While power meters have an error range of +/- 2% or so, they are at least consistent from one ride to the next, provided the rider zeroes out the baseline reading. So, when a guy says he improved by, say, 10 watts, there isn't a need for an error range of a material size. Even if the precision is +/- 2%, that's only a 0.2 watt range around the reported result.

As for an absolute power reading, what is the 95% confidence interval around a ride-long average of, say, 200 watts, when my power meter is +/- 2% accurate*? I'll leave that to you, the statistics expert. But, I'll give everyone else a hint: You can have great confidence in your power meter.

*Assuming that +/- 2% is two standard deviations around a mean of zero; normally distributed.