While adding information I had gleaned from several new papers I have read over the last week I realised that I had made an error in my analyses. The power analysis of trend is a method of detecting the power of a time series based on simple linear regression models and was developed by Gerrodette in 1987. The coefficient of variation (CV) which is the standard deviation (SD) divided by the mean, is central to this analysis. I noticed this evening that I had been rounding this value incorrectly and when I corrected this flaw it made all of the lower precision data unusable as they were no longer able to accurately show any change. I have now realised that I have been calculating these statistics incorrectly as well. In that I have been rounding these smaller values by digits rather than significant figures.

Rounding by significant figures is different in that the information stored within a number means more than simply what the numbers are. Their placement around the decimal place and how many zeroes are in front of any real numbers is relevant, too. So data collected with a precision of 0.1 must have more than one significant figure past the decimal. But I have incorrectly been rounding by decimal places this whole time, meaning if the SD of a time series with a precision of 0.1 is found to be 0.043443778…, I have been rounding it down to 0.0 as this is the closest value at a precision of 0.1 however!; it would be more appropriate to round this value to 0.04. If the precision had been 0.01, then it would be best to round the previous example to 0.043, and not 0.04 as I would have done previously. This is a pretty stupid mistake to have made and is really going to allow my analyses to run a lot more smoothly… but then I noticed something even worse.

As mentioned previously, CV is at the heart of the power analysis of trend. This is clearly explained in Gerrodette (1987, 1991) and I assumed was the case with the function from the fishmethods package in R. Boy was I wrong! 🙁 It turns out they use proportional standard error (PSE) which is calculated by taking the standard error (SE) and dividing that by the sample size. This number is much much smaller than the SD for these same time series and so will likely cause the power of every time series to increase greatly. Why the authors of this package chose to use PSE rather than CV is confusing and unclear. And frankly rather annoying. I must now redo all of my analyses and re-write up my entire paper. Thankfully I have done everything in R so the analyses should be able to be reworked within a few hours. And much of the re-write will be small. But the work is there to do and must be done.