A school selected with a disproportionately low probability relative to its size could result in the school having an excessively large base weight that may need to be trimmed. Unusually large weights are likely to produce large sampling variances of statistics of interest, especially when the large weights are associated with sample cases reflective of rare or atypical characteristics. While the trimming of large weights reduces variances, it also introduces a small bias. However, it is presumed that the reduction in the variances more than compensates for the increase in the bias, thereby reducing the mean square error and thus improving the accuracy of survey estimates (Potter 1988).
When a school base weight has been trimmed, most often it is because of one of two reasons: either the school is a relatively large school that has come in through the new school procedure from a school district selected with a low probability of selection or the school is a private school whose size and affiliation was not known at the time of sampling which was sampled at a rate inappropriate for its large size.
A comparison between each school's base weight and its ideal weight (i.e., the weight that would have resulted had the school been selected from the original public school sampling frame for new schools and from the correct stratum at the appropriate rate for private schools) yielded the desired trimming factor. If the school base weight was more than three times the ideal weight, the trimming factor scaled the base weight back to three times the ideal weight. For a new or private school s in jurisdiction j, the trim factor TRIMjs is:
Ejs-1 is the ideal school base weight and
Sixteen eligible new schools had their weights trimmed: eight out of 64 at grade 4 and eight out of 67 at grade 8. Seventeen eligible unknown-affiliated private schools had their weights trimmed: seven out of 27 at grade 4 and ten out of 32 at grade 8.