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Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon (\u3ci\u3eAddendum added October 2012\u3c/i\u3e)
Likert questionnaires are widely used in survey research, but it is unclear whether the item data should be investigated by means of parametric or nonparametric procedures. This study compared the Type I and II error rates of the t test versus the Mann-Whitney-Wilcoxon (MWW) for five-point Likert items. Fourteen population distributions were defined and pairs of samples were drawn from the populations and submitted to the t test and the t test on ranks, which yields the same results as MWW. The results showed that the two tests had equivalent power for most of the pairs. MWW had a power advantage when one of the samples was drawn from a skewed or peaked distribution. Strong power differences between the t test and MWW occurred when one of the samples was drawn from a multimodal distribution. Notably, the Type I error rate of both methods was never more than 3% above the nominal rate of 5%, even not when sample sizes were highly unequal. In conclusion, for five-point Likert items, the t test and MWW generally have similar power, and researchers do not have to worry about finding a difference whilst there is none in the population.Accessed 61,170 times on https://pareonline.net from October 06, 2010 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right
Amplification of surface plasmon polaritons in the presence of nonlinearity and spectral signatures of threshold crossover
We describe effects of nonlinearity on propagation of surface plasmon
polaritons (SPPs) at an interface between a metal and an amplifying medium of
the externally pumped two-level atoms. Using Maxwell equations we derive the
nonlinear dispersion law and demonstrate that, the nonlinear saturation of the
linear gain leads to formation of stationary SPP modes with the intensities
independent from the propagation distance. Transition to the regime of
stationary propagation is similar to the threshold crossover in lasers and
leads to narrowing of the SPP spectrum.Comment: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-34-18-286
The Stellar Composition of the Star Formation Region CMa R1. II. Spectroscopic and Photometric Observations of 9 Young Stars
We present new high and low resolution spectroscopic and photometric data of
nine members of the young association CMa R1. All the stars have circumstellar
dust at some distance as could be expected from their association with
reflection nebulosity. Four stars (HD 52721, HD 53367, LkHalpha 220 and
LkHalpha 218) show Halpha emission and we argue that they are Herbig Be stars
with discs. Our photometric and spectroscopic observations on these stars
reveal new characteristics of their variability. We present first
interpretations of the variability of HD 52721, HD 53367 and the two LkHalpha
stars in terms of a partially eclipsing binary, a magnetic activity cycle and
circumstellar dust variations, respectively. The remaining five stars show no
clear indications of Halpha emission in their spectra, although their spectral
types and ages are comparable with those of HD 52721 and HD 53367. This
indicates that the presence of a disc around a star in CMa R1 may depend on the
environment of the star. In particular we find that all Halpha emission stars
are located at or outside the arc-shaped border of the H II region, which
suggests that the stars inside the arc have lost their discs through
evaporation by UV photons from nearby O stars, or from the nearby (< 25 pc)
supernova, about 1 Myr ago.Comment: 17 pages, 13 figures, accepted by MNRA
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