In the case where you are trying to distinguish a shift in cancer rates at the 1 in 1000 level it is statistically insignificant, because your now measuring hit rates in the single digits and trying to distinguish that from other cancer causing factors that are probably at the 1 in 100 level or less (i.e, old people get breast and prostate cancer).
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There is very clear data showing people do not handle radiation well. Plenty of data from Japan that shows a clear correlation of increased cancer rates with increased radiation exposure rates. This data is statistically significant as there were a lot more people than usual getting cancer.
Getting statistical significant data at lower radiation levels is very hard, as the shot noise goes way up as cancer rate deltas go down to near zero. We just don't have enough data to know for sure what the correlations are, and no ethical way to get it.