Final answer:
The researcher should conduct a repeated measures design experiment, allowing each participant to experience both conditions and controlling for individual differences.
Step-by-step explanation:
The appropriate type of experiment for a researcher who wants to determine if the order of two conditions affects the outcome is a repeated measures design. This design enables each participant to experience both conditions, and the order in which they do so can be randomized. The repeated measures design is particularly useful in such a situation because it controls for individual differences among participants since each participant serves as their own control. In contrast, a cross-sectional study compares different segments of a population at a single time, a longitudinal study observes the same subjects over a long period, and an independent samples t-test compares the means of two separate groups rather than the same individuals under different conditions.