test Variable(s).
3. Select Characterize Posterior Distribution as the Bayesian Analysis. The Bayesian inference is made from a perspective that is approached by characterizing posterior distributions. You can investigate the marginal posterior distribution of the parameter(s) of interest by integrating out the other nuisance parameters, and further construct Bayesian confidence intervals to draw direct inference.
4. Click Priors and define the following prior distribution settings:

   

   1. Select Variance as the Prior on Variance/Precision setting. The setting specifies the prior distribution for the variance parameter.
   2. Select Inverse Chi-Square as the Prior Distribution method. The setting specifies the distribution and parameters for inverse-χ²(ν₀,σ²₀), where ν₀ > 0 is the degree of freedom, and σ²₀ > 0 is the scale parameter.
   3. Enter 2 as the Shape Parameter value. The value specifies the shape parameter a₀ for Inverse-Gamma distribution.
   4. Enter 1 as the Scale Parameter value. The value specifies the scale parameter b₀ for Inverse-Gamma distribution.
   5. Select Normal as the Prior on Mean Given Variance/Precision setting. The setting specifies the distribution and parameters for Normal(μ₀, K^-1₀σ²₀) on variance or Normal(μ₀, K₀/σ²₀) on precision, where μ₀∈ (-∞, ∞) and σ² > 0.
   6. Enter 10 as the Location Parameter value. The value specifies the location parameter for the distribution.
   7. Enter 2 as the Kappa value. The value specifies the value of K₀ in Normal(μ₀, K^-1₀σ²₀) or Normal(μ₀, K₀/σ²₀).
   8. Click Run Analysis.

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