### Table 2: Power (%) of score test statistic S2 2 with no covariates when data are simulated from binomial (10;p): =:05; based on 10,000 replications.

"... In PAGE 6: ....05, 0.1, 0.2, 0.3, 0.4. Each experiment for size or power was based on 10,000 replications. The results in Table 1 and Table2 indicate that the score tests hold the nominal level reasonably well, although in some instances these show some conservative behaviour. The power of the tests for detecting zero-inflation increases very slowly for low and p.... ..."

### Table 3a Estimated power of proposed test, based on simulations from mixture models using 50 litters beta-binomial binomial mixing

2000

"... In PAGE 8: ... Table 2a illustrates that the estimated size is somewhat close to its nominal level, 0, although the tendency is to be slightly above it. Table3 a tends to suggest that large mixing probabilities produce large power when the overall mean, , of the beta-binomial model di ers greatly from the response probability, p, in the binomial model. Large mixing probabilities ( 0:95) frequently produce at least one extreme value of y.... In PAGE 9: ...shows greater power than Table3 a for the binomial probability p = 0:9. The other values of p did not result in much di erence in power between Tables 3a and 3b.... ..."

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### Table 3b Estimated power of proposed test, based on simulations from mixture models using 100 litters beta-binomial binomial mixing

2000

"... In PAGE 8: ... Table 2a illustrates that the estimated size is somewhat close to its nominal level, 0, although the tendency is to be slightly above it. Table3 a tends to suggest that large mixing probabilities produce large power when the overall mean, , of the beta-binomial model di ers greatly from the response probability, p, in the binomial model. Large mixing probabilities ( 0:95) frequently produce at least one extreme value of y.... In PAGE 9: ...shows greater power than Table3 a for the binomial probability p = 0:9. The other values of p did not result in much di erence in power between Tables 3a and 3b.... ..."

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### Table 1. Summary statistics for the measures of differential expression (DE) and differential connection (DC) in each of the three data sets

"... In PAGE 3: ...nteractions accounted for 0.2% and 9.9% of the total variation, respectively. Table1 presents summary statistics for the measures of DE and DC. As seen, DE measures in all data sets, as well as DC measures in the adipogenesis data, were well-centered around zero, while DC measurements in the inflammation data were skewed towards positive values, indicating an increase in the network connectivity from placebo to infected states.... In PAGE 6: ... 3.5 Relevance of results from the cancer data The identity of the top 50 DE/DC genes in cancerous tissues is given in Table1 of Supplementary Material, and Figure 5 of Supplementary Material presents their heat map obtained from the normalized expression across the 16 tissues for which data from both conditions, cancer and normal, were available. As expected, none of the genes were uniformly DE/DC in all tissues.... In PAGE 6: ... Instead, their ranking reflects a combination of the magnitude of DE and the breadth of tissue representation. While many of the under- and most of the over-expressed genes have been reported in one or more of the many studies in the recent literature (see last column of Table1 of Supplementary Material), most studies have concentrated on a single type of cancer. In addition, the simultaneous identification of DE and DC genes has allowed the detection of many key processes and some of the key effector proteins involved in neoplasia.... ..."

### Table 5 Known differentially 2s-uniform power functions xd on F2m.

in Dedication

"... In PAGE 42: ... Table 4 (resp. Table5 ) gives all known values of exponents d (up to cyclotomic equivalence) that xd is s-nonlinear (resp. differentially 2s- uniform).... ..."

### TABLE 3 Industry Distribution of the Private Firms Compared to Small Firms, IPOs and Firms on Compustat * denotes that a binomial test of differences in proportions indicates significantly different proportions in industries of private firms compared to firms on Compustat or IPOs (but not SSBF firms) at the 10% or lower level of significance. Data for firms in the Survey of Small Business Finance are taken from Cavalluzzo and Wolken (2002). IPOs from 1997-1999 are identified in SDC and data are taken from Compustat for the year of the IPO

### Table 2 Posterior means and SD apos;s (in brackets) for model parameters for six di erent models and six distinct data sets. Note that for the binomial/beta-binomial model, the binomial component is assumed to be rst so that w corresponds to the probability of being assigned to the binomial component. Note also that for the mixtures with more than one component, the weight of the nal component is omitted. Bin BBin 2-Bin Mixture Bin/BBin Mixture Data

