Advances in science typically follow a sequence of steps shown here.
Dr. Hultquist focuses on the experiment aspect of this sequence. In particular, he studies the mathematics associated with the design of experiments. Some of his interests are in Latin squares, confounding, balanced and partially balanced incomplete block designs, and fractional factorial designs. These designs have been widely used in agriculture, industry, education, medicine, and more recently have been used in space experiments. NASA in particular uses fractional factorial designs. Most of the experiments conducted in space involve many factors for most investigations. If all combinations of factor levels were performed in space, a large number of payloads would be required. With a six-year backlog of payloads waiting their turn, NASA must restrict the number of treatment combinations, and they do this by running particularly important and useful fractions of factorials.
Representative Publications:
Hultquist, R. A., and J. Thomas. 1978. Interval Estimation for the Unbalanced Case of the One-way Random Effects Model. Annals of Statistics 6:582-587.
Hultquist, R. A., G. Mullen, and H. Niederreiter. 1988. Association schemes and derived PBIB designs of prime power order. ARS COMBINATORIA 25:65-82.
Hultquist, R. A., and L. Suchower. 1990. A new property of the association matrices for EGD and hypercubic association schemes. The Journal of Statistical Planning and Inference 25:105-108.