Sample A: Cover Page of Thesis, Project, or Dissertation Proposal

Table 3.1: Down selection numbers. Number of ProbeSets giving values in the down selected gene lists
that result from applying Welch’s T-test to the output of each probe cleansing method, per dataset, with the
Base Model giving the original size of each dataset. Each of the down-selected lists is then used as input
into the 3 types of models. All of these data are provided in the Supplementary Material Data Folder.
RMA dCHIP BaFL
Base Model 12,625 12,625 4,200
Stearman DE 5,291 5,208 3,344
Bhattacharjee DE 6,595 6,429 480
Cross-Experiment
Intersection !DE
3,761 3,407 325
Figure 3.1 presents the p-value kernel densities resulting from each of the probe cleansing
methods, for the Bhattacharjee data and normally distributed random sampling. The top left graph
estimates the probability distribution (default Gaussian smoothing) for all the p-values for the 3
methods, with respect to the random population. The top right graph presents the quantiles for
the three methods, with respect to the random population. While we observe that the RMA and
dCHIP kernels appear to be more normal, they also demonstrate a large, exaggerated skew and
the quantiles deviate from the expected. The skewed tail represents the population of null p-
values, as shown in the lower left graph, with the accompanying quantiles presented in the lower
right graph. This disproportion of the RMA and dCHIP t-test hypothesis testing results is
associated with the skewed batch intensity distributions we presented in Chapter 2. In stark
contrast, the BaFL p-value density demonstrates a skew for the upper quantiles and becomes
more pronounced for the null p-values [39]. These graphs explain the observed weakness of the
t-test for RMA and dCHIP and are intriguing for the BaFL hypothesis tests, since there seems to
have been an increase in the power of the t-test. Is this increase due to the BaFL cleansing
process or as a result of the bias in the dataset?
76