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Extra resources for Breakthroughs in Statistics [Vol I - Foundns, Basic Theory]
1. On the left are familiar methods used for uncensored data sets, data without censored observations. On the right are the equivalent methods used for censored data. Some of the censored methods are direct extensions of the uncensored procedure. Others are computationally very different, but perform the same function. 3 Reporting Limits “Reporting limit” is an intentionally generalized term that represents a variety of thresholds used to censor analytical results. It is a limit above which data values are reported as single numbers without qualiﬁcation by the analytical laboratory.
4 APPLICATION OF SURVIVAL ANALYSIS METHODS TO ENVIRONMENTAL DATA Consider a typical survival analysis problem, a test of whether light bulbs with a new ﬁlament composition last longer than those with the existing ﬁlament. A group of 15 light bulbs for each ﬁlament type is connected to power, and the length of time each burns is measured. After 48 h, it is decided that this sample size is too small, and 20 additional light bulbs of each type are added to the test. After 6 weeks (1008 h) from when it was begun, the experiment is stopped.
The same percent of values near each boundary will by chance fall into a higher category as those falling into a lower category. So from a perspective of the overall data set, there is little need to censor data based on an avoidance of false negatives. They are balanced by errors in the opposite direction. Perhaps the most helpful way to distinguish these two philosophies is that the critical level/USEPA deﬁnition provides a (1 À a)% probability that a true (mean) concentration of zero will be below this limit, while the IUPAC higher deﬁnition provides a (1 À a)% probability that a mean concentration at the detection limit will not overlap measurements of blanks.