The current gold standard for measuring antibody-based immunity to influenza viruses relies on the hemagglutinin inhibition assay (HAI), an 80-year-old technology, and the microneutralization assay (MN). Both assays use serial dilution to provide a discrete, ranked readout of 8-14 categorical titer values for each sample. In contrast to other methods of measuring vaccine antibody levels that produce a continuous readout (i.e., mPLEX-Flu and ELISA), titering methods introduce imprecision and increase false discovery rates (FDR). In this paper, we assess the degree of such statistical errors, first with simulation studies comparing continuous data with titer data in influenza vaccine study group comparison analyses and then by analyzing actual sample data from an influenza vaccine trial. Our results show the superiority of using continuous, rather than discrete, readout assays. Compared to continuous readout assays, titering assays have a lower statistical precision and a higher FDR. The results suggested that traditional titering assays could lead to increased Type-II errors in the comparison of different therapeutic arms of an influenza vaccine trial. These statistical issues are related to the mathematical nature of titer-based assays, which we examine in detail in the simulation studies. Continuous readout assays are free of this issue, and thus it is possible that comparisons of study groups could provide different results with these two methods as we have shown in our case study.