A reader by the name of “Will” fails to understand why trends can be established with confidence even if the uncertainty of the individual values is unknown, even if those values are averages rather than raw data values. It’s a failure he shares with William M. Briggs, numerologist to the stars. Perhaps we can enlighten reader “Will” — I very much doubt anyone can enlighten William M. Briggs.
But first, let’s dispense with a challenge issued by “Will”:
Please make sure that you explain why the time series I presented (102, 97, 98), given the experiment Gator described, is in fact showing a negative trend.
That time series does not show a negative trend. More to the point, nobody claimed it does.
However, we can use a similar example to illustrate when we might actually need to know the uncertainty to detect change, and when we can detect change (in particular, trend) in the absence of knowing the uncertainty.