Fig 1.
Illustration of a point null hypothesis, H0; the estimated effect that is the best supported hypothesis, ; the 95% confidence interval (CI) for the estimated effect [CI−, CI+]; and the interval null hypothesis
.
Fig 2.
Forest plot and p-value statistics of mock results from 8 studies of systolic blood pressure.
Here the point null is 146 mmHg, indicated by the vertical dashed line, with an indifference zone, or interval null hypothesis, from 144 mmHg to 148 mmHg shaded in blue-grey.
Table 1.
Mock results from 8 studies of systolic blood pressure.
Fig 3.
Display of 95% confidence intervals for gene specific fold-changes (AML vs. ALL) in the gene expression levels of patients from the Leukemia Microarray study [23].
All 7128 genes are sorted on the x-axis by classical p-value rank. Interval null hypothesis (blue-grey zone) shows all absolute fold changes between ½ and 2. Red genes have a second-generation p-value of 0, blue genes do not. Vertical dashed lines show various traditional p-value cutoffs at the 0.05 level (Bonferroni, Benjamini-Hochberg false discovery rate, and unadjusted).
Fig 4.
Top 1,000 ranked genes from the Leukemia Microarray study [23].
Display of 95% confidence intervals for gene specific fold-changes (AML vs. ALL). Genes sorted by classical p-value rank. Interval null hypothesis (blue-grey zone) shows all absolute fold changes between ½ and 2. Red genes have a second-generation p-value of 0, blue genes do not. Genes 3252 (light blue) and 2288 (green) have a second-generation p-value of 0, while gene 350 (dark blue) has a second-generation p-value of 1.
Table 2.
Cross-tabulation of second generation p-values with Bonferroni corrected p-values.
Fig 5.
Survival in patients with advanced lung cancer from the North Central Cancer Treatment Group study.
Kaplan-Meier survival curves by gender (blue for men, pink for women). Rug plot on x-axis displays second-generation p-values for the difference in survival time. Green ticks indicate incompatibility with null hypotheses; red indicate compatibility; gray indicate inconclusive results.
Fig 6.
Illustration of the false discovery rate (red) and false confirmation rate (blue) for second-generation p-values (solid lines).
The false discovery rate (red) and false non-discovery rate (blue) from a comparable hypothesis test are shown as dotted lines. This example uses r = 1, α = 0.05, δ = σ/2, and n = 16, but the ordering of the curves is quite general.