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UNIFoRU sarnpling MEDfUM sahpl ing SMALL sanpfing
FULL VON B SIGM FULL VON B SIGT.,I FUL], VON B SIGM
HL
+
-+
NS
+
NS-+
Ll0
+
NS+
+NS
t
+NS+
AL
NS+
NS+NS
Table 6: IiIodeI bias in estinatinq three paraneters
under three sampling schehes. n+n indicated- statistlcally
significant over-estinates; n-n ind cates statistically
significant under-estirnates;'rNSn indicated no
statistically significant difference betveen popufation
paraneters and estirnates. rz
Again, no clear pattern emerltes, and one sees no terribly
convincing ernpirical argument for preferring the correct. FULL
model over its reduced conpetitors. perhaps thatts fortunate
since itrs so hard to denonstrate that the FULL model is the
right one.
C. In addition to our concern about model selection, we
can also exanine to some degree the ihportance of sarlpling
schene. When we exanine estinates for our three l-ength
parameters (HL, L[lO], and AL), r^re find that in 17 out of 18
cases, for whatever modeI, predicted lengths are lbetterr, for
the UNIFORM sanpling scheme than for either the IifEDIttM or SI.{ALL
sanpling schehes or for both taken together. Furthernore, as
the follor4'ing tabfe indicales, several of the differences are
significant (though the sheer nunber of hypothesis tests should
rnake us slightly uncornfortable) . Thus we hawe at least linited
statistical evidence that sanpling schemes can be inportant.
12 caution should be used in interpreting this tab1e, for
statistically significant biases can result from both (1) large
average errors in estimating a paraneter (rarhich is bad) and (2)
small variance in estinates (which is good).