Signed rank statistics for coherent predictions
Related Experiment Videos
1Department of Statistics, University of Pennsylvania, Philadelphia 19104-6302, USA.
Abstract:
A generalization of Wilcoxon's signed rank test is proposed for testing a dose-response relationship with one or more outcomes. The test is useful in matched observational studies or in nonrandomized experiments that use dose-response relationships and predictions about multiple outcomes in an effort to distinguish actual treatment effects from hidden biases. A sensitivity analysis indicating whether a dose-response relationship or multiple predictions are confirmed with sufficient strength to reduce sensitivity to hidden bias is performed. Together, the test and the sensitivity analysis help to quantify the degree to which a coherent pattern of associations is present or absent, and the degree to which this strengthens or fails to strengthen evidence of cause and effect. Formal properties of tests of this kind are examined. The form of the optimal test is determined, though this test is not usable because it depends upon the values of the unknown parameters under study. Also examined are the conditions under which the proposed test resembles the optimal test, as well as the impact of various violations of those conditions on power. An example involving matched pairs exposed to varying doses of cadmium is considered in detail.
Related Concept Videos
Ranks
Spearman's Rank Correlation Test
Spearman's test calculates correlation by...
Friedman Two-way Analysis of Variance by Ranks
Confidence Coefficient
The Mantel-Cox Log-Rank Test
Prediction Intervals
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The...