G*Power (Erdfelder, Faul, & Buchner, 1996) was designed as a general stand-alone power analysis program for statistical tests commonly used in social and behavioral research. G*Power 3 is a major extension of, and improvement over, the previous versions. It runs on widely used computer platforms (i.e., Windows XP, Windows Vista, and Mac OS X 10.4) and covers many different statistical tests of thet, F, and χ2 test families. In addition, it includes power analyses forz tests and some exact tests. G*Power 3 provides improved effect size calculators and graphic options, supports both distribution-based and design-based input modes, and offers all types of power analyses in which users might be interested. Like its predecessors, G*Power 3 is free.

https://link.springer.com/content/pdf/10.3758/BF03193146.pdf

G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences

https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(13)60844-2.pdf

Burden and aetiology of diarrhoeal disease in infants and young children in developing countries (the Global Enteric Multicenter Study, GEMS): a prospective, case-control study.

Several existing unconditional methods for setting confidence intervals for the difference between binomial proportions are evaluated. Computationally simpler methods are prone to a variety of aberrations and poor coverage properties. The closely interrelated methods of Mee and Miettinen and Nurminen perform well but require a computer program. Two new approaches which also avoid aberrations are developed and evaluated. A tail area profile likelihood based method produces the best coverage properties, but is difficult to calculate for large denominators. A method combining Wilson score intervals for the two proportions to be compared also performs well, and is readily implemented irrespective of sample size.

Interval estimation for the difference between independent proportions: comparison of eleven methods

Advanced Statistical Methods in Biometric Research.

RESULTS In 2001, 4958 of 3.3 million youth were diagnosed with type 1 diabetes for a prevalence of 1.48 per 1000 (95% CI, 1.44-1.52). In 2009, 6666 of 3.4 million youth were diagnosed with type 1 diabetes for a prevalence of 1.93 per 1000 (95% CI, 1.88-1.97). In 2009, the highest prevalence of type 1 diabetes was 2.55 per 1000 among white youth (95% CI, 2.48-2.62) and the lowest was 0.35 per 1000 in American Indian youth (95% CI, 0.26-0.47) and type 1 diabetes increased between 2001 and 2009 in all sex, age, and race/ethnic subgroups except for those with the lowest prevalence (age 0-4 years and American Indians). Adjusted for completeness of ascertainment, there was a 21.1% (95% CI, 15.6%-27.0%) increase in type 1 diabetes over 8 years. In 2001, 588 of 1.7 million youth were diagnosed with type 2 diabetes for a prevalence of 0.34 per 1000 (95% CI, 0.31-0.37). In 2009, 819 of 1.8 million were diagnosed with type 2 diabetes for a prevalence of 0.46 per 1000 (95% CI, 0.43-0.49). In 2009, the prevalence of type 2 diabetes was 1.20 per 1000 among American Indian youth (95% CI, 0.96-1.51); 1.06 per 1000 among black youth (95% CI, 0.93-1.22); 0.79 per 1000 among Hispanic youth (95% CI, 0.70-0.88); and 0.17 per 1000 among white youth (95% CI, 0.15-0.20). Significant increases occurred between 2001 and 2009 in both sexes, all age-groups, and in white, Hispanic, and black youth, with no significant changes for Asian Pacific Islanders and American Indians. Adjusted for completeness of ascertainment, there was a 30.5% (95% CI, 17.3%-45.1%) overall increase in type 2 diabetes. CONCLUSIONS AND RELEVANCE Between 2001 and 2009 in 5 areas of the United States, the prevalence of both type 1 and type 2 diabetes among children and adolescents increased. Further studies are required to determine the causes of these increases.

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Prevalence of Type 1 and Type 2 Diabetes Among Children and Adolescents From 2001 to 2009

Various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically. It is found that the method based on likelihood scores (Koopman, 1984, Biometrics 40, 513-517; Miettinen and Nurminen, 1985, Statistics in Medicine 4, 213-226) performs best in achieving the nominal confidence coefficient, but it may distribute the tail probabilities quite disparately. Using general theory of Bartlett (1953, Biometrika 40, 306-317; 1955, Biometrika 42, 201-203), we correct this method for asymptotic skewness. Following Gart (1985, Biometrika 72, 673-677), we extend this correction to the case of estimating the common ratio in a series of two-by-two tables. Computing algorithms are given and applied to numerical examples. Parallel methods for the odds ratio and the ratio of Poisson parameters are noted.

https://www.jstor.org/stable/pdfplus/2531848.pdf

Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness.

Fourteen chemicals of varied uses were tested for carcinogenicity by oral administration in male and female Charles River CD rats. Under the conditions of the tests, propane sultone, propylene imine, and ethylenethiourea, in addition to the positive control N-2-fluorenylacetamide, were carcinogenic. Avadex, bis(2-chloroethyl) ether, the potassium salt of bis(2-hydroxyethyl) dithiocarbamic acid, ethylene carbonate, and semicarbazide hydrochloride were not carcinogenic under the test conditions. Dithiooxamide, glycerol alpha-monochlorohydrin, and thiosemicarbazide gave somewhat ambiguous results, though administered at high enough dose levels to be toxic. An inadequate number of animals survived treatments with sodium azide, sodium bisulfide, and vinylene carbonate, or the animals may not have received sufficiently high doses of the test chemicals to provide maximum test sensitivity. However, there were no indications that these three chemicals were carcinogenic under the test conditions.

Carcinogenicity Tests of Certain Environmental and Industrial Chemicals

Recently, Beal (1987, Biometrics 43, 941-950) found Mee's modification of Anbar's approximate interval estimation for the difference in binomial parameters to be a good choice in small sample sizes. As this method can be derived from the score theory of Bartlett, it is easily corrected for skewness. Exact numerical evaluation shows that this correction is not as important for this case as for the ratio of binomial parameters (Gart and Nam, 1988, Biometrics 44, 323-338). The score theory is also used to extend this method to the stratified or multiple-table case. Thus, good approximate interval estimates for differences, ratios, and odds ratios of binomial parameters can all be derived from the same general theory.

Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to multiple tables.

In generalized ABO-like genetic systems, particularly for certain human leukocyte antigen (HLA) loci, it is quite likely, even for large sample sizes, that no double recessives (or 'double blanks') may be found. It has been suggested that all such data should be analyzed as if the true recessive gene frequency were 0. We derive an easily computed score [or C(alpha)] statistic which tests for the possibility that, in such instances, this frequency may exceed 0. An associated point estimator is suggested. The methods are applied to the data analyzed by Smouse and Williams (1982, Biometrics 38, 757-768).

A score test for the possible presence of recessive alleles in generalized ABO-like genetic systems.

The general method of the discrepancy or heterogeneity chi-square is applied to ABO-like data in which there are no observed double blanks in either the disease or the control group. When the recessive gene frequency is assumed zero, this method leads to an approximate chi-square test identical to that suggested by Smouse and Williams (1982, Biometrics 38, 757-768). When this assumption is relaxed, there arise two cases which are determined by whether the maximum likelihood estimate of this frequency is zero or not. It is shown that the value of the simple score statistic of Gart and Nam (1984, Biometrics 40, 887-894) discriminates between the two cases. The various omnibus test statistics for comparing groups are shown to differ little in several practical examples. However, under the more general assumption the appropriate degrees of freedom is one more than the number previously suggested.

Jun-mo Nam

Papers

Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness.

Carcinogenicity Tests of Certain Environmental and Industrial Chemicals

Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to multiple tables.

A score test for the possible presence of recessive alleles in generalized ABO-like genetic systems.

The ML estimation and testing of generalized ABO-like data with no observed double recessives