# How do you interpret/feedback IRT theta scores?

In classical test theory (CTT), we would say something like: "Your score is higher than 80% of people in the normgroup."

In item response theory (IRT), how do we interpret/feedback a theta score of 0.85? I know that it is supposed to be 'item-referenced' as opposed to be 'norm-referenced', but I am unsure how to put this to practice.

You are able to solve tasks that are so difficult that only 20% of others can?

• Could you expand "CTT". IRT is a family of models, so i is important to say which models you consider (binary, 2-parameter Rasch model?). Commented Feb 2, 2016 at 12:04
• I am using a 2 parameter model now. Is the interpretation of theta that different depending upon the number of parameters in the model? Commented Feb 2, 2016 at 14:48
• And what is the most important - what is the distribution of thetas? Typically it's Gaussian (mean 0 std 1, or something different?) but may be something different (fixed or fitted to the data). Commented Feb 4, 2016 at 9:29
• @PiotrMigdal CTT is classical test theory from psychometrics. Commented Feb 23, 2021 at 2:34

As @user136371 says, item response theory (IRT) theta scores estimates $$\hat\theta$$ can be interpreted as standardized z-scores when the latent variable mean $$\mu_\theta$$ and standard deviation $$\sigma_\theta$$ are fixed to 0 and 1 respectively. Remember that this is only the case when an estimation method such as the marginal maximum likelihood (MML) is used.
Additionally, a strength of IRT methods is that reliability is not fixed across $$\theta$$, so $$SE(\hat\theta)$$ should be used in conjunction with $$\hat\theta$$ when interpreting $$\hat\theta$$ as standardized z-scores.