A Statistical Comparison of Call Volume Uniformity Due to Mailing Strategy

Abstract For operations such as a decennial census, the U.S. Census Bureau sends mail to potential respondents inviting a self-response. It is suspected that the mailing strategy affects the distribution of call volumes to the U.S. Census Bureau's telephone helplines. For staffing purposes, more uniform call volumes throughout the week are desirable. In this work, we formulate tests and confidence intervals to compare uniformity of call volumes resulting from competing mailing strategies. Regarding the data as multinomial observations, we compare pairs of call volume observations to determine whether one mailing strategy has multinomial cell probabilities closer to the uniform probability vector compared to another strategy. A motivating illustration is provided by call volume data recorded in three studies which were carried out in advance of the 2020 Decennial Census.