In multifactor fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for main effects. Our primary focus is the case when the levels of the factor of interest are ordered. Likewise, ...in multifactor equally replicated fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for interactions. The primary focus here is on interactions when both factors are ordered, although the approach also applies if just one factor is ordered. Interactions with both factors ordered may be interpreted in terms of generalised correlations.
Variations in the total solar irradiance (TSI) associated with solar activity have been argued to influence the Earth's climate system, in particular when solar activity deviates from the average for ...a substantial period. One such example is the 17th Century Maunder Minimum during which sunspot numbers were extremely low, as Earth experienced the Little Ice Age. Estimation of the TSI during that period has relied on extrapolations of correlations with sunspot numbers or even more indirectly with modulations of galactic cosmic rays. We argue that there is a minimum state of solar magnetic activity associated with a population of relatively small magnetic bipoles which persists even when sunspots are absent, and that consequently estimates of TSI for the Little Ice Age that are based on scalings with sunspot numbers are generally too low. The minimal solar activity, which measurements show to be frequently observable between active‐region decay products regardless of the phase of the sunspot cycle, was approached globally after an unusually long lull in sunspot activity in 2008–2009. Therefore, the best estimate of magnetic activity, and presumably TSI, for the least‐active Maunder Minimum phases appears to be provided by direct measurement in 2008–2009. The implied marginally significant decrease in TSI during the least active phases of the Maunder Minimum by 140 to 360 ppm relative to 1996 suggests that drivers other than TSI dominate Earth's long‐term climate change.
The Cochran-Mantel-Haenszel (CMH) and nonparametric analysis of variance (NP ANOVA) methodologies are both sets of tests for categorical response data. The latter are competitor tests for the ordinal ...CMH tests in which the response variable is necessarily ordinal; the treatment variable may be either ordinal or nominal. The CMH mean score test seeks to detect mean treatment differences, while the CMH correlation test assesses ordinary or (1, 1) generalized correlation. Since the corresponding nonparametric ANOVA tests assess arbitrary univariate and bivariate moments, the ordinal CMH tests have been extended to enable a fuller comparison. The CMH tests are conditional tests, assuming that certain marginal totals in the data table are known. They have been extended to have unconditional analogues. The NP ANOVA tests are unconditional. Here, we give a brief overview of both methodologies to address the question “which methodology is preferable?”.
The photospheric solar oxygen project Steffen, M; Prakapavicius, D; Caffau, E ...
Astronomy and astrophysics (Berlin),
11/2015, Letnik:
583
Journal Article
Recenzirano
Odprti dostop
The solar photospheric oxygen abundance is still widely debated. Adopting the solar chemical composition based on the "low" oxygen abundance, as determined with the use of three-dimensional (3D) ...hydrodynamical model atmospheres, results in a well-known mismatch between theoretical solar models and helioseismic measurements that is so far unresolved. We carry out an independent re-determination of the solar oxygen abundance by investigating the center-to-limb variation of the O I IR triplet lines at 777 nm in different sets of spectra. The high-resolution and high signal-to-noise solar center-to-limb spectra are analyzed with the help of detailed synthetic line profiles based on 3D hydrodynamical CO5BOLD model atmospheres and 3D non-LTE line formation calculations with NLTE3D. The analysis of various observations of the triplet lines with different methods yields oxygen abundance values that fall in the range 8.74 < A(O) < 8.78, and our best estimate of the 3D non-LTE solar oxygen abundance is A(O) = 8.76 + or - 0.02.
We consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. ...A general construction is given that takes observations, typically treatment sums or treatment rank sums, constructs a simple quadratic form and expresses it as a sum of squares of orthogonal contrasts. For the case of ordered treatment levels, the Kruskal–Wallis, Friedman and Durbin tests are recovered by this construction. A dataset where the design is the supplemented balanced, which is an unbalanced design in our terminology, is analyzed. When treatment levels are not ordered the construction also applies. We then focus on Helmert contrasts.
Abstract
The relative rarity of giant planets around low-mass stars compared with solar-type stars is a key prediction from the core-accretion planet formation theory. In this paper we report on the ...discovery of four gas giant planets that transit low-mass late K and early M dwarfs. The planets HATS-74Ab (TOI 737b), HATS-75b (TOI 552b), HATS-76b (TOI 555b), and HATS-77b (TOI 730b) were all discovered from the HATSouth photometric survey and follow-up using TESS and other photometric facilities. We use the new ESPRESSO facility at the VLT to confirm systems and measure their masses. We find that these planets have masses of 1.46 ± 0.14
M
J, 0.491 ± 0.039
M
J, 2.629 ± 0.089
M
J, and
1.374
−
0.074
+
0.100
M
J, respectively, and radii of 1.032 ± 0.021
R
J, 0.884 ± 0.013
R
J, 1.079 ± 0.031
R
J, and 1.165 ± 0.021
R
J, respectively. The planets all orbit close to their host stars with orbital periods ranging from 1.7319 days to 3.0876 days. With further work, we aim to test core-accretion theory by using these and further discoveries to quantify the occurrence rate of giant planets around low-mass host stars.
In testing for main effects, the use of orthogonal contrasts for balanced designs with the factor levels not ordered is well known. Here, we consider two-factor fixed-effects ANOVA with the levels of ...one factor ordered and one not ordered. The objective is to extend the idea of decomposing the main effect to decomposing the interaction. This is achieved by defining level–degree coefficients and testing if they are zero using permutation testing. These tests give clear insights into what may be causing a significant interaction, even for the unbalanced model.
The Friedman test is used to nonparametrically test the null hypothesis of equality of the treatment distributions in the randomized block design. The simple form of the test statistic is for data ...that is untied within blocks. When ties occur and mid-ranks are used, an adjustment to the simple form of the test statistic is needed. Here such adjustments are given, and it is shown that the Friedman tests, both with untied rank data and with tied data using mid-ranks, are Cochran-Mantel-Haenszel mean score tests. Additionally, for the randomized block design, the Cochran-Mantel-Haenszel mean score statistic is shown to be a simple function of the ANOVA F statistic. Using this relationship for the Friedman tests is shown to give more accurate p-values close to the nominal significance level. Moreover, since the ANOVA F test null hypothesis specifies equality of mean treatment ranks, so does the Friedman test. Therefore the null hypothesis of the Friedman test is sharper than equality of the treatment distributions.
Van Valen’s test is usually applied as a two sample test for equality of dispersion for multivariate data. Motivated by a comment of Manly (Van Valen’s test. Encyclopedia of Statistical Sciences, ...2006) that “Little is known about the properties of Van Valen’s test” we develop an alternative test and compare the Van Valen test with our alternative robust test in an extensive simulation study. We find that Van Valen’s test does not actually test for equality of variance sums; however, for that null hypothesis it still performs well in terms of closeness to the nominal significance level. Due to testing the correct null hypothesis and the excellent adherence to the nominal significance level, we recommend the use of the robust test as a permutation test.
The Kruskal–Wallis tests are appropriate tests for the completely randomised design, both for when the data are untied ranks, and, with adjustment, for when there are ties and mid-ranks are used. ...Both these tests are shown to be Cochran–Mantel–Haenszel mean score tests. The relationship between the Kruskal–Wallis test statistic and the ANOVA F test statistic when there are no ties generalises to the same relationship between the Cochran–Mantel–Haenszel mean score test statistic and the ANOVA F test statistic. It thus also relates both Kruskal–Wallis test statistics to the ANOVA F test statistic. A small simulation study finds that p-values may be more accurately found using the F test.
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