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.