Biases Induced by Coarse Measurement Scales

Krieg, Edward F.

doi:10.1177/00131649921970125

“…A dichotomous scale changes the probability of a Type I error for methods in all cases when all sample sizes are small and in many other cases when at least one sample size is small. However, the effect seems to decline as the number of scale points is increased, which is in line with theory (Krieg, 1999) and with similar published simulation results (e.g., Bevan et al, 1974). The probability of a Type II error also seems to decline as the number of scale points is increased, although the pattern is different for different methods and sample size combinations.…”

Section: Resultssupporting

confidence: 89%

“…Krieg (1999) derived equations for calculating the bias induced by coarse measurement scales, and showed that the bias is reduced as the number of scale points increases. Hence, one would assume that statistical comparisons of locations across groups should be relatively unproblematic even if data are discrete as long as the number of possible variable values is large.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Continuity Violation on ANOVA and Alternative Methods

Lantz

¹

2013

J. Mod. App. Stat. Meth.

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“…A dichotomous scale changes the probability of a Type I error for methods in all cases when all sample sizes are small and in many other cases when at least one sample size is small. However, the effect seems to decline as the number of scale points is increased, which is in line with theory (Krieg, 1999) and with similar published simulation results (e.g., Bevan et al, 1974). The probability of a Type II error also seems to decline as the number of scale points is increased, although the pattern is different for different methods and sample size combinations.…”

Section: Resultssupporting

confidence: 89%

Vol. 12, No. 2 (Full Issue)

2013

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. Normality is a distributional requirement of classical test statistics. In order for the test statistic to provide valid results leading to sound and reliable conclusions this requirement must be satisfied. In the not too distant past, it was claimed that violations of normality would not likely jeopardize scientific findings (See Hsu & Feldt, 1969; Lunney, 1970). Recent revelations suggest otherwise (See e.g., Micceri, 1989; Keselman, Huberty, Lix et al., 1998;Erceg-Hurn, Wilcox, & Keselman, 2013; Wilcox and Keselman, 2003; Wilcox, 2012a, b). Unfortunately the data obtained in psychological investigations rarely, if ever, meet the requirement of normally distributed data (Micceri, 1989; Wilcox, 2012a, b). Consequently, it could be the case that the results from many of the investigations conducted in psychology provide invalid results. Accordingly, authors recommend that researchers attempt to assess the validity of assuming data are normal in form prior to conducting a test of significance (Erceg-Hurn, et al., 2013; Keselman, et al., 1998). Present evidence suggests that a popular fit-statistic, the Kolmogorov-Smirnov test does a poor job of evaluating whether data are normal. Our investigation based on this statistic and other fit-statistics provides a more favorable picture of preliminary testing for normality. Keywords:Assessing normality, fit statistics, g-and-h non-normal skewed and kurtotic data, contaminated mixed-normal distributions; outlying value(s), Likert scales IntroductionPsychological researchers are often reminded that the validity of their statistical tests and the conclusions derived from these tests depends to a great extent on whether the derivational assumptions of the test procedures have been satisfied (e.g., See Keselman, Huberty, Lix et al., 1998; Wilcox, 2012a, b; Wilcox & KESELMAN ET AL 3 Keselman, 2003). Consequently, though not a common practice, researchers are still reminded about assessing derivational assumptions (See Erce...

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“…The desire for half score use by raters is not new. It is a rating issue that emerges in studies which use discrete Likert scales, as the basic design of the scale forces subjects to categorize their responses into restricted choices resulting in information loss [36,37]. Although half scores in Likert scales may appear to add more precision, psychometrically they should not alter the thrust of the instrument because the number of choices available may not be an important issue [38] and scale coarseness, rather than the use of halfscores, is more likely to affect the variance and reliability of scores [37].…”

Section: Discussionmentioning

confidence: 99%