Quality-Adjusted Life Years (QALYs) estimate the utility derived from health states by taking account of life expectancy and quality of life. In applying QALYs to situations where health varies over time, it is usual to assume that we can add the utilities from constituent health states. This assumption of additive independence has been challenged by research suggesting that people's preferences for health states are affected by the sequence in which health states occur. This paper investigates two tests of additive independence as well as a test of the consistency of preferences over time. The main test of additive independence is based on a new method using stylised health profiles of deteriorating, improving or temporarily-improving health. The advantage of this new method is that the test relies only on a comparison of health states occurring in the same time period and therefore controls for the effects of time preference. The other test of additive independence determines whether people strictly prefer one type of health profile over another and collects qualitative data on the issues considered by people in these choices. In the main test of additive independence, only one of the two cases considered detected a statistical difference. In the other test of additive independence, the sample was split almost equally between those strictly preferring one or other of the choices. The qualitative data revealed contrasting viewpoints about the benefits derived from such choices which led to this split. The paper also found that preferences were consistent over time. The tests of additive independence were, therefore, unable to conclusively reject additive independence.