Article Figures & Data
Figures
- Figure 1.
Low sample size produces high variance. A, Map of the average kidney cancer incidence in each of the 3141 counties of the United States between 2010 and 2014. B, Plot of incidence as a function of county population. C, Five-year trend in incidence versus population. Data from the CDC National Program of Cancer Registries.
- Figure 2.
Microarray clustering procedure drastically alters the visual pattern. The data were from dentate granule cells provided by seven laboratories and consist of median log2 expression values of 398 genes that were differentially expressed (FDR < 0.05) with ≥2-fold expression change between control rats and rats in three status epilepticus (SE) models at different times after SE (Dingledine et al., 2017). Complete linkage and row (gene)-clustering only; the relative positions of columns (treatment groups) in A, B are unvarying. The only difference in the two procedures was the distance measurement used. The Heatmapper tool was used for clustering and visualization (http://www1.heatmapper.ca/expression/).
- Figure 3.
Pockets of seeming regularity in a random process. The left panel shows the location of each of the bombs dropped on London during the eight-month blitzkrieg of 1940–1941. Although the city was blanket-bombed, there were isolated neighborhood-size areas in which no bombs fell as shown on the right panel (from http://www.dailymail.co.uk/sciencetech/article-2243951/The-astonishing-interactive-map-EVERY-bomb-dropped-London-Blitz.html).
- Figure 4.
Similarity of judgments in populations of undergraduates and scientists separated by 45 years.
- Figure 5.
Demonstration of the value of a Bayesian approach when interpreting a single experiment. A, Consider the scientist facing the challenge of testing 1000 hypotheses, for example, in a proteomics or drug screening experiment, in which each protein measured or compound assayed tests the hypothesis that the protein expression is changed or the compound is active. Without knowledge of the target class only a small fraction of these hypotheses (say 10%) are true. If the power of the experiment is 80%, 80 hypotheses will be correctly identified as true (marked “true +”) and 20 will be false negatives (“false –”) as shown in the expected outcomes table. Of the 900 remaining false hypotheses, 45 will be incorrectly ascribed as being true (“false +” in the table) with α = 0.05, and 855 will be correctly ascertained as negatives (“true –”). Thus, the chance of correctly interpreting a positive outcome (equivalent to precision in a ROC analysis) is only 64% (=80/125). B, If the statistical power of the experiment is 30%, the chance of correctly interpreting a positive result drops to only 40% (=45/75). Blue in the outcomes table represent numbers that have changed from the previous panel. C, Now imagine that, with experience, one is working in a more restricted target space in which 40% of hypotheses are expected to be true: the chance of correctly interpreting a positive result jumps to 80% even when power = 30% (=120/150). D, A plot of these variables (plus the 10% power case) shows that the chance of correctly interpreting a single outcome depends on α, power, and the a priori probability that the hypothesis is true.
Tables
- Table 1.
Failure to take employment numbers into account when guessing professional field.
2018Rank Mean score Field 2016 United States employment* 1 2.7 Computer science 4,165,140 2 3.0 Engineering 2,499,050 3 3.5 Physics or biology 150,970 4 4.4 Library science 222,760 5 4.8 Law 1,075,520 6 5.5 Business administration 14,371,980 7 6.3 Healthcare 12,361,980 8 7.0 Humanities and education 12,928,630 9 7.9 Social sciences and social work 2,264,070 *Bureau of Labor Statistics.
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