Location quotients are used to quickly explain the concentration of something in a small area compared with the whole.

I'd like to use these statistics to compare the concentration of various immigrant groups in a metro with the country overall. The basic quotient is simple to calculate, but I'm not sure I'm calculating the MoE correctly.

Here's a simple example. I calculate the prop_moe following the formula described here, under "Calculating Measures of Error for User-Derived Proportions and Percentages."

subgroup | subgroup_moe | pop | pop_moe | prop | prop_moe | |

local | 3449 | 727 | 1571784 | 0 | 0.00219 | 0.00046 |

nation | 155955 | 5145 | 329725481 | 0 | 0.00047 | 0.00002 |

The location quotient is the ratio of the local proportion to the national proportion, or 0.00219 / 0.00047 = 4.659574.

I calculated the MoE for this ratio using the formula under "Calculating Measures of Error for Derived Ratios" (from the same ACS handbook as linked above).

The result is 0.9898, which passes the smell test.

In the ACS handbook example of this formula, X and Y are both counts, not proportions.

Is it still correct to use this formula to calculate the MoE of a ratio of proportions, as I have done above?