Fast Permutation Tests that Maximize Power Under Conventional Monte Carlo Sampling for Pairwise and Multiple Comparisons

While the distribution-free nature of permutation tests makes them the most appropriate method for hypothesis testing under a wide range of conditions, their computational demands can be runtime prohibitive, especially if samples are not very small and/or many tests must be conducted (e.g. all pairwise comparisons). This paper presents statistical code that performs continuous-data permutation tests under such conditions very quickly often more than an order of magnitude faster than widely available commercial alternatives when many tests must be performed and some of the sample pairs contain a large sample. Also presented is an efficient method for obtaining a set of permutation samples containing no duplicates, thus maximizing the power of a pairwise permutation test under a conventional Monte Carlo approach with negligible runtime cost (well under 1% when runtimes are greatest). For multiple comparisons, the code is structured to provide an additional speed premium, making permutation-style p-value adjustments practical to use with permutation test p-values (although for relatively few comparisons at a time). No-replacement sampling also provides a power gain for such multiple comparisons, with similarly negligible runtime cost

A Single, Powerful, Nonparametric Statistic for Continuous-data Telecommunications Parity Testing

Since the enactment of the Telecommunications Act of 1996, extensive expert testimony has justified use of the modified t statistic (Brownie et al., 1990) for performing two-sample hypothesis tests comparing Bell companies’ CLEC and ILEC performance measurement data (known as parity testing). However, Opdyke (Telecommunications Policy, 2004) demonstrated this statistic to be potentially manipulable and to have literally zero power to detect inferior CLEC service provision under a wide range of relevant data conditions. This article develops a single, nonparametric statistic that is easily implemented (i.e., not computationally intensive) and typically provides dramatic power gains over the modified t while simultaneously providing much better Type I error control. The statistic should be useful in a wide range of quality control settings

Multicomponent magnetizations from the Mississippian Mauch Chunk Formation of the central Appalachians and their tectonic implications

Previous paleomagnetic study of Mississippian red beds of the Mauch Chunk Formation from the central Appalachians reported shallow inclination directions. A positive fold test was obtained after thermal demagnetization, typically to only 550°C. The near-equatorial position for North America indicated by these results has been used to support the idea of a circa 15° latitudinal tectonic offset of the Acadia displaced terrain in the northern Appalachians. The present study of 153 samples from 29 sites occupied in the Mauch Chunk Formation of eastern and southern Pennsylvania reveals multicomponent magnetizations. A characteristic component (Declination (D) = 161.0°, Inclination (I)=27.8°, alpha95 (a95)=7.9°) with unblocking temperatures usually concentrated above 650°C and with dual polarity (10 sites normal, 13 sites reversed) is isolated in 23 sites and passes a fold test at the 99% confidence level. It is interpreted as an early acquired hematitic (detrital or chemical) magnetization of pre-Alleghanian orogeny and pre-Kiaman Reverse Polarity Interval age; a southern hemisphere paleolatitude of 15° for the sampling area is indicated. Another component has generally lower unblocking temperatures which, however, can extend up to 650°C or more and therefore is also likely to be carried by hematite. This secondary magnetization (D=170.6°, I=-5.3°, a95=5.0°) isolated in 25 sites is of uniform reverse polarity, and application of fold tests suggests that it is of synfolding origin; a near-equatorial paleolatitude (3°N) at the time of acquisition is obtained, consistent with Permo-Carboniferous Kiaman directions from North America. Incomplete removal of the secondary component can explain the previous results from the Mauch Chunk. Comparison of the present paleomagnetic results with those from similar age rocks in the Canadian Maritimes does not support a latitudinal offset of Acadia with respect to interior North America in the Early Carboniferous. In fact, according to these and other paleomagnetic data thought to be representative of this age, the Atlantic-bordering continents already were near to a Pangea configuration. The Alleghanian and particularly the Hercynian orogenies therefore may not be associated with the closure of a large (latitudinal) ocean later in the Carboniferous and Permian. Alleghanian deformation, however may have resulted in the partial bending of the Pennsylvanian salient on the basis of apparently systematic deviations in paleomagnetic declinations

Paleomagnetism of the Devonian Catskill Red Beds: Evidence for Motion of the Coastal New England-Canadian Maritime Region Relative to Cratonic North America

The natural remanent magnetizations of reddish clay stones, siltstones, and sandstones from the nearly flat lying Middle to Upper Devonian Catskill sequence of southeastern New York were analyzed with thermal, alternating field, and chemical demagnetization techniques. After removal of a low blocking temperature component along the present geomagnetic field direction a characteristic direction of magnetization was isolated: D = 172.3°, I = 1.0°, k = 116, and α_95 = 4.7° for N = 9 sites (43 samples), giving a paleomagnetic north pole at 46.8°N, 116.7°E, dp = 2.4°, and dm = 4.7°. The combined demagnetization analyses show this to be the only stable component of magnetization present in these rocks. The derived pole position agrees well with the poles reported for some Devonian limestones in Ohio, all falling near the Permian poles for North America, but disagrees with Devonian results from eastern Maine-New Brunswick and eastern Massachusetts which give poles at lower latitudes. A similar geographical grouping with similar directions is also apparent for Lower Carboniferous (Mississippian) paleomagnetic poles for North America. We interpret these and other late Paleozoic paleomagnetic data to show that the coastal Canadian Maritime-New England region was not an integral part of cratonic North America until about the Late Carboniferous. Geological considerations suggest that the Carboniferous relative motion was along transcurrent shear zones

Plio-Pleistocene time-averaged field in southern Patagonia recorded in lava flows

