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Data Reduction Prior to Inference: Is it Sensible to Use Principal Component Scores to Make Group Comparisons in a Student's t-test or ANOVA?

Data Reduction Prior to Inference: Is it Sensible to Use Principal Component Scores to Make Group Comparisons in a Student's t-test or ANOVA?

Series: Statistics GIDP Colloquium
Location: ENR2 S395
Presenter: Edward Bedrick, University of Arizona

There has been a significant recent development of statistical methods, for inference with high-dimensional data.  Despite these developments, which includes research by faculty at the UofA, biomedical researchers and computational scientists often use a simple two-step step process to analyze high dimensional data. First, the dimensionality is reduced using a standard technique such as principal component analysis, followed by a group comparison using a t-test or analysis of variance. In this talk, I will try to untangle a number of issues associated with this approach, stating with the simplest but most vexing question (since this is left unstated)- what hypothesis is being tested? I will use a combination of approaches, including asymptotics, analytical construction of worst case scenarios, and simulation based on actual data to address whether this approach is sensible. Although asymptotics will consider a non-sparse setting, some discussion of implications in sparse problems will be given. 

(Refreshments will be served.)

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