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3 results

  • Simultaneous Analysis of Multivariate Polytomous Variates in Several Groups

  • Sik-Yum Lee, Wai-Yin Poon, P. M. Bentler
  • Journal:
    Psychometrika / Volume 54 / Issue 1 / March 1989
    Published online by Cambridge University Press:
    01 January 2025, pp. 63-73

  • The frequencies of m independent p-way contingency tables are analyzed by a model that assumes that the ordinal categorical data in each of m groups are generated from a latent continuous multivariate normal distribution. The parameters of these multivariate distributions and of the relations between the ordinal and latent variables are estimated by maximum likelihood. Goodness-of-fit statistics based on the likelihood ratio criterion and the Pearsonian chisquare are provided to test the hypothesis that the proposed model is correct, that is, it fits the observed sample data. Hypotheses on the invariance of means, variances, and polychoric correlations of the latent variables across populations are tested by Wald statistics. The method is illustrated on an example involving data on three five-point ordinal scales obtained from male and female samples.

  • 3 - Measurement

  • from Part 1
  • Daniel S. Scheller, Texas Tech University
  • Book:
    Elementary Statistics for Public Administration
    Published online:
    01 November 2024
    Print publication:
    12 September 2024, pp 62-77

  • Summary

    The focus of the chapter is on turning concepts into measurable variables, also known as operationalization.Best practices in created variable based on the concept are covered.The differences between nominal, ordinal, and interval level variables are discussed along with their relevance for statistical tests later covered in the book.The importance of measurement validity and reliability and their implications for research provide another focus of the chapter.

  • 6 - Central Tendency

  • from Part 2
  • Daniel S. Scheller, Texas Tech University
  • Book:
    Elementary Statistics for Public Administration
    Published online:
    01 November 2024
    Print publication:
    12 September 2024, pp 115-132

  • Summary

    Central tendency describes the typical value of a variable.Measures of central tendency by level of measurement are covered including the mean, median, and mode.Appropriate use of each measure by level of measurement is the central theme of the chapter.The chapter shows how to find these measures of central tendency by hand and in the R Commander with detailed instructions and steps.Skewed distributions and outliers of data are also covered, as is the relationship between the mean and median in these cases.