Paleomagnetic directions were obtained from stepwise alternating-field or thermal demagnetization of 53 lava flows from southern Patagonia (latitudes 49.5°-52.1 °S) that include the Pali-Aike volcanic field and the Meseta Viscachas plateau lavas. In addition to previous Miocene-late Quaternary ages of these flows, 40Ar/39Ar dates spanning from 0.1 to 15.4 Ma were obtained for 17 of the sites. All except one of the magnetic polarities coincide with the expected polarities of the magnetic polarity timescale [Cande and Kent, 1995] for the obtained 40Ar/39Ar ages. The mean direction from 33 sites (eliminating sites <4 Ma) that pass a selection criteria of α95 ≤5° is Dec = 358.7°,Inc = - 68.2°, α95 = 3.5°, a value that coincides within the statistical uncertainty with the direction of the geocentric axial dipole for that area (Inc = - 68.1°). Likewise, the mean virtual geomagnetic pole (VGP) coincides within the statistical uncertainty with the geographic North Pole. The secular variation described by the VGP angular standard deviation for these sites is 17.1°, a value expected for that latitude according to Model G of paleosecular variation [McFadden et al., 1988]. The characteristics of the data presented are optimum for time-averaged field (TAF) studies because of the good age control and good quality of the paleomagnetic data: (1) primary components of magnetization were obtained using principal component analysis [Kirschvink, 1980] from at least five points and maximum angular deviation ≤5°, (2) site means were calculated with Fisher statistics using at least three samples, and (c) 38 of the 53 flows had α95 ≤ 5°. No results (five sites) or high α95 values (≤5°) were obtained primarily from sites affected by lightning.Fil: Mejia, V.. University of Florida; Estados UnidosFil: Opdyke, N. D.. University of Florida; Estados UnidosFil: Vilas, Juan Francisco A.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Geología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires; ArgentinaFil: Singer, B. S.. University of Wisconsin; Estados UnidosFil: Stoner, J. S.. State University of Colorado at Boulder; Estados Unido

The Early Carboniferous paleomagnetic field of North America and its bearing on tectonics of the Northern Appalachians

We have obtained additional evidence for the Early Carboniferous paleomagnetic field for cratonic North America from study of the Barnett Formation of central Texas. A characteristic magnetization of this unit was isolated after thermal demagnetization at four sites (36 samples) out of eight sites (65 samples) collected. The mean direction of declination = 156.3°, inclination = 5.8° (N = 4 ,k = 905 , α95 = 3.0°), corresponds to a paleomagnetic pole position at lat. = 49.1°N,long. = 119.3°E (dp = 1.5° , dm = 3.0°). Field evidence suggests that characteristic magnetization was acquired very early in the history of the rock unit whereas the rejected sites are comprised of weakly magnetized limestones dominated by secondary components near the present-day field direction. Comparison of the Barnett pole with other Early Carboniferous (Mississippian) paleopoles from North America shows that it lies close to the apparent polar wander path for stable North America and that the divergence of paleopoles from the Northern Appalachians noted previously for the Devonian persisted into the Early Carboniferous. We interpret this difference in paleopoles as further evidence for the Northern Appalachian displaced terrain which we refer to here as Acadia, and the apparent coherence of Late Carboniferous paleopoles as indicating a large (∼1500 km) motion of Acadia with respect to stable North America over a rather short time interval in the Carboniferou

Climate Change in the North Pacific Using Ice-Rafted Detritus as a Climatic Indicator

The variations in weight percent of the grain size fraction greater than 250 μ in nine cores from the North Pacific were determined using sampling intervals of 5 to 20 cm. Material in this size fraction is interpreted as transported by icebergs, and fluctuations are attributed to the waxing and waning of glaciers on the surrounding continents. At least eleven periods of increased ice rafting are detected in the cores during the time from 1.2 m.y. ago to the present, whereas only about four are identified from 1.2 m.y. to 2.5 m.y. B.P. The dating and time correlations are based on the magnetic stratigraphy, ash falls, and faunal extinctions. The ice-rafted detritus indicates a cooling beginning about 1.2 m.y. ago and becoming very intense between the Jaramillo event and the Brunhes-Matuyama boundary. This time may correspond to the initiation of mid-latitude glaciations of Europe and North America. At least six zones of ice-rafted sediment are present in the Brunhes normal polarity series. The correlations between these and the carbonate fluctuations of the central Pacific are good. Evidence for a marked interglacial ranging from about 460,000 to 530,000 yrs B.P. occurs within these cores. This interglacial may be worldwide in extent

Details of magnetic polarity transitions recorded in a high deposition rate deep-sea core

Measurements of the NRM of a 26 m long deep-sea core from the southern Indian Ocean indicated the presence of three transitions of magnetic polarity which have been identified as the upper and lower Jaramillo and the upper Olduvai on the basis of micropaleontological criteria. Detailed studies of the magnetic reversals were made in view of the high deposition rates (~9 cm/10^3 yr) present over sections of the core. The NRM was found stable against alternating fields. Magnetic mineralogy studies indicated the presence of titanomagnetite and magnetite which probably have not undergone any significant low-temperature oxidation. The three polarity changes had the following features in common: (1) presence of intermediate directions of magnetization; (2) a pronounced drop in the intensity of magnetization; (3) the drop in intensity of magnetization was coincident with the large directional fluctuations. Measurements of saturation isothermal and anhysteretic remanence, and bulk susceptibility, show that the decrease in NRM intensity associated with each polarity change is not due to a low concentration of the magnetic minerals. The best estimate for the duration of a polarity transition is approximately 4600 yr. There is evidence for both eastward and westward drift of the non-dipole field, which appears to be dominant during the polarity transition interval. The data presented here support a model of a reversing field in which the main dipole field decays to a low value and then builds up in the opposite direction