Two Sample Tests - Agricultural Statistical Data Analysis Using Stata - page 73

The other values presented are rarely if ever presented in agri-
cultural experiments; however, a brief explanation is in order. The
Intraclass correlation is the upper bounds of the response _ var
explained by the group _ var and is a similar evaluation of the data
to the R-squared. The asymptotic standard error (Asy. S.E.) and 95%
confidence interval relate to the reliability or dispersion of the intra-
class correlation. The estimated standard deviation (SD) of between
and within treatment effects can be compared to the square root of the
mean square values in the ANOVA table. In the case of the estimated
SD between treatments, a percent of the treatment effect can be seen
by comparing it to the square root of the mean square for the between
treatment effect in the ANOVA table.
One-way Analysis of Variance for absorb:
Number of obs = 99
R-squared = 0.9284
Source SS df MS F Prob > F
----------------------------------------------------------------
Between trt 3.129412 8 .3911765 145.97 0.0000
Within trt .24118409 90 .00267982
----------------------------------------------------------------
Total 3.370596 98 .03439384
Intraclass Asy.
correlation S.E. [95% Conf. Interval]
------------------------------------------------
0.92947 0.03444 0.86198 0.99697
Estimated SD of trt effect .1879305
Estimated SD within trt .051767
Est. reliability of a trt mean 0.99315
(evaluated at n=11.00)