"... In PAGE 10: ... 5.1 Parameter Estimates Under independent uniform priors for all model parameters, Table2 presents the corre- sponding posterior means and standard deviations for the six data sets, and with the binomial and ve generally well supported models (as listed in Table 4). [Table 2 about here.... In PAGE 10: ...1 Parameter Estimates Under independent uniform priors for all model parameters, Table 2 presents the corre- sponding posterior means and standard deviations for the six data sets, and with the binomial and ve generally well supported models (as listed in Table 4). [ Table2 about here.] We note the strong general similarity between the posterior means and standard devi- ations obtained in Table 2 and the MLE apos;s and associated errors reported by Brooks et al.... In PAGE 10: ... [Table 2 about here.] We note the strong general similarity between the posterior means and standard devi- ations obtained in Table2 and the MLE apos;s and associated errors reported by Brooks et al. (1997).... In PAGE 10: ... Of course the two need not be the same, but under a uniform prior, the posterior mode is exactly the MLE, so that when the likelihood is roughly symmetric, the posterior mean and the MLE will take similar values. We also observe from Table2 , the occasional very large posterior means for the param- eters. It turns out that the posterior marginal distributions for are generally skewed to the left but sometimes also possess a very heavy right-hand tail.... In PAGE 10: ... With such a heavy-tailed posterior marginal, an absolute-error-loss function may be more appropriate and, under this loss function, the Bayes estimate become the pos- terior median. For example, the posterior median for under the binomial/beta-binomial model with the HS2 data is given by ^ m = 2:140, considerably less than the posterior mean given in Table2 . Note also that ^ m=(1 + ^ m) = 0:682, roughly the posterior mean for .... In PAGE 11: ...i.e. small and large values of r), and not just one. Thus, we should expect the smallest probabilities to be associated with cells placed most centrally within the table and that these probabilities should increase as we move further out into the tails of the r-values. Finally, we note from Table2 that the posterior mean for w is 0.858, which corresponds to the \overall quot; probability of being assigned to the binomial component.... ..."

### Table 3. Estimates of power when = :05, = 1:5, and the data are beta-binomial( ). Number of = 0:0 = 0:2 = 0:8

1995

"... In PAGE 13: ...as not included here. TMH results are only given when = 0. The results are summarized in Table 3. Table3 shows that when = 0, the power of TP and TU is almost equal to the power of the Mantel-Haenszel test. When k is small, the power of TP and TU is much better than TL.... In PAGE 14: ...Table3 (nij = mij = 5, = 0:0). Similarly for column 5 of Table 3 (nij = mij = 5 ? 10, = 0:2), we obtained powers of .... In PAGE 14: ... = 0:0). Similarly for column 5 of Table3 (nij = mij = 5 ? 10, = 0:2), we obtained powers of .... ..."

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### Table 2 Posterior means and SD apos;s (in brackets) for model parameters for six di erent models and six distinct data sets. Note that for the binomial/beta-binomial model, the binomial component is assumed to be rst so that w corresponds to the probability of being assigned to the binomial component. Note also that for the 3-Bin mixture, w3 = 1 ? w1 ? w2.

"... In PAGE 9: ...Parameter Estimates Under independent uniform(0; 1) priors for all model parameters, the correspond- ing posterior means and standard deviations for the six data sets and six models are presented in Table 2. [ Table2 about here.] We note the strong general similarity between the posterior means and standard deviations obtained in Table 2 and the MLE apos;s and associated errors reported by Brooks et al.... In PAGE 9: ... [Table 2 about here.] We note the strong general similarity between the posterior means and standard deviations obtained in Table2 and the MLE apos;s and associated errors reported by Brooks et al. (1997).... In PAGE 9: ... (1997) as estimates 1 and 2 respectively. Finally we observe, from Table2 , the occasional very large posterior means for the parameters. It turns out that the posterior marginal distributions for are generally skewed to the left but sometimes also possess a very heavy right-hand tail.... In PAGE 9: ... With such a heavy-tailed posterior marginal, an absolute-error-loss function may be more appropriate and, under this loss function, the Bayes estimate become the posterior median. For example, the posterior median for under the binomial/beta-binomial model with the HS2 data is given by ^ m = 2:140, considerably less than the posterior mean given in Table2 . Note also that ^ m=(1 + ^ m) = 0:682, roughly the posterior mean for .... In PAGE 13: ... Thus, we should expect the smallest probabilities to be associated with cells placed most centrally within the table and that these probabilities should increase as we move further out into the tails of the r-values. Finally, we note from Table2 that the posterior mean for w is 0.858, which corre- sponds to the \overall quot; probability of being assigned to the binomial component.... ..."