A user of my Introductory Fisheries Analyses with R book recently asked me how to compute standard errors (SE) for the various PSD indices by using the usual equation for the SE of a proportion (square root of p times (1-p) divided by n). Below is my response using the Inch Lake data from the book.

Load required packages.

Load (and prepare) the Inch Lake data used in the Size Structure chapter of the book (this and next step is from this script).

Compute the PSD-X values.

Compute the row sums for the freq table to get the total number of fish (that are stock size or greater). These will be n in the SE calculations.

Compute the SE for PSD-Q.

Repeat for other size indices. For example, for PSD-P.

Note that the SE formula is usually used for proportions (and then multiplied by 100 to get a SE for percentages). However, it can also be shown algebraically to be useful for percentages.

I would caution against using these standard errors to produce confidence intervals for the PSD-X values. If confidence intervals are the end-product for this analysis, then I suggest using the methods described in my book.