Intraclass Correlation/2Way Mixed Effects Model
Input Data
The dataset shown below is included in one of the example worksheets of AgreeStat 360 and can therefore be downloaded from the program (This video shows how you may import your own data into AgreeStat360). It contains the ratings that 2 judges J1 and J2 assigned to 5 subjects (or targets).
The objective is to use AgreeStat360 to compute the intraclass correlation coefficient and associated precision measures under the 2way mixed effects model, where the rater effect is fixed while the subject effect is random.
Analysis with AgreeStat/360
To see how AgreeStat360 processes this dataset to produce the intraclass correlation coefficients and associated precision measures, please play the video below. This video can also be watched on youtube.com for more clarity if needed.
Results
The output that AgreeStat360 produces is shown below and has 4 parts. The basic descriptive statistics constitute the first part. The second part shows different variance components, while the third and fourth parts shows the interrater and intrarater reliability estimates respectively, along with their precision measures.

Descriptive statistics: The first part of this output displays basic statistics about the number of nonmissing observations for each variable as well as their mean values or number subjects.

Variance components: This section will typically show the error variance, the subject variance, the rater variance, as well as the subjectrater interaction variance. These variance components are used for calculating the interrater and intrarater reliability coefficients, and could help explain the magnitude of the reliability coefficients.
Note that the rater variance is undefined in this case due to the rater effect being fixed. 
Interrater reliability: This part shows the interrater reliability coefficient, its confidence interval and associated pvalues. You can modify both the confidence level and the ICC null value to obtain the corresponding confidence intervals and pvalues. The blue cells contain dropdown lists contains new confidence levels and ICC null values to choose from.

Intrarater reliability
This part shows the intrarater reliability coefficient, its confidence intervals and associated pvalues. Again, you can modify both the confidence level and the ICC null value to update the corresponding confidence intervals and pvalues.