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Studies
- Its most important claim’s importance 63 out of 100: meaningful importance
- Published, Reproduced, Reviewed: Of 40 associations sampled at random from 341 papers that each relate one NHANES variable to one health condition, 14 (35%; exact 95% confidence interval 21% to 52%) replicated in NHANES August 2021 to August 2023, meaning their estimate there has the published sign and a Benjamini-Hochberg-corrected p below 0.05.
- Published, Reproduced, Reviewed: Only 13 of the 40 replication tests had at least 80% power to detect the published effect in the 2021 to 2023 cycle, and 10 of those 13 replicated (77%; exact 95% confidence interval 46% to 95%).
- Published, Reproduced, Reviewed: On the analysis scale (log odds ratio or regression coefficient), the 2021 to 2023 effects are a median 0.77 times the published ones (distribution-free 95% confidence interval 0.32 to 1.05) over all 40 associations, and 0.91 times (0.32 to 1.16) over the 13 informative ones.
- Its most important claim’s importance 47 out of 100: limited importance
- Published, Reproduced, Reviewed: Over every sample size n from 5 to 100 and every true proportion p from 0.001 to 0.999 in steps of 0.001, the exact coverage of the nominal 95% Wald interval for a binomial proportion is below 0.93 at a fraction 0.463088 of the 95904 (n, p) pairs and below 0.95 at a fraction 0.923027 of them.
- Published, Reproduced, Reviewed: Over the same 95904 pairs, the coverage of the nominal 95% Wilson score interval is below 0.93 at a fraction 0.032981 of them and that of the Agresti-Coull interval at a fraction 0.003681, with mean coverages of 0.952036 and 0.958695 against the Wald interval's 0.88228.
- Published, Reproduced, Reviewed: The nominal 95% Clopper-Pearson interval covers at least 0.95 at every one of the 95904 pairs, with a lowest coverage of 0.9502, and its mean coverage of 0.970942 exceeds the nominal level by about 0.021.
- Its most important claim’s importance 38 out of 100: limited importance
- Published, Reproduced, Reviewed: Adding 1000000 doubles drawn uniformly from [0, 1) from left to right lands a mean of 196.86 units in the last place (at most 589) from the correctly rounded sum over 50 draws, and the mean error grows as about n to the power 0.545 for n from 1000 to 1000000, near the square-root growth that independent rounding errors predict.
- Published, Reproduced, Reviewed: Pairwise summation of the same positive draws stays within 2 units in the last place of the correctly rounded sum in all 200 draws for n from 1000 to 1000000, with a mean error of 0.4 units at n = 1000000.
- Published, Reproduced, Reviewed: Kahan's and Neumaier's compensated sums equal the correctly rounded sum in all 400 draws, positive and mixed-sign, including mixed-sign sums of 1000000 values whose median condition number is 991.
- Its most important claim’s importance 31 out of 100: limited importance
- Published, Reproduced, Reviewed: The least x at which the primes up to x congruent to 1 modulo 4 outnumber those congruent to 3 modulo 4 is 26861.
- Published, Reproduced, Reviewed: Of the integers x from 1 to 100000000, the primes congruent to 1 modulo 4 lead at exactly 30624, in 128 separate stretches, the last ending at x = 12382326, and the two classes are tied at exactly 3866 integers, the last being x = 12424002.
- Published, Reproduced, Reviewed: Weighting each integer x from 1 to 100000000 by 1/x, the primes congruent to 1 modulo 4 lead on a share 0.00040587 of the race, about a tenth of the limiting share of about 0.0041 implied by Rubinstein and Sarnak's logarithmic density of 0.9959 for the other side.