To help prevent anaemia, it is a requisite for blood donors to undergo a haemoglobin test to ensure levels are not too low before donation. It is therefore important to have an accurate testing device and strategy to ensure donors are not being inappropriately bled. A recent study in blood donors used a selective testing strategy where if a donor's haemoglobin level is below the level required for donation, then another reading is taken and if this occurs again, a third and final reading is used. This strategy can reduce the average number of readings required per donor compared to taking three measurements for all donors. However, the final decision-making measurement will on average be higher than a single measurement. In this paper, a selective testing strategy is compared against other strategies. Individual-level biases are derived for the selective strategy and are shown to depend on how close a donor's true haemoglobin level is to the donation threshold and the magnitude of error in the testing device. A simulation study was conducted using the distribution of haemoglobin levels from a large donor population to investigate the effects different strategies have on population performance. We consider scenarios based on varying the measurement device bias and error, including differential biases that depend on the underlying haemoglobin level. Discriminatory performance is shown to be affected when using the selective testing strategies, especially when measurement error is large and when differential bias is present in the device. We recommend that the average of a number of readings should be used in preference to selective testing strategies if multiple measurements are available.