Table 2 shows the result of a simulation experiment. The approximate
frequency distribution of t is displayed for the case when the parent
population is chi-squared and when it is normal.
As can be seen, there are substantial differences in the distribution of the
estimated t-statistic when the sample is taken from the chi-squared distribution instead of the normal. These differences will be exacerbated if 2 varies
over time.
How do we cope with statistical problems caused by this bias effect? There
are several approaches: First, we could construct frequency tables of the
estimated t-statistics. These tables could be used for confidence interval
estimation, just as regular t-tables are used to construct confidence intervals
for regression estimates when residuals are homoscedastic and normal.