A Type of Correlated Data in Operational Testing
ARMY OPERATIONAL TEST AND EVALUATION AGENCY FALLS CHURCH VA
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During a portion of a test, N gunners fired two rounds apiece. The overall proportion of hits on first rounds was very close to the overall proportion of hits on second round shots. However, an individual gunners performance on his second shot was positively correlated with his performance on the first round. The parameter of interest was p, the probability of hit using the firing device. The proportion of hits among the 2N shots was the natural point estimate of p. However, in calculating interval estimates for p at a given confidence level, or tests of hypothesis of the form p or p delta at a given significance level, the situation became more subtle. Since the first round outcome did not deterministically predict the second round outcome, we clearly had more information than just the N first round shots. On the other hand, the assumption that we had 2n independent trials was not justified. In this paper, a model is proposed for the analysis of this and similiar situations. This model generalizes the two round case and considers data in blocks when the observations within blocks are not independent.
- Statistics and Probability