What does this sampling weight mean? - Cross Validated most recent 30 from stats.stackexchange.com 2019-11-22T15:03:50Z https://stats.stackexchange.com/feeds/question/273866 https://creativecommons.org/licenses/by-sa/4.0/rdf https://stats.stackexchange.com/q/273866 5 What does this sampling weight mean? NonSleeper https://stats.stackexchange.com/users/21006 2017-04-15T14:14:30Z 2019-01-29T09:32:14Z <p>The data comes from agricultural market research on farming. The sample was derived based on stratification of farming industries (sheep, beef, grains, etc.) and random sampling within each stratum.</p> <p>We have population estimates (frequencies, percentages/proportions) of these industry strata. Likewise, we have frequencies and proportions of each stratum in the sample.</p> <p>A weight was calculated for each farming stratum by dividing the population proportion by the sample proportion.</p> <p>I'm not sure what that weight means. What I know is weight is an inverse probability of selection of a unit into the sample. Can you give a hint?</p> https://stats.stackexchange.com/questions/273866/-/273992#273992 4 Answer by Roberto for What does this sampling weight mean? Roberto https://stats.stackexchange.com/users/32462 2017-04-16T10:56:09Z 2017-04-18T13:46:36Z <p>Let $N$ be the population size and $n$ the sample size, let $N_h$ and $n_h$ be the population and sample sizes for stratum $h$.</p> <p>Then, the weight you defined is given by</p> <p>$W_h = \frac{N_h/N}{n_h/n} = \frac{N_h}{n_h}\frac{n}{N}$ </p> <p>where $\frac{n}{N}$ is the sampling fraction $f$ for the whole sample and $\frac{N_h}{n_h}$ is the inverse of the sampling fraction, i.e., of the probability of selection, in the $h$-th stratum, $f_h$. Put it differently, $w_{hi}=N_h/n_h$ is the inverse probability sampling weight of a unit $i$ in stratum $h$ that you are familiar with.</p> <p>Writing it as $W_h = \frac{f}{f_h}$, you can see that \begin{equation} \begin{cases} W_h &lt; 1 ,\qquad f_h &gt; f\\ W_h = 1 , \qquad f_h = f\\ W_h &gt; 1 , \qquad f_h &lt;f\\ \end{cases} \end{equation}</p> <p>These are relative weights showing by how much a given stratum was under- or oversampled. These are OK weights to deal with the ratio-type statistics (means, proportions, regression estimates). For the totals, e.g. total acreage under a given crop, or a total harvest, you need the correct inverse probability weights rather than relative weights.</